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",[1113,1165,1167,1181],{"className":1166},[1116],[1113,1168,1170],{"className":1169},[1120],[1122,1171,1172],{"xmlns":1124},[1126,1173,1174,1179],{},[1129,1175,1176],{},[1132,1177,1178],{},"Y",[1136,1180,1178],{"encoding":1138},[1113,1182,1184],{"className":1183,"ariaHidden":1143},[1142],[1113,1185,1187,1190],{"className":1186},[1147],[1113,1188],{"className":1189,"style":1152},[1151],[1113,1191,1178],{"className":1192,"style":1193},[1156,1157],"margin-right:0.2222em;"," 上。输出空间是一个无限集（通常是实数集 ",[1113,1196,1198,1214],{"className":1197},[1116],[1113,1199,1201],{"className":1200},[1120],[1122,1202,1203],{"xmlns":1124},[1126,1204,1205,1211],{},[1129,1206,1207],{},[1132,1208,1210],{"mathvariant":1209},"double-struck","R",[1136,1212,1213],{"encoding":1138},"\\mathbb{R}",[1113,1215,1217],{"className":1216,"ariaHidden":1143},[1142],[1113,1218,1220,1224],{"className":1219},[1147],[1113,1221],{"className":1222,"style":1223},[1151],"height:0.6889em;",[1113,1225,1210],{"className":1226},[1156,1227],"mathbb"," 的某个区间）。输出的值之间是有大小关系的，且可以无限细分，如线性回归。",[1107,1230,1097],{"id":1097},[1091,1232,1111,1233,1261,1262,1163,1265,1295,1296,1299],{},[1113,1234,1236,1249],{"className":1235},[1116],[1113,1237,1239],{"className":1238},[1120],[1122,1240,1241],{"xmlns":1124},[1126,1242,1243,1247],{},[1129,1244,1245],{},[1132,1246,1134],{},[1136,1248,1134],{"encoding":1138},[1113,1250,1252],{"className":1251,"ariaHidden":1143},[1142],[1113,1253,1255,1258],{"className":1254},[1147],[1113,1256],{"className":1257,"style":1152},[1151],[1113,1259,1134],{"className":1260,"style":1158},[1156,1157]," 划分到",[1095,1263,1264],{},"预定义的、离散的类别",[1113,1266,1268,1282],{"className":1267},[1116],[1113,1269,1271],{"className":1270},[1120],[1122,1272,1273],{"xmlns":1124},[1126,1274,1275,1280],{},[1129,1276,1277],{},[1132,1278,1279],{},"C",[1136,1281,1279],{"encoding":1138},[1113,1283,1285],{"className":1284,"ariaHidden":1143},[1142],[1113,1286,1288,1291],{"className":1287},[1147],[1113,1289],{"className":1290,"style":1152},[1151],[1113,1292,1279],{"className":1293,"style":1294},[1156,1157],"margin-right:0.0715em;"," 中。输出空间是一个有限集。输出的值之间",[1095,1297,1298],{},"没有大小关系","，只是一个标签，如逻辑回归，KNN,SVM。",[1091,1301,1302],{},"--",[1304,1305,1307],"h2",{"id":1306},"一线性回归","一、线性回归",[1091,1309,1310,1311,1341,1342,1373],{},"线性回归的目标是在自变量 ",[1113,1312,1314,1328],{"className":1313},[1116],[1113,1315,1317],{"className":1316},[1120],[1122,1318,1319],{"xmlns":1124},[1126,1320,1321,1326],{},[1129,1322,1323],{},[1132,1324,1325],{},"x",[1136,1327,1325],{"encoding":1138},[1113,1329,1331],{"className":1330,"ariaHidden":1143},[1142],[1113,1332,1334,1338],{"className":1333},[1147],[1113,1335],{"className":1336,"style":1337},[1151],"height:0.4306em;",[1113,1339,1325],{"className":1340},[1156,1157]," 与因变量 ",[1113,1343,1345,1359],{"className":1344},[1116],[1113,1346,1348],{"className":1347},[1120],[1122,1349,1350],{"xmlns":1124},[1126,1351,1352,1357],{},[1129,1353,1354],{},[1132,1355,1356],{},"y",[1136,1358,1356],{"encoding":1138},[1113,1360,1362],{"className":1361,"ariaHidden":1143},[1142],[1113,1363,1365,1369],{"className":1364},[1147],[1113,1366],{"className":1367,"style":1368},[1151],"height:0.625em;vertical-align:-0.1944em;",[1113,1370,1356],{"className":1371,"style":1372},[1156,1157],"margin-right:0.0359em;"," 之间建立一个线性模型:",[1091,1375,1376],{},[1113,1377,1379,1462],{"className":1378},[1116],[1113,1380,1382],{"className":1381},[1120],[1122,1383,1384],{"xmlns":1124},[1126,1385,1386,1459],{},[1129,1387,1388,1390,1394,1404,1407,1414,1420,1422,1429,1435,1437,1440,1442,1448,1454,1456],{},[1132,1389,1356],{},[1391,1392,1393],"mo",{},"=",[1395,1396,1397,1400],"msub",{},[1132,1398,1399],{},"β",[1401,1402,1403],"mn",{},"0",[1391,1405,1406],{},"+",[1395,1408,1409,1411],{},[1132,1410,1399],{},[1401,1412,1413],{},"1",[1395,1415,1416,1418],{},[1132,1417,1325],{},[1401,1419,1413],{},[1391,1421,1406],{},[1395,1423,1424,1426],{},[1132,1425,1399],{},[1401,1427,1428],{},"2",[1395,1430,1431,1433],{},[1132,1432,1325],{},[1401,1434,1428],{},[1391,1436,1406],{},[1391,1438,1439],{},"⋯",[1391,1441,1406],{},[1395,1443,1444,1446],{},[1132,1445,1399],{},[1132,1447,1091],{},[1395,1449,1450,1452],{},[1132,1451,1325],{},[1132,1453,1091],{},[1391,1455,1406],{},[1132,1457,1458],{},"ε",[1136,1460,1461],{"encoding":1138},"y = \\beta_0 + \\beta_1 x_1 + \\beta_2 x_2 + \\cdots + \\beta_p x_p + \\varepsilon",[1113,1463,1465,1486,1560,1656,1751,1771,1869],{"className":1464,"ariaHidden":1143},[1142],[1113,1466,1468,1471,1474,1479,1483],{"className":1467},[1147],[1113,1469],{"className":1470,"style":1368},[1151],[1113,1472,1356],{"className":1473,"style":1372},[1156,1157],[1113,1475],{"className":1476,"style":1478},[1477],"mspace","margin-right:0.2778em;",[1113,1480,1393],{"className":1481},[1482],"mrel",[1113,1484],{"className":1485,"style":1478},[1477],[1113,1487,1489,1493,1550,1553,1557],{"className":1488},[1147],[1113,1490],{"className":1491,"style":1492},[1151],"height:0.8889em;vertical-align:-0.1944em;",[1113,1494,1496,1500],{"className":1495},[1156],[1113,1497,1399],{"className":1498,"style":1499},[1156,1157],"margin-right:0.0528em;",[1113,1501,1504],{"className":1502},[1503],"msupsub",[1113,1505,1509,1541],{"className":1506},[1507,1508],"vlist-t","vlist-t2",[1113,1510,1513,1536],{"className":1511},[1512],"vlist-r",[1113,1514,1518],{"className":1515,"style":1517},[1516],"vlist","height:0.3011em;",[1113,1519,1521,1526],{"style":1520},"top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;",[1113,1522],{"className":1523,"style":1525},[1524],"pstrut","height:2.7em;",[1113,1527,1533],{"className":1528},[1529,1530,1531,1532],"sizing","reset-size6","size3","mtight",[1113,1534,1403],{"className":1535},[1156,1532],[1113,1537,1540],{"className":1538},[1539],"vlist-s","​",[1113,1542,1544],{"className":1543},[1512],[1113,1545,1548],{"className":1546,"style":1547},[1516],"height:0.15em;",[1113,1549],{},[1113,1551],{"className":1552,"style":1193},[1477],[1113,1554,1406],{"className":1555},[1556],"mbin",[1113,1558],{"className":1559,"style":1193},[1477],[1113,1561,1563,1566,1606,1647,1650,1653],{"className":1562},[1147],[1113,1564],{"className":1565,"style":1492},[1151],[1113,1567,1569,1572],{"className":1568},[1156],[1113,1570,1399],{"className":1571,"style":1499},[1156,1157],[1113,1573,1575],{"className":1574},[1503],[1113,1576,1578,1598],{"className":1577},[1507,1508],[1113,1579,1581,1595],{"className":1580},[1512],[1113,1582,1584],{"className":1583,"style":1517},[1516],[1113,1585,1586,1589],{"style":1520},[1113,1587],{"className":1588,"style":1525},[1524],[1113,1590,1592],{"className":1591},[1529,1530,1531,1532],[1113,1593,1413],{"className":1594},[1156,1532],[1113,1596,1540],{"className":1597},[1539],[1113,1599,1601],{"className":1600},[1512],[1113,1602,1604],{"className":1603,"style":1547},[1516],[1113,1605],{},[1113,1607,1609,1612],{"className":1608},[1156],[1113,1610,1325],{"className":1611},[1156,1157],[1113,1613,1615],{"className":1614},[1503],[1113,1616,1618,1639],{"className":1617},[1507,1508],[1113,1619,1621,1636],{"className":1620},[1512],[1113,1622,1624],{"className":1623,"style":1517},[1516],[1113,1625,1627,1630],{"style":1626},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1113,1628],{"className":1629,"style":1525},[1524],[1113,1631,1633],{"className":1632},[1529,1530,1531,1532],[1113,1634,1413],{"className":1635},[1156,1532],[1113,1637,1540],{"className":1638},[1539],[1113,1640,1642],{"className":1641},[1512],[1113,1643,1645],{"className":1644,"style":1547},[1516],[1113,1646],{},[1113,1648],{"className":1649,"style":1193},[1477],[1113,1651,1406],{"className":1652},[1556],[1113,1654],{"className":1655,"style":1193},[1477],[1113,1657,1659,1662,1702,1742,1745,1748],{"className":1658},[1147],[1113,1660],{"className":1661,"style":1492},[1151],[1113,1663,1665,1668],{"className":1664},[1156],[1113,1666,1399],{"className":1667,"style":1499},[1156,1157],[1113,1669,1671],{"className":1670},[1503],[1113,1672,1674,1694],{"className":1673},[1507,1508],[1113,1675,1677,1691],{"className":1676},[1512],[1113,1678,1680],{"className":1679,"style":1517},[1516],[1113,1681,1682,1685],{"style":1520},[1113,1683],{"className":1684,"style":1525},[1524],[1113,1686,1688],{"className":1687},[1529,1530,1531,1532],[1113,1689,1428],{"className":1690},[1156,1532],[1113,1692,1540],{"className":1693},[1539],[1113,1695,1697],{"className":1696},[1512],[1113,1698,1700],{"className":1699,"style":1547},[1516],[1113,1701],{},[1113,1703,1705,1708],{"className":1704},[1156],[1113,1706,1325],{"className":1707},[1156,1157],[1113,1709,1711],{"className":1710},[1503],[1113,1712,1714,1734],{"className":1713},[1507,1508],[1113,1715,1717,1731],{"className":1716},[1512],[1113,1718,1720],{"className":1719,"style":1517},[1516],[1113,1721,1722,1725],{"style":1626},[1113,1723],{"className":1724,"style":1525},[1524],[1113,1726,1728],{"className":1727},[1529,1530,1531,1532],[1113,1729,1428],{"className":1730},[1156,1532],[1113,1732,1540],{"className":1733},[1539],[1113,1735,1737],{"className":1736},[1512],[1113,1738,1740],{"className":1739,"style":1547},[1516],[1113,1741],{},[1113,1743],{"className":1744,"style":1193},[1477],[1113,1746,1406],{"className":1747},[1556],[1113,1749],{"className":1750,"style":1193},[1477],[1113,1752,1754,1758,1762,1765,1768],{"className":1753},[1147],[1113,1755],{"className":1756,"style":1757},[1151],"height:0.6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",[1113,1882,1884,1902],{"className":1883},[1116],[1113,1885,1887],{"className":1886},[1120],[1122,1888,1889],{"xmlns":1124},[1126,1890,1891,1899],{},[1129,1892,1893],{},[1395,1894,1895,1897],{},[1132,1896,1399],{},[1401,1898,1403],{},[1136,1900,1901],{"encoding":1138},"\\beta_0",[1113,1903,1905],{"className":1904,"ariaHidden":1143},[1142],[1113,1906,1908,1911],{"className":1907},[1147],[1113,1909],{"className":1910,"style":1492},[1151],[1113,1912,1914,1917],{"className":1913},[1156],[1113,1915,1399],{"className":1916,"style":1499},[1156,1157],[1113,1918,1920],{"className":1919},[1503],[1113,1921,1923,1943],{"className":1922},[1507,1508],[1113,1924,1926,1940],{"className":1925},[1512],[1113,1927,1929],{"className":1928,"style":1517},[1516],[1113,1930,1931,1934],{"style":1520},[1113,1932],{"className":1933,"style":1525},[1524],[1113,1935,1937],{"className":1936},[1529,1530,1531,1532],[1113,1938,1403],{"className":1939},[1156,1532],[1113,1941,1540],{"className":1942},[1539],[1113,1944,1946],{"className":1945},[1512],[1113,1947,1949],{"className":1948,"style":1547},[1516],[1113,1950],{}," 吸收进系数向量:做法是把常数项移除,并在设计矩阵 ",[1113,1953,1955,1968],{"className":1954},[1116],[1113,1956,1958],{"className":1957},[1120],[1122,1959,1960],{"xmlns":1124},[1126,1961,1962,1966],{},[1129,1963,1964],{},[1132,1965,1134],{},[1136,1967,1134],{"encoding":1138},[1113,1969,1971],{"className":1970,"ariaHidden":1143},[1142],[1113,1972,1974,1977],{"className":1973},[1147],[1113,1975],{"className":1976,"style":1152},[1151],[1113,1978,1134],{"className":1979,"style":1158},[1156,1157]," 的",[1095,1982,1983],{},"最前面加上一列全 1",",这样模型就统一写成",[1091,1986,1987],{},[1113,1988,1990,2016],{"className":1989},[1116],[1113,1991,1993],{"className":1992},[1120],[1122,1994,1995],{"xmlns":1124},[1126,1996,1997,2013],{},[1129,1998,1999,2007,2009,2011],{},[2000,2001,2002,2004],"mover",{"accent":1143},[1132,2003,1356],{},[1391,2005,2006],{},"^",[1391,2008,1393],{},[1132,2010,1134],{},[1132,2012,1399],{},[1136,2014,2015],{"encoding":1138},"\\hat{y} = X\\beta",[1113,2017,2019,2083],{"className":2018,"ariaHidden":1143},[1142],[1113,2020,2022,2025,2074,2077,2080],{"className":2021},[1147],[1113,2023],{"className":2024,"style":1492},[1151],[1113,2026,2029],{"className":2027},[1156,2028],"accent",[1113,2030,2032,2065],{"className":2031},[1507,1508],[1113,2033,2035,2062],{"className":2034},[1512],[1113,2036,2039,2049],{"className":2037,"style":2038},[1516],"height:0.6944em;",[1113,2040,2042,2046],{"style":2041},"top:-3em;",[1113,2043],{"className":2044,"style":2045},[1524],"height:3em;",[1113,2047,1356],{"className":2048,"style":1372},[1156,1157],[1113,2050,2051,2054],{"style":2041},[1113,2052],{"className":2053,"style":2045},[1524],[1113,2055,2059],{"className":2056,"style":2058},[2057],"accent-body","left:-0.1944em;",[1113,2060,2006],{"className":2061},[1156],[1113,2063,1540],{"className":2064},[1539],[1113,2066,2068],{"className":2067},[1512],[1113,2069,2072],{"className":2070,"style":2071},[1516],"height:0.1944em;",[1113,2073],{},[1113,2075],{"className":2076,"style":1478},[1477],[1113,2078,1393],{"className":2079},[1482],[1113,2081],{"className":2082,"style":1478},[1477],[1113,2084,2086,2089,2092],{"className":2085},[1147],[1113,2087],{"className":2088,"style":1492},[1151],[1113,2090,1134],{"className":2091,"style":1158},[1156,1157],[1113,2093,1399],{"className":2094,"style":1499},[1156,1157],[1091,2096,2097,2098,2101],{},"参数可以用",[1095,2099,2100],{},"最小二乘估计","求出闭式解:",[1091,2103,2104],{},[1113,2105,2107,2162],{"className":2106},[1116],[1113,2108,2110],{"className":2109},[1120],[1122,2111,2112],{"xmlns":1124},[1126,2113,2114,2159],{},[1129,2115,2116,2122,2124,2128,2137,2139,2151,2157],{},[2000,2117,2118,2120],{"accent":1143},[1132,2119,1399],{},[1391,2121,2006],{},[1391,2123,1393],{},[1391,2125,2127],{"stretchy":2126},"false","(",[2129,2130,2131,2133],"msup",{},[1132,2132,1134],{},[1132,2134,2136],{"mathvariant":2135},"normal","⊤",[1132,2138,1134],{},[2129,2140,2141,2144],{},[1391,2142,2143],{"stretchy":2126},")",[1129,2145,2146,2149],{},[1391,2147,2148],{},"−",[1401,2150,1413],{},[2129,2152,2153,2155],{},[1132,2154,1134],{},[1132,2156,2136],{"mathvariant":2135},[1132,2158,1356],{},[1136,2160,2161],{"encoding":1138},"\\hat\\beta = (X^{\\top}X)^{-1}X^{\\top}y",[1113,2163,2165,2226],{"className":2164,"ariaHidden":1143},[1142],[1113,2166,2168,2172,2217,2220,2223],{"className":2167},[1147],[1113,2169],{"className":2170,"style":2171},[1151],"height:1.1523em;vertical-align:-0.1944em;",[1113,2173,2175],{"className":2174},[1156,2028],[1113,2176,2178,2209],{"className":2177},[1507,1508],[1113,2179,2181,2206],{"className":2180},[1512],[1113,2182,2185,2193],{"className":2183,"style":2184},[1516],"height:0.9579em;",[1113,2186,2187,2190],{"style":2041},[1113,2188],{"className":2189,"style":2045},[1524],[1113,2191,1399],{"className":2192,"style":1499},[1156,1157],[1113,2194,2196,2199],{"style":2195},"top:-3.2634em;",[1113,2197],{"className":2198,"style":2045},[1524],[1113,2200,2203],{"className":2201,"style":2202},[2057],"left:-0.1667em;",[1113,2204,2006],{"className":2205},[1156],[1113,2207,1540],{"className":2208},[1539],[1113,2210,2212],{"className":2211},[1512],[1113,2213,2215],{"className":2214,"style":2071},[1516],[1113,2216],{},[1113,2218],{"className":2219,"style":1478},[1477],[1113,2221,1393],{"className":2222},[1482],[1113,2224],{"className":2225,"style":1478},[1477],[1113,2227,2229,2233,2237,2271,2274,2311,2343],{"className":2228},[1147],[1113,2230],{"className":2231,"style":2232},[1151],"height:1.0991em;vertical-align:-0.25em;",[1113,2234,2127],{"className":2235},[2236],"mopen",[1113,2238,2240,2243],{"className":2239},[1156],[1113,2241,1134],{"className":2242,"style":1158},[1156,1157],[1113,2244,2246],{"className":2245},[1503],[1113,2247,2249],{"className":2248},[1507],[1113,2250,2252],{"className":2251},[1512],[1113,2253,2256],{"className":2254,"style":2255},[1516],"height:0.8491em;",[1113,2257,2259,2262],{"style":2258},"top:-3.063em;margin-right:0.05em;",[1113,2260],{"className":2261,"style":1525},[1524],[1113,2263,2265],{"className":2264},[1529,1530,1531,1532],[1113,2266,2268],{"className":2267},[1156,1532],[1113,2269,2136],{"className":2270},[1156,1532],[1113,2272,1134],{"className":2273,"style":1158},[1156,1157],[1113,2275,2278,2281],{"className":2276},[2277],"mclose",[1113,2279,2143],{"className":2280},[2277],[1113,2282,2284],{"className":2283},[1503],[1113,2285,2287],{"className":2286},[1507],[1113,2288,2290],{"className":2289},[1512],[1113,2291,2294],{"className":2292,"style":2293},[1516],"height:0.8141em;",[1113,2295,2296,2299],{"style":2258},[1113,2297],{"className":2298,"style":1525},[1524],[1113,2300,2302],{"className":2301},[1529,1530,1531,1532],[1113,2303,2305,2308],{"className":2304},[1156,1532],[1113,2306,2148],{"className":2307},[1156,1532],[1113,2309,1413],{"className":2310},[1156,1532],[1113,2312,2314,2317],{"className":2313},[1156],[1113,2315,1134],{"className":2316,"style":1158},[1156,1157],[1113,2318,2320],{"className":2319},[1503],[1113,2321,2323],{"className":2322},[1507],[1113,2324,2326],{"className":2325},[1512],[1113,2327,2329],{"className":2328,"style":2255},[1516],[1113,2330,2331,2334],{"style":2258},[1113,2332],{"className":2333,"style":1525},[1524],[1113,2335,2337],{"className":2336},[1529,1530,1531,1532],[1113,2338,2340],{"className":2339},[1156,1532],[1113,2341,2136],{"className":2342},[1156,1532],[1113,2344,1356],{"className":2345,"style":1372},[1156,1157],[1091,2347,2348,2349,2429,2430,2687],{},"预测一个新样本 ",[1113,2350,2352,2372],{"className":2351},[1116],[1113,2353,2355],{"className":2354},[1120],[1122,2356,2357],{"xmlns":1124},[1126,2358,2359,2369],{},[1129,2360,2361],{},[1395,2362,2363,2365],{},[1132,2364,1325],{},[2366,2367,2368],"mtext",{},"new",[1136,2370,2371],{"encoding":1138},"x_{\\text{new}}",[1113,2373,2375],{"className":2374,"ariaHidden":1143},[1142],[1113,2376,2378,2382],{"className":2377},[1147],[1113,2379],{"className":2380,"style":2381},[1151],"height:0.5806em;vertical-align:-0.15em;",[1113,2383,2385,2388],{"className":2384},[1156],[1113,2386,1325],{"className":2387},[1156,1157],[1113,2389,2391],{"className":2390},[1503],[1113,2392,2394,2421],{"className":2393},[1507,1508],[1113,2395,2397,2418],{"className":2396},[1512],[1113,2398,2400],{"className":2399,"style":1796},[1516],[1113,2401,2402,2405],{"style":1626},[1113,2403],{"className":2404,"style":1525},[1524],[1113,2406,2408],{"className":2407},[1529,1530,1531,1532],[1113,2409,2411],{"className":2410},[1156,1532],[1113,2412,2415],{"className":2413},[1156,2414,1532],"text",[1113,2416,2368],{"className":2417},[1156,1532],[1113,2419,1540],{"className":2420},[1539],[1113,2422,2424],{"className":2423},[1512],[1113,2425,2427],{"className":2426,"style":1547},[1516],[1113,2428],{}," 时,直接代入 ",[1113,2431,2433,2472],{"className":2432},[1116],[1113,2434,2436],{"className":2435},[1120],[1122,2437,2438],{"xmlns":1124},[1126,2439,2440,2469],{},[1129,2441,2442,2452,2454,2463],{},[1395,2443,2444,2450],{},[2000,2445,2446,2448],{"accent":1143},[1132,2447,1356],{},[1391,2449,2006],{},[2366,2451,2368],{},[1391,2453,1393],{},[2455,2456,2457,2459,2461],"msubsup",{},[1132,2458,1325],{},[2366,2460,2368],{},[1132,2462,2136],{"mathvariant":2135},[2000,2464,2465,2467],{"accent":1143},[1132,2466,1399],{},[1391,2468,2006],{},[1136,2470,2471],{"encoding":1138},"\\hat{y}_{\\text{new}} = x_{\\text{new}}^{\\top}\\hat\\beta",[1113,2473,2475,2576],{"className":2474,"ariaHidden":1143},[1142],[1113,2476,2478,2481,2567,2570,2573],{"className":2477},[1147],[1113,2479],{"className":2480,"style":1492},[1151],[1113,2482,2484,2526],{"className":2483},[1156],[1113,2485,2487],{"className":2486},[1156,2028],[1113,2488,2490,2518],{"className":2489},[1507,1508],[1113,2491,2493,2515],{"className":2492},[1512],[1113,2494,2496,2504],{"className":2495,"style":2038},[1516],[1113,2497,2498,2501],{"style":2041},[1113,2499],{"className":2500,"style":2045},[1524],[1113,2502,1356],{"className":2503,"style":1372},[1156,1157],[1113,2505,2506,2509],{"style":2041},[1113,2507],{"className":2508,"style":2045},[1524],[1113,2510,2512],{"className":2511,"style":2058},[2057],[1113,2513,2006],{"className":2514},[1156],[1113,2516,1540],{"className":2517},[1539],[1113,2519,2521],{"className":2520},[1512],[1113,2522,2524],{"className":2523,"style":2071},[1516],[1113,2525],{},[1113,2527,2529],{"className":2528},[1503],[1113,2530,2532,2559],{"className":2531},[1507,1508],[1113,2533,2535,2556],{"className":2534},[1512],[1113,2536,2538],{"className":2537,"style":1796},[1516],[1113,2539,2541,2544],{"style":2540},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1113,2542],{"className":2543,"style":1525},[1524],[1113,2545,2547],{"className":2546},[1529,1530,1531,1532],[1113,2548,2550],{"className":2549},[1156,1532],[1113,2551,2553],{"className":2552},[1156,2414,1532],[1113,2554,2368],{"className":2555},[1156,1532],[1113,2557,1540],{"className":2558},[1539],[1113,2560,2562],{"className":2561},[1512],[1113,2563,2565],{"className":2564,"style":1547},[1516],[1113,2566],{},[1113,2568],{"className":2569,"style":1478},[1477],[1113,2571,1393],{"className":2572},[1482],[1113,2574],{"className":2575,"style":1478},[1477],[1113,2577,2579,2583,2645],{"className":2578},[1147],[1113,2580],{"className":2581,"style":2582},[1151],"height:1.2049em;vertical-align:-0.247em;",[1113,2584,2586,2589],{"className":2585},[1156],[1113,2587,1325],{"className":2588},[1156,1157],[1113,2590,2592],{"className":2591},[1503],[1113,2593,2595,2636],{"className":2594},[1507,1508],[1113,2596,2598,2633],{"className":2597},[1512],[1113,2599,2601,2619],{"className":2600,"style":2255},[1516],[1113,2602,2604,2607],{"style":2603},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1113,2605],{"className":2606,"style":1525},[1524],[1113,2608,2610],{"className":2609},[1529,1530,1531,1532],[1113,2611,2613],{"className":2612},[1156,1532],[1113,2614,2616],{"className":2615},[1156,2414,1532],[1113,2617,2368],{"className":2618},[1156,1532],[1113,2620,2621,2624],{"style":2258},[1113,2622],{"className":2623,"style":1525},[1524],[1113,2625,2627],{"className":2626},[1529,1530,1531,1532],[1113,2628,2630],{"className":2629},[1156,1532],[1113,2631,2136],{"className":2632},[1156,1532],[1113,2634,1540],{"className":2635},[1539],[1113,2637,2639],{"className":2638},[1512],[1113,2640,2643],{"className":2641,"style":2642},[1516],"height:0.247em;",[1113,2644],{},[1113,2646,2648],{"className":2647},[1156,2028],[1113,2649,2651,2679],{"className":2650},[1507,1508],[1113,2652,2654,2676],{"className":2653},[1512],[1113,2655,2657,2665],{"className":2656,"style":2184},[1516],[1113,2658,2659,2662],{"style":2041},[1113,2660],{"className":2661,"style":2045},[1524],[1113,2663,1399],{"className":2664,"style":1499},[1156,1157],[1113,2666,2667,2670],{"style":2195},[1113,2668],{"className":2669,"style":2045},[1524],[1113,2671,2673],{"className":2672,"style":2202},[2057],[1113,2674,2006],{"className":2675},[1156],[1113,2677,1540],{"className":2678},[1539],[1113,2680,2682],{"className":2681},[1512],[1113,2683,2685],{"className":2684,"style":2071},[1516],[1113,2686],{}," 即可。",[2689,2690],"hr",{},[1304,2692,2694],{"id":2693},"二逻辑回归","二、逻辑回归",[1091,2696,2697,2698,2701,2702,2731,2732,2800],{},"逻辑回归属于",[1095,2699,2700],{},"广义线性模型","。广义线性模型的一般形式是通过一个联系函数 ",[1113,2703,2705,2719],{"className":2704},[1116],[1113,2706,2708],{"className":2707},[1120],[1122,2709,2710],{"xmlns":1124},[1126,2711,2712,2717],{},[1129,2713,2714],{},[1132,2715,2716],{},"g",[1136,2718,2716],{"encoding":1138},[1113,2720,2722],{"className":2721,"ariaHidden":1143},[1142],[1113,2723,2725,2728],{"className":2724},[1147],[1113,2726],{"className":2727,"style":1368},[1151],[1113,2729,2716],{"className":2730,"style":1372},[1156,1157]," 把线性预测值 ",[1113,2733,2735,2755],{"className":2734},[1116],[1113,2736,2738],{"className":2737},[1120],[1122,2739,2740],{"xmlns":1124},[1126,2741,2742,2752],{},[1129,2743,2744,2750],{},[2129,2745,2746,2748],{},[1132,2747,1325],{},[1132,2749,2136],{"mathvariant":2135},[1132,2751,1399],{},[1136,2753,2754],{"encoding":1138},"x^{\\top}\\beta",[1113,2756,2758],{"className":2757,"ariaHidden":1143},[1142],[1113,2759,2761,2765,2797],{"className":2760},[1147],[1113,2762],{"className":2763,"style":2764},[1151],"height:1.0435em;vertical-align:-0.1944em;",[1113,2766,2768,2771],{"className":2767},[1156],[1113,2769,1325],{"className":2770},[1156,1157],[1113,2772,2774],{"className":2773},[1503],[1113,2775,2777],{"className":2776},[1507],[1113,2778,2780],{"className":2779},[1512],[1113,2781,2783],{"className":2782,"style":2255},[1516],[1113,2784,2785,2788],{"style":2258},[1113,2786],{"className":2787,"style":1525},[1524],[1113,2789,2791],{"className":2790},[1529,1530,1531,1532],[1113,2792,2794],{"className":2793},[1156,1532],[1113,2795,2136],{"className":2796},[1156,1532],[1113,2798,1399],{"className":2799,"style":1499},[1156,1157]," 映射到响应:",[1091,2802,2803],{},[1113,2804,2806,2836],{"className":2805},[1116],[1113,2807,2809],{"className":2808},[1120],[1122,2810,2811],{"xmlns":1124},[1126,2812,2813,2833],{},[1129,2814,2815,2817,2819,2821,2823,2825,2831],{},[1132,2816,2716],{},[1391,2818,2127],{"stretchy":2126},[1132,2820,1356],{},[1391,2822,2143],{"stretchy":2126},[1391,2824,1393],{},[2129,2826,2827,2829],{},[1132,2828,1325],{},[1132,2830,2136],{"mathvariant":2135},[1132,2832,1399],{},[1136,2834,2835],{"encoding":1138},"g(y) = x^{\\top}\\beta",[1113,2837,2839,2867],{"className":2838,"ariaHidden":1143},[1142],[1113,2840,2842,2846,2849,2852,2855,2858,2861,2864],{"className":2841},[1147],[1113,2843],{"className":2844,"style":2845},[1151],"height:1em;vertical-align:-0.25em;",[1113,2847,2716],{"className":2848,"style":1372},[1156,1157],[1113,2850,2127],{"className":2851},[2236],[1113,2853,1356],{"className":2854,"style":1372},[1156,1157],[1113,2856,2143],{"className":2857},[2277],[1113,2859],{"className":2860,"style":1478},[1477],[1113,2862,1393],{"className":2863},[1482],[1113,2865],{"className":2866,"style":1478},[1477],[1113,2868,2870,2873,2905],{"className":2869},[1147],[1113,2871],{"className":2872,"style":2764},[1151],[1113,2874,2876,2879],{"className":2875},[1156],[1113,2877,1325],{"className":2878},[1156,1157],[1113,2880,2882],{"className":2881},[1503],[1113,2883,2885],{"className":2884},[1507],[1113,2886,2888],{"className":2887},[1512],[1113,2889,2891],{"className":2890,"style":2255},[1516],[1113,2892,2893,2896],{"style":2258},[1113,2894],{"className":2895,"style":1525},[1524],[1113,2897,2899],{"className":2898},[1529,1530,1531,1532],[1113,2900,2902],{"className":2901},[1156,1532],[1113,2903,2136],{"className":2904},[1156,1532],[1113,2906,1399],{"className":2907,"style":1499},[1156,1157],[1091,2909,2910,2911,2914],{},"逻辑回归取 ",[1095,2912,2913],{},"对数几率函数"," (logit)作为联系函数。把 logit 代入,就得到逻辑回归模型:",[1091,2916,2917],{},[1113,2918,2920,3018],{"className":2919},[1116],[1113,2921,2923],{"className":2922},[1120],[1122,2924,2925],{"xmlns":1124},[1126,2926,2927,3015],{},[1129,2928,2929,2932,2934,2936,2938,2940,2943,2945,2947,2949,2977,2979],{},[1132,2930,2931],{},"P",[1391,2933,2127],{"stretchy":2126},[1132,2935,1356],{},[1391,2937,1393],{},[1401,2939,1413],{},[1391,2941,2942],{},"∣",[1132,2944,1325],{},[1391,2946,2143],{"stretchy":2126},[1391,2948,1393],{},[2950,2951,2952,2954],"mfrac",{},[1401,2953,1413],{},[1129,2955,2956,2958,2960],{},[1401,2957,1413],{},[1391,2959,1406],{},[2129,2961,2962,2965],{},[1132,2963,2964],{},"e",[1129,2966,2967,2969,2975],{},[1391,2968,2148],{},[2129,2970,2971,2973],{},[1132,2972,1325],{},[1132,2974,2136],{"mathvariant":2135},[1132,2976,1399],{},[1391,2978,1393],{},[2950,2980,2981,2995],{},[2129,2982,2983,2985],{},[1132,2984,2964],{},[1129,2986,2987,2993],{},[2129,2988,2989,2991],{},[1132,2990,1325],{},[1132,2992,2136],{"mathvariant":2135},[1132,2994,1399],{},[1129,2996,2997,2999,3001],{},[1401,2998,1413],{},[1391,3000,1406],{},[2129,3002,3003,3005],{},[1132,3004,2964],{},[1129,3006,3007,3013],{},[2129,3008,3009,3011],{},[1132,3010,1325],{},[1132,3012,2136],{"mathvariant":2135},[1132,3014,1399],{},[1136,3016,3017],{"encoding":1138},"P(y=1\\mid x) = \\frac{1}{1 + e^{-x^{\\top}\\beta}} = \\frac{e^{x^{\\top}\\beta}}{1 + e^{x^{\\top}\\beta}}",[1113,3019,3021,3046,3064,3085,3252],{"className":3020,"ariaHidden":1143},[1142],[1113,3022,3024,3027,3031,3034,3037,3040,3043],{"className":3023},[1147],[1113,3025],{"className":3026,"style":2845},[1151],[1113,3028,2931],{"className":3029,"style":3030},[1156,1157],"margin-right:0.1389em;",[1113,3032,2127],{"className":3033},[2236],[1113,3035,1356],{"className":3036,"style":1372},[1156,1157],[1113,3038],{"className":3039,"style":1478},[1477],[1113,3041,1393],{"className":3042},[1482],[1113,3044],{"className":3045,"style":1478},[1477],[1113,3047,3049,3052,3055,3058,3061],{"className":3048},[1147],[1113,3050],{"className":3051,"style":2845},[1151],[1113,3053,1413],{"className":3054},[1156],[1113,3056],{"className":3057,"style":1478},[1477],[1113,3059,2942],{"className":3060},[1482],[1113,3062],{"className":3063,"style":1478},[1477],[1113,3065,3067,3070,3073,3076,3079,3082],{"className":3066},[1147],[1113,3068],{"className":3069,"style":2845},[1151],[1113,3071,1325],{"className":3072},[1156,1157],[1113,3074,2143],{"className":3075},[2277],[1113,3077],{"className":3078,"style":1478},[1477],[1113,3080,1393],{"className":3081},[1482],[1113,3083],{"className":3084,"style":1478},[1477],[1113,3086,3088,3092,3243,3246,3249],{"className":3087},[1147],[1113,3089],{"className":3090,"style":3091},[1151],"height:1.4079em;vertical-align:-0.5628em;",[1113,3093,3095,3099,3240],{"className":3094},[1156],[1113,3096],{"className":3097},[2236,3098],"nulldelimiter",[1113,3100,3102],{"className":3101},[2950],[1113,3103,3105,3231],{"className":3104},[1507,1508],[1113,3106,3108,3228],{"className":3107},[1512],[1113,3109,3112,3202,3213],{"className":3110,"style":3111},[1516],"height:0.8451em;",[1113,3113,3115,3118],{"style":3114},"top:-2.4956em;",[1113,3116],{"className":3117,"style":2045},[1524],[1113,3119,3121],{"className":3120},[1529,1530,1531,1532],[1113,3122,3124,3127,3130],{"className":3123},[1156,1532],[1113,3125,1413],{"className":3126},[1156,1532],[1113,3128,1406],{"className":3129},[1556,1532],[1113,3131,3133,3136],{"className":3132},[1156,1532],[1113,3134,2964],{"className":3135},[1156,1157,1532],[1113,3137,3139],{"className":3138},[1503],[1113,3140,3142],{"className":3141},[1507],[1113,3143,3145],{"className":3144},[1512],[1113,3146,3149],{"className":3147,"style":3148},[1516],"height:0.992em;",[1113,3150,3152,3156],{"style":3151},"top:-2.992em;margin-right:0.0714em;",[1113,3153],{"className":3154,"style":3155},[1524],"height:2.706em;",[1113,3157,3161],{"className":3158},[1529,3159,3160,1532],"reset-size3","size1",[1113,3162,3164,3167,3199],{"className":3163},[1156,1532],[1113,3165,2148],{"className":3166},[1156,1532],[1113,3168,3170,3173],{"className":3169},[1156,1532],[1113,3171,1325],{"className":3172},[1156,1157,1532],[1113,3174,3176],{"className":3175},[1503],[1113,3177,3179],{"className":3178},[1507],[1113,3180,3182],{"className":3181},[1512],[1113,3183,3186],{"className":3184,"style":3185},[1516],"height:0.9884em;",[1113,3187,3189,3193],{"style":3188},"top:-2.9884em;margin-right:0.1em;",[1113,3190],{"className":3191,"style":3192},[1524],"height:2.6944em;",[1113,3194,3196],{"className":3195},[1156,1532],[1113,3197,2136],{"className":3198},[1156,1532],[1113,3200,1399],{"className":3201,"style":1499},[1156,1157,1532],[1113,3203,3205,3208],{"style":3204},"top:-3.23em;",[1113,3206],{"className":3207,"style":2045},[1524],[1113,3209],{"className":3210,"style":3212},[3211],"frac-line","border-bottom-width:0.04em;",[1113,3214,3216,3219],{"style":3215},"top:-3.394em;",[1113,3217],{"className":3218,"style":2045},[1524],[1113,3220,3222],{"className":3221},[1529,1530,1531,1532],[1113,3223,3225],{"className":3224},[1156,1532],[1113,3226,1413],{"className":3227},[1156,1532],[1113,3229,1540],{"className":3230},[1539],[1113,3232,3234],{"className":3233},[1512],[1113,3235,3238],{"className":3236,"style":3237},[1516],"height:0.5628em;",[1113,3239],{},[1113,3241],{"className":3242},[2277,3098],[1113,3244],{"className":3245,"style":1478},[1477],[1113,3247,1393],{"className":3248},[1482],[1113,3250],{"className":3251,"style":1478},[1477],[1113,3253,3255,3259],{"className":3254},[1147],[1113,3256],{"className":3257,"style":3258},[1151],"height:1.8077em;vertical-align:-0.5628em;",[1113,3260,3262,3265,3452],{"className":3261},[1156],[1113,3263],{"className":3264},[2236,3098],[1113,3266,3268],{"className":3267},[2950],[1113,3269,3271,3444],{"className":3270},[1507,1508],[1113,3272,3274,3441],{"className":3273},[1512],[1113,3275,3278,3356,3364],{"className":3276,"style":3277},[1516],"height:1.2449em;",[1113,3279,3280,3283],{"style":3114},[1113,3281],{"className":3282,"style":2045},[1524],[1113,3284,3286],{"className":3285},[1529,1530,1531,1532],[1113,3287,3289,3292,3295],{"className":3288},[1156,1532],[1113,3290,1413],{"className":3291},[1156,1532],[1113,3293,1406],{"className":3294},[1556,1532],[1113,3296,3298,3301],{"className":3297},[1156,1532],[1113,3299,2964],{"className":3300},[1156,1157,1532],[1113,3302,3304],{"className":3303},[1503],[1113,3305,3307],{"className":3306},[1507],[1113,3308,3310],{"className":3309},[1512],[1113,3311,3313],{"className":3312,"style":3148},[1516],[1113,3314,3315,3318],{"style":3151},[1113,3316],{"className":3317,"style":3155},[1524],[1113,3319,3321],{"className":3320},[1529,3159,3160,1532],[1113,3322,3324,3353],{"className":3323},[1156,1532],[1113,3325,3327,3330],{"className":3326},[1156,1532],[1113,3328,1325],{"className":3329},[1156,1157,1532],[1113,3331,3333],{"className":3332},[1503],[1113,3334,3336],{"className":3335},[1507],[1113,3337,3339],{"className":3338},[1512],[1113,3340,3342],{"className":3341,"style":3185},[1516],[1113,3343,3344,3347],{"style":3188},[1113,3345],{"className":3346,"style":3192},[1524],[1113,3348,3350],{"className":3349},[1156,1532],[1113,3351,2136],{"className":3352},[1156,1532],[1113,3354,1399],{"className":3355,"style":1499},[1156,1157,1532],[1113,3357,3358,3361],{"style":3204},[1113,3359],{"className":3360,"style":2045},[1524],[1113,3362],{"className":3363,"style":3212},[3211],[1113,3365,3366,3369],{"style":3215},[1113,3367],{"className":3368,"style":2045},[1524],[1113,3370,3372],{"className":3371},[1529,1530,1531,1532],[1113,3373,3375],{"className":3374},[1156,1532],[1113,3376,3378,3381],{"className":3377},[1156,1532],[1113,3379,2964],{"className":3380},[1156,1157,1532],[1113,3382,3384],{"className":3383},[1503],[1113,3385,3387],{"className":3386},[1507],[1113,3388,3390],{"className":3389},[1512],[1113,3391,3394],{"className":3392,"style":3393},[1516],"height:1.2156em;",[1113,3395,3397,3401],{"style":3396},"top:-3.2156em;margin-right:0.0714em;",[1113,3398],{"className":3399,"style":3400},[1524],"height:2.7846em;",[1113,3402,3404],{"className":3403},[1529,3159,3160,1532],[1113,3405,3407,3438],{"className":3406},[1156,1532],[1113,3408,3410,3413],{"className":3409},[1156,1532],[1113,3411,1325],{"className":3412},[1156,1157,1532],[1113,3414,3416],{"className":3415},[1503],[1113,3417,3419],{"className":3418},[1507],[1113,3420,3422],{"className":3421},[1512],[1113,3423,3426],{"className":3424,"style":3425},[1516],"height:1.0984em;",[1113,3427,3429,3432],{"style":3428},"top:-3.0984em;margin-right:0.1em;",[1113,3430],{"className":3431,"style":3192},[1524],[1113,3433,3435],{"className":3434},[1156,1532],[1113,3436,2136],{"className":3437},[1156,1532],[1113,3439,1399],{"className":3440,"style":1499},[1156,1157,1532],[1113,3442,1540],{"className":3443},[1539],[1113,3445,3447],{"className":3446},[1512],[1113,3448,3450],{"className":3449,"style":3237},[1516],[1113,3451],{},[1113,3453],{"className":3454},[2277,3098],[1091,3456,3457],{},"对\"几率\"取对数,可以得到",[1091,3459,3460],{},[1113,3461,3463,3529],{"className":3462},[1116],[1113,3464,3466],{"className":3465},[1120],[1122,3467,3468],{"xmlns":1124},[1126,3469,3470,3526],{},[1129,3471,3472,3475,3478,3516,3518,3524],{},[1132,3473,3474],{},"ln",[1391,3476,3477],{},"⁡",[2950,3479,3480,3498],{},[1129,3481,3482,3484,3486,3488,3490,3492,3494,3496],{},[1132,3483,2931],{},[1391,3485,2127],{"stretchy":2126},[1132,3487,1356],{},[1391,3489,1393],{},[1401,3491,1413],{},[1391,3493,2942],{},[1132,3495,1325],{},[1391,3497,2143],{"stretchy":2126},[1129,3499,3500,3502,3504,3506,3508,3510,3512,3514],{},[1132,3501,2931],{},[1391,3503,2127],{"stretchy":2126},[1132,3505,1356],{},[1391,3507,1393],{},[1401,3509,1403],{},[1391,3511,2942],{},[1132,3513,1325],{},[1391,3515,2143],{"stretchy":2126},[1391,3517,1393],{},[2129,3519,3520,3522],{},[1132,3521,1325],{},[1132,3523,2136],{"mathvariant":2135},[1132,3525,1399],{},[1136,3527,3528],{"encoding":1138},"\\ln\\frac{P(y=1\\mid x)}{P(y=0\\mid x)} = x^{\\top}\\beta",[1113,3530,3532,3670],{"className":3531,"ariaHidden":1143},[1142],[1113,3533,3535,3539,3543,3547,3661,3664,3667],{"className":3534},[1147],[1113,3536],{"className":3537,"style":3538},[1151],"height:1.53em;vertical-align:-0.52em;",[1113,3540,3474],{"className":3541},[3542],"mop",[1113,3544],{"className":3545,"style":3546},[1477],"margin-right:0.1667em;",[1113,3548,3550,3553,3658],{"className":3549},[1156],[1113,3551],{"className":3552},[2236,3098],[1113,3554,3556],{"className":3555},[2950],[1113,3557,3559,3649],{"className":3558},[1507,1508],[1113,3560,3562,3646],{"className":3561},[1512],[1113,3563,3566,3602,3610],{"className":3564,"style":3565},[1516],"height:1.01em;",[1113,3567,3569,3572],{"style":3568},"top:-2.655em;",[1113,3570],{"className":3571,"style":2045},[1524],[1113,3573,3575],{"className":3574},[1529,1530,1531,1532],[1113,3576,3578,3581,3584,3587,3590,3593,3596,3599],{"className":3577},[1156,1532],[1113,3579,2931],{"className":3580,"style":3030},[1156,1157,1532],[1113,3582,2127],{"className":3583},[2236,1532],[1113,3585,1356],{"className":3586,"style":1372},[1156,1157,1532],[1113,3588,1393],{"className":3589},[1482,1532],[1113,3591,1403],{"className":3592},[1156,1532],[1113,3594,2942],{"className":3595},[1482,1532],[1113,3597,1325],{"className":3598},[1156,1157,1532],[1113,3600,2143],{"className":3601},[2277,1532],[1113,3603,3604,3607],{"style":3204},[1113,3605],{"className":3606,"style":2045},[1524],[1113,3608],{"className":3609,"style":3212},[3211],[1113,3611,3613,3616],{"style":3612},"top:-3.485em;",[1113,3614],{"className":3615,"style":2045},[1524],[1113,3617,3619],{"className":3618},[1529,1530,1531,1532],[1113,3620,3622,3625,3628,3631,3634,3637,3640,3643],{"className":3621},[1156,1532],[1113,3623,2931],{"className":3624,"style":3030},[1156,1157,1532],[1113,3626,2127],{"className":3627},[2236,1532],[1113,3629,1356],{"className":3630,"style":1372},[1156,1157,1532],[1113,3632,1393],{"className":3633},[1482,1532],[1113,3635,1413],{"className":3636},[1156,1532],[1113,3638,2942],{"className":3639},[1482,1532],[1113,3641,1325],{"className":3642},[1156,1157,1532],[1113,3644,2143],{"className":3645},[2277,1532],[1113,3647,1540],{"className":3648},[1539],[1113,3650,3652],{"className":3651},[1512],[1113,3653,3656],{"className":3654,"style":3655},[1516],"height:0.52em;",[1113,3657],{},[1113,3659],{"className":3660},[2277,3098],[1113,3662],{"className":3663,"style":1478},[1477],[1113,3665,1393],{"className":3666},[1482],[1113,3668],{"className":3669,"style":1478},[1477],[1113,3671,3673,3676,3708],{"className":3672},[1147],[1113,3674],{"className":3675,"style":2764},[1151],[1113,3677,3679,3682],{"className":3678},[1156],[1113,3680,1325],{"className":3681},[1156,1157],[1113,3683,3685],{"className":3684},[1503],[1113,3686,3688],{"className":3687},[1507],[1113,3689,3691],{"className":3690},[1512],[1113,3692,3694],{"className":3693,"style":2255},[1516],[1113,3695,3696,3699],{"style":2258},[1113,3697],{"className":3698,"style":1525},[1524],[1113,3700,3702],{"className":3701},[1529,1530,1531,1532],[1113,3703,3705],{"className":3704},[1156,1532],[1113,3706,2136],{"className":3707},[1156,1532],[1113,3709,1399],{"className":3710,"style":1499},[1156,1157],[1091,3712,3713,3714,3717],{},"由此可以看出,",[1095,3715,3716],{},"逻辑回归实际上是在用线性回归的预测结果去逼近真实标记的对数几率","。",[1091,3719,3720,3721,3724,3725,3813,3814,3844,3845,3848,3849,3959,3960,3717],{},"与线性回归不同,逻辑回归问题",[1095,3722,3723],{},"没有闭式解",",只能用迭代方法(如梯度下降、牛顿法)求解。预测新样本时,算出 ",[1113,3726,3728,3756],{"className":3727},[1116],[1113,3729,3731],{"className":3730},[1120],[1122,3732,3733],{"xmlns":1124},[1126,3734,3735,3753],{},[1129,3736,3737,3739,3741,3743,3745,3747,3749,3751],{},[1132,3738,2931],{},[1391,3740,2127],{"stretchy":2126},[1132,3742,1356],{},[1391,3744,1393],{},[1401,3746,1413],{},[1391,3748,2942],{},[1132,3750,1325],{},[1391,3752,2143],{"stretchy":2126},[1136,3754,3755],{"encoding":1138},"P(y=1\\mid x)",[1113,3757,3759,3783,3801],{"className":3758,"ariaHidden":1143},[1142],[1113,3760,3762,3765,3768,3771,3774,3777,3780],{"className":3761},[1147],[1113,3763],{"className":3764,"style":2845},[1151],[1113,3766,2931],{"className":3767,"style":3030},[1156,1157],[1113,3769,2127],{"className":3770},[2236],[1113,3772,1356],{"className":3773,"style":1372},[1156,1157],[1113,3775],{"className":3776,"style":1478},[1477],[1113,3778,1393],{"className":3779},[1482],[1113,3781],{"className":3782,"style":1478},[1477],[1113,3784,3786,3789,3792,3795,3798],{"className":3785},[1147],[1113,3787],{"className":3788,"style":2845},[1151],[1113,3790,1413],{"className":3791},[1156],[1113,3793],{"className":3794,"style":1478},[1477],[1113,3796,2942],{"className":3797},[1482],[1113,3799],{"className":3800,"style":1478},[1477],[1113,3802,3804,3807,3810],{"className":3803},[1147],[1113,3805],{"className":3806,"style":2845},[1151],[1113,3808,1325],{"className":3809},[1156,1157],[1113,3811,2143],{"className":3812},[2277],",以 ",[1113,3815,3817,3831],{"className":3816},[1116],[1113,3818,3820],{"className":3819},[1120],[1122,3821,3822],{"xmlns":1124},[1126,3823,3824,3829],{},[1129,3825,3826],{},[1401,3827,3828],{},"0.5",[1136,3830,3828],{"encoding":1138},[1113,3832,3834],{"className":3833,"ariaHidden":1143},[1142],[1113,3835,3837,3841],{"className":3836},[1147],[1113,3838],{"className":3839,"style":3840},[1151],"height:0.6444em;",[1113,3842,3828],{"className":3843},[1156]," 为阈值判类,因此",[1095,3846,3847],{},"分类判别线","就是 ",[1113,3850,3852,3884],{"className":3851},[1116],[1113,3853,3855],{"className":3854},[1120],[1122,3856,3857],{"xmlns":1124},[1126,3858,3859,3881],{},[1129,3860,3861,3863,3865,3867,3869,3871,3873,3875,3877,3879],{},[1132,3862,2931],{},[1391,3864,2127],{"stretchy":2126},[1132,3866,1356],{},[1391,3868,1393],{},[1401,3870,1413],{},[1391,3872,2942],{},[1132,3874,1325],{},[1391,3876,2143],{"stretchy":2126},[1391,3878,1393],{},[1401,3880,3828],{},[1136,3882,3883],{"encoding":1138},"P(y=1\\mid x) = 0.5",[1113,3885,3887,3911,3929,3950],{"className":3886,"ariaHidden":1143},[1142],[1113,3888,3890,3893,3896,3899,3902,3905,3908],{"className":3889},[1147],[1113,3891],{"className":3892,"style":2845},[1151],[1113,3894,2931],{"className":3895,"style":3030},[1156,1157],[1113,3897,2127],{"className":3898},[2236],[1113,3900,1356],{"className":3901,"style":1372},[1156,1157],[1113,3903],{"className":3904,"style":1478},[1477],[1113,3906,1393],{"className":3907},[1482],[1113,3909],{"className":3910,"style":1478},[1477],[1113,3912,3914,3917,3920,3923,3926],{"className":3913},[1147],[1113,3915],{"className":3916,"style":2845},[1151],[1113,3918,1413],{"className":3919},[1156],[1113,3921],{"className":3922,"style":1478},[1477],[1113,3924,2942],{"className":3925},[1482],[1113,3927],{"className":3928,"style":1478},[1477],[1113,3930,3932,3935,3938,3941,3944,3947],{"className":3931},[1147],[1113,3933],{"className":3934,"style":2845},[1151],[1113,3936,1325],{"className":3937},[1156,1157],[1113,3939,2143],{"className":3940},[2277],[1113,3942],{"className":3943,"style":1478},[1477],[1113,3945,1393],{"className":3946},[1482],[1113,3948],{"className":3949,"style":1478},[1477],[1113,3951,3953,3956],{"className":3952},[1147],[1113,3954],{"className":3955,"style":3840},[1151],[1113,3957,3828],{"className":3958},[1156],",等价于 ",[1113,3961,3963,3987],{"className":3962},[1116],[1113,3964,3966],{"className":3965},[1120],[1122,3967,3968],{"xmlns":1124},[1126,3969,3970,3984],{},[1129,3971,3972,3978,3980,3982],{},[2129,3973,3974,3976],{},[1132,3975,1325],{},[1132,3977,2136],{"mathvariant":2135},[1132,3979,1399],{},[1391,3981,1393],{},[1401,3983,1403],{},[1136,3985,3986],{"encoding":1138},"x^{\\top}\\beta = 0",[1113,3988,3990,4040],{"className":3989,"ariaHidden":1143},[1142],[1113,3991,3993,3996,4028,4031,4034,4037],{"className":3992},[1147],[1113,3994],{"className":3995,"style":2764},[1151],[1113,3997,3999,4002],{"className":3998},[1156],[1113,4000,1325],{"className":4001},[1156,1157],[1113,4003,4005],{"className":4004},[1503],[1113,4006,4008],{"className":4007},[1507],[1113,4009,4011],{"className":4010},[1512],[1113,4012,4014],{"className":4013,"style":2255},[1516],[1113,4015,4016,4019],{"style":2258},[1113,4017],{"className":4018,"style":1525},[1524],[1113,4020,4022],{"className":4021},[1529,1530,1531,1532],[1113,4023,4025],{"className":4024},[1156,1532],[1113,4026,2136],{"className":4027},[1156,1532],[1113,4029,1399],{"className":4030,"style":1499},[1156,1157],[1113,4032],{"className":4033,"style":1478},[1477],[1113,4035,1393],{"className":4036},[1482],[1113,4038],{"className":4039,"style":1478},[1477],[1113,4041,4043,4046],{"className":4042},[1147],[1113,4044],{"className":4045,"style":3840},[1151],[1113,4047,1403],{"className":4048},[1156],[1107,4050,4052],{"id":4051},"线性判别的适用性两种情况","线性判别的适用性:两种情况",[4054,4055,4056,4067],"ul",{},[4057,4058,4059,4062,4063,4066],"li",{},[1095,4060,4061],{},"情况一",":两类数据分别来自两个",[1095,4064,4065],{},"方差相同、均值不同","的高斯分布。此时,基于线性回归的判别准则基本上就是最优的——线性边界足够。",[4057,4068,4069,4072,4073,4076,4077,4080],{},[1095,4070,4071],{},"情况二",":两类数据分别来自一个",[1095,4074,4075],{},"由 10 个高斯分布混合而成","的复杂分布。此时数据结构远比一条直线复杂,基于线性回归的判别准则",[1095,4078,4079],{},"远远不够",",需要更灵活的非线性方法。",[1091,4082,4083],{},"这组对比说明了线性模型的局限:只有当类别边界本质上是线性(或近似线性)时,线性判别才好用。",[2689,4085],{},[1304,4087,4089],{"id":4088},"三最近邻方法knn","三、最近邻方法(KNN)",[1091,4091,4092,4095,4096,4099],{},[1095,4093,4094],{},"定义",":要预测一个样本属于哪一类,可以借助它周围",[1095,4097,4098],{},"相邻的样本","来判别——\"物以类聚\",邻居是什么类,它大概率也是什么类。",[1091,4101,4102,4105,4106,4134,4135,4165,4166,4255],{},[1095,4103,4104],{},"模型形式",":对样本 ",[1113,4107,4109,4122],{"className":4108},[1116],[1113,4110,4112],{"className":4111},[1120],[1122,4113,4114],{"xmlns":1124},[1126,4115,4116,4120],{},[1129,4117,4118],{},[1132,4119,1325],{},[1136,4121,1325],{"encoding":1138},[1113,4123,4125],{"className":4124,"ariaHidden":1143},[1142],[1113,4126,4128,4131],{"className":4127},[1147],[1113,4129],{"className":4130,"style":1337},[1151],[1113,4132,1325],{"className":4133},[1156,1157],",取它的 ",[1113,4136,4138,4152],{"className":4137},[1116],[1113,4139,4141],{"className":4140},[1120],[1122,4142,4143],{"xmlns":1124},[1126,4144,4145,4150],{},[1129,4146,4147],{},[1132,4148,4149],{},"k",[1136,4151,4149],{"encoding":1138},[1113,4153,4155],{"className":4154,"ariaHidden":1143},[1142],[1113,4156,4158,4161],{"className":4157},[1147],[1113,4159],{"className":4160,"style":2038},[1151],[1113,4162,4149],{"className":4163,"style":4164},[1156,1157],"margin-right:0.0315em;"," 个最近邻组成的邻域 ",[1113,4167,4169,4194],{"className":4168},[1116],[1113,4170,4172],{"className":4171},[1120],[1122,4173,4174],{"xmlns":1124},[1126,4175,4176,4191],{},[1129,4177,4178,4185,4187,4189],{},[1395,4179,4180,4183],{},[1132,4181,4182],{},"N",[1132,4184,4149],{},[1391,4186,2127],{"stretchy":2126},[1132,4188,1325],{},[1391,4190,2143],{"stretchy":2126},[1136,4192,4193],{"encoding":1138},"N_k(x)",[1113,4195,4197],{"className":4196,"ariaHidden":1143},[1142],[1113,4198,4200,4203,4246,4249,4252],{"className":4199},[1147],[1113,4201],{"className":4202,"style":2845},[1151],[1113,4204,4206,4210],{"className":4205},[1156],[1113,4207,4182],{"className":4208,"style":4209},[1156,1157],"margin-right:0.109em;",[1113,4211,4213],{"className":4212},[1503],[1113,4214,4216,4238],{"className":4215},[1507,1508],[1113,4217,4219,4235],{"className":4218},[1512],[1113,4220,4223],{"className":4221,"style":4222},[1516],"height:0.3361em;",[1113,4224,4226,4229],{"style":4225},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[1113,4227],{"className":4228,"style":1525},[1524],[1113,4230,4232],{"className":4231},[1529,1530,1531,1532],[1113,4233,4149],{"className":4234,"style":4164},[1156,1157,1532],[1113,4236,1540],{"className":4237},[1539],[1113,4239,4241],{"className":4240},[1512],[1113,4242,4244],{"className":4243,"style":1547},[1516],[1113,4245],{},[1113,4247,2127],{"className":4248},[2236],[1113,4250,1325],{"className":4251},[1156,1157],[1113,4253,2143],{"className":4254},[2277],",预测值为",[1091,4257,4258],{},[1113,4259,4261,4329],{"className":4260},[1116],[1113,4262,4264],{"className":4263},[1120],[1122,4265,4266],{"xmlns":1124},[1126,4267,4268,4326],{},[1129,4269,4270,4277,4279,4281,4283,4285,4291,4320],{},[2000,4271,4272,4275],{"accent":1143},[1132,4273,4274],{},"f",[1391,4276,2006],{},[1391,4278,2127],{"stretchy":2126},[1132,4280,1325],{},[1391,4282,2143],{"stretchy":2126},[1391,4284,1393],{},[2950,4286,4287,4289],{},[1401,4288,1413],{},[1132,4290,4149],{},[1395,4292,4293,4296],{},[1391,4294,4295],{},"∑",[1129,4297,4298,4305,4308,4314,4316,4318],{},[1395,4299,4300,4302],{},[1132,4301,1325],{},[1132,4303,4304],{},"i",[1391,4306,4307],{},"∈",[1395,4309,4310,4312],{},[1132,4311,4182],{},[1132,4313,4149],{},[1391,4315,2127],{"stretchy":2126},[1132,4317,1325],{},[1391,4319,2143],{"stretchy":2126},[1395,4321,4322,4324],{},[1132,4323,1356],{},[1132,4325,4304],{},[1136,4327,4328],{"encoding":1138},"\\hat{f}(x) = \\frac{1}{k}\\sum_{x_i \\in N_k(x)} y_i",[1113,4330,4332,4401],{"className":4331,"ariaHidden":1143},[1142],[1113,4333,4335,4339,4383,4386,4389,4392,4395,4398],{"className":4334},[1147],[1113,4336],{"className":4337,"style":4338},[1151],"height:1.2079em;vertical-align:-0.25em;",[1113,4340,4342],{"className":4341},[1156,2028],[1113,4343,4345,4375],{"className":4344},[1507,1508],[1113,4346,4348,4372],{"className":4347},[1512],[1113,4349,4351,4360],{"className":4350,"style":2184},[1516],[1113,4352,4353,4356],{"style":2041},[1113,4354],{"className":4355,"style":2045},[1524],[1113,4357,4274],{"className":4358,"style":4359},[1156,1157],"margin-right:0.1076em;",[1113,4361,4362,4365],{"style":2195},[1113,4363],{"className":4364,"style":2045},[1524],[1113,4366,4369],{"className":4367,"style":4368},[2057],"left:-0.0833em;",[1113,4370,2006],{"className":4371},[1156],[1113,4373,1540],{"className":4374},[1539],[1113,4376,4378],{"className":4377},[1512],[1113,4379,4381],{"className":4380,"style":2071},[1516],[1113,4382],{},[1113,4384,2127],{"className":4385},[2236],[1113,4387,1325],{"className":4388},[1156,1157],[1113,4390,2143],{"className":4391},[2277],[1113,4393],{"className":4394,"style":1478},[1477],[1113,4396,1393],{"className":4397},[1482],[1113,4399],{"className":4400,"style":1478},[1477],[1113,4402,4404,4408,4477,4480,4625,4628],{"className":4403},[1147],[1113,4405],{"className":4406,"style":4407},[1151],"height:1.3198em;vertical-align:-0.4747em;",[1113,4409,4411,4414,4474],{"className":4410},[1156],[1113,4412],{"className":4413},[2236,3098],[1113,4415,4417],{"className":4416},[2950],[1113,4418,4420,4465],{"className":4419},[1507,1508],[1113,4421,4423,4462],{"className":4422},[1512],[1113,4424,4426,4440,4448],{"className":4425,"style":3111},[1516],[1113,4427,4428,4431],{"style":3568},[1113,4429],{"className":4430,"style":2045},[1524],[1113,4432,4434],{"className":4433},[1529,1530,1531,1532],[1113,4435,4437],{"className":4436},[1156,1532],[1113,4438,4149],{"className":4439,"style":4164},[1156,1157,1532],[1113,4441,4442,4445],{"style":3204},[1113,4443],{"className":4444,"style":2045},[1524],[1113,4446],{"className":4447,"style":3212},[3211],[1113,4449,4450,4453],{"style":3215},[1113,4451],{"className":4452,"style":2045},[1524],[1113,4454,4456],{"className":4455},[1529,1530,1531,1532],[1113,4457,4459],{"className":4458},[1156,1532],[1113,4460,1413],{"className":4461},[1156,1532],[1113,4463,1540],{"className":4464},[1539],[1113,4466,4468],{"className":4467},[1512],[1113,4469,4472],{"className":4470,"style":4471},[1516],"height:0.345em;",[1113,4473],{},[1113,4475],{"className":4476},[2277,3098],[1113,4478],{"className":4479,"style":3546},[1477],[1113,4481,4483,4489],{"className":4482},[3542],[1113,4484,4295],{"className":4485,"style":4488},[3542,4486,4487],"op-symbol","small-op","position:relative;top:0em;",[1113,4490,4492],{"className":4491},[1503],[1113,4493,4495,4616],{"className":4494},[1507,1508],[1113,4496,4498,4613],{"className":4497},[1512],[1113,4499,4502],{"className":4500,"style":4501},[1516],"height:0.2253em;",[1113,4503,4505,4508],{"style":4504},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1113,4506],{"className":4507,"style":1525},[1524],[1113,4509,4511],{"className":4510},[1529,1530,1531,1532],[1113,4512,4514,4558,4561,4604,4607,4610],{"className":4513},[1156,1532],[1113,4515,4517,4520],{"className":4516},[1156,1532],[1113,4518,1325],{"className":4519},[1156,1157,1532],[1113,4521,4523],{"className":4522},[1503],[1113,4524,4526,4549],{"className":4525},[1507,1508],[1113,4527,4529,4546],{"className":4528},[1512],[1113,4530,4533],{"className":4531,"style":4532},[1516],"height:0.3281em;",[1113,4534,4536,4540],{"style":4535},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[1113,4537],{"className":4538,"style":4539},[1524],"height:2.5em;",[1113,4541,4543],{"className":4542},[1529,3159,3160,1532],[1113,4544,4304],{"className":4545},[1156,1157,1532],[1113,4547,1540],{"className":4548},[1539],[1113,4550,4552],{"className":4551},[1512],[1113,4553,4556],{"className":4554,"style":4555},[1516],"height:0.143em;",[1113,4557],{},[1113,4559,4307],{"className":4560},[1482,1532],[1113,4562,4564,4567],{"className":4563},[1156,1532],[1113,4565,4182],{"className":4566,"style":4209},[1156,1157,1532],[1113,4568,4570],{"className":4569},[1503],[1113,4571,4573,4595],{"className":4572},[1507,1508],[1113,4574,4576,4592],{"className":4575},[1512],[1113,4577,4580],{"className":4578,"style":4579},[1516],"height:0.3448em;",[1113,4581,4583,4586],{"style":4582},"top:-2.3488em;margin-left:-0.109em;margin-right:0.0714em;",[1113,4584],{"className":4585,"style":4539},[1524],[1113,4587,4589],{"className":4588},[1529,3159,3160,1532],[1113,4590,4149],{"className":4591,"style":4164},[1156,1157,1532],[1113,4593,1540],{"className":4594},[1539],[1113,4596,4598],{"className":4597},[1512],[1113,4599,4602],{"className":4600,"style":4601},[1516],"height:0.1512em;",[1113,4603],{},[1113,4605,2127],{"className":4606},[2236,1532],[1113,4608,1325],{"className":4609},[1156,1157,1532],[1113,4611,2143],{"className":4612},[2277,1532],[1113,4614,1540],{"className":4615},[1539],[1113,4617,4619],{"className":4618},[1512],[1113,4620,4623],{"className":4621,"style":4622},[1516],"height:0.4747em;",[1113,4624],{},[1113,4626],{"className":4627,"style":3546},[1477],[1113,4629,4631,4634],{"className":4630},[1156],[1113,4632,1356],{"className":4633,"style":1372},[1156,1157],[1113,4635,4637],{"className":4636},[1503],[1113,4638,4640,4661],{"className":4639},[1507,1508],[1113,4641,4643,4658],{"className":4642},[1512],[1113,4644,4647],{"className":4645,"style":4646},[1516],"height:0.3117em;",[1113,4648,4649,4652],{"style":2540},[1113,4650],{"className":4651,"style":1525},[1524],[1113,4653,4655],{"className":4654},[1529,1530,1531,1532],[1113,4656,4304],{"className":4657},[1156,1157,1532],[1113,4659,1540],{"className":4660},[1539],[1113,4662,4664],{"className":4663},[1512],[1113,4665,4667],{"className":4666,"style":1547},[1516],[1113,4668],{},[1091,4670,4671,4674,4675,4703,4704,4732,4733,4761],{},[1095,4672,4673],{},"判别标准",":如果在 ",[1113,4676,4678,4691],{"className":4677},[1116],[1113,4679,4681],{"className":4680},[1120],[1122,4682,4683],{"xmlns":1124},[1126,4684,4685,4689],{},[1129,4686,4687],{},[1132,4688,1325],{},[1136,4690,1325],{"encoding":1138},[1113,4692,4694],{"className":4693,"ariaHidden":1143},[1142],[1113,4695,4697,4700],{"className":4696},[1147],[1113,4698],{"className":4699,"style":1337},[1151],[1113,4701,1325],{"className":4702},[1156,1157]," 的 ",[1113,4705,4707,4720],{"className":4706},[1116],[1113,4708,4710],{"className":4709},[1120],[1122,4711,4712],{"xmlns":1124},[1126,4713,4714,4718],{},[1129,4715,4716],{},[1132,4717,4149],{},[1136,4719,4149],{"encoding":1138},[1113,4721,4723],{"className":4722,"ariaHidden":1143},[1142],[1113,4724,4726,4729],{"className":4725},[1147],[1113,4727],{"className":4728,"style":2038},[1151],[1113,4730,4149],{"className":4731,"style":4164},[1156,1157]," 个近邻中,多数样本属于某一特定类,就把 ",[1113,4734,4736,4749],{"className":4735},[1116],[1113,4737,4739],{"className":4738},[1120],[1122,4740,4741],{"xmlns":1124},[1126,4742,4743,4747],{},[1129,4744,4745],{},[1132,4746,1325],{},[1136,4748,1325],{"encoding":1138},[1113,4750,4752],{"className":4751,"ariaHidden":1143},[1142],[1113,4753,4755,4758],{"className":4754},[1147],[1113,4756],{"className":4757,"style":1337},[1151],[1113,4759,1325],{"className":4760},[1156,1157]," 也判为这些近邻里占多数的那一类(多数表决)。",[1091,4763,4764,4767,4770,4771,4799,4800,4828],{},[1095,4765,4766],{},"决策边界",[4768,4769],"knn",{}," 的决策边界是不规则的、随数据分布而变的分段边界,不像线性回归那样是一条直线;",[1113,4772,4774,4787],{"className":4773},[1116],[1113,4775,4777],{"className":4776},[1120],[1122,4778,4779],{"xmlns":1124},[1126,4780,4781,4785],{},[1129,4782,4783],{},[1132,4784,4149],{},[1136,4786,4149],{"encoding":1138},[1113,4788,4790],{"className":4789,"ariaHidden":1143},[1142],[1113,4791,4793,4796],{"className":4792},[1147],[1113,4794],{"className":4795,"style":2038},[1151],[1113,4797,4149],{"className":4798,"style":4164},[1156,1157]," 越小边界越弯曲(易过拟合),",[1113,4801,4803,4816],{"className":4802},[1116],[1113,4804,4806],{"className":4805},[1120],[1122,4807,4808],{"xmlns":1124},[1126,4809,4810,4814],{},[1129,4811,4812],{},[1132,4813,4149],{},[1136,4815,4149],{"encoding":1138},[1113,4817,4819],{"className":4818,"ariaHidden":1143},[1142],[1113,4820,4822,4825],{"className":4821},[1147],[1113,4823],{"className":4824,"style":2038},[1151],[1113,4826,4149],{"className":4827,"style":4164},[1156,1157]," 越大边界越平滑。",[2689,4830],{},[1304,4832,4834],{"id":4833},"四期望预测误差与贝叶斯准则","四、期望预测误差与贝叶斯准则",[1091,4836,4837,4838,4841,4842,4845],{},"在给定损失函数下,什么样的预测函数误差最小,那个最优预测就叫",[1095,4839,4840],{},"贝叶斯准则",",对应的最小误差叫",[1095,4843,4844],{},"贝叶斯误差(风险)","\n最小化期望风险所求得的理论最优预测规则即为贝叶斯准则（回归时猜均值，分类时猜最大概率），其对应的理论下界误差称为贝叶斯误差，构成了所有实际学习算法性能的渐近极限。",[1107,4847,4848],{"id":4848},"平方损失函数下",[1091,4850,4851,4854,4855,3717],{},[1095,4852,4853],{},"平方损失",":",[1113,4856,4858,4912],{"className":4857},[1116],[1113,4859,4861],{"className":4860},[1120],[1122,4862,4863],{"xmlns":1124},[1126,4864,4865,4909],{},[1129,4866,4867,4870,4872,4874,4877,4879,4881,4883,4885,4887,4889,4891,4893,4895,4897,4899,4901,4903],{},[1132,4868,4869],{},"L",[1391,4871,2127],{"stretchy":2126},[1132,4873,1356],{},[1391,4875,4876],{"separator":1143},",",[1132,4878,4274],{},[1391,4880,2127],{"stretchy":2126},[1132,4882,1325],{},[1391,4884,2143],{"stretchy":2126},[1391,4886,2143],{"stretchy":2126},[1391,4888,1393],{},[1391,4890,2127],{"stretchy":2126},[1132,4892,1356],{},[1391,4894,2148],{},[1132,4896,4274],{},[1391,4898,2127],{"stretchy":2126},[1132,4900,1325],{},[1391,4902,2143],{"stretchy":2126},[2129,4904,4905,4907],{},[1391,4906,2143],{"stretchy":2126},[1401,4908,1428],{},[1136,4910,4911],{"encoding":1138},"L(y, f(x)) = (y - f(x))^2",[1113,4913,4915,4959,4980],{"className":4914,"ariaHidden":1143},[1142],[1113,4916,4918,4921,4924,4927,4930,4934,4937,4940,4943,4946,4950,4953,4956],{"className":4917},[1147],[1113,4919],{"className":4920,"style":2845},[1151],[1113,4922,4869],{"className":4923},[1156,1157],[1113,4925,2127],{"className":4926},[2236],[1113,4928,1356],{"className":4929,"style":1372},[1156,1157],[1113,4931,4876],{"className":4932},[4933],"mpunct",[1113,4935],{"className":4936,"style":3546},[1477],[1113,4938,4274],{"className":4939,"style":4359},[1156,1157],[1113,4941,2127],{"className":4942},[2236],[1113,4944,1325],{"className":4945},[1156,1157],[1113,4947,4949],{"className":4948},[2277],"))",[1113,4951],{"className":4952,"style":1478},[1477],[1113,4954,1393],{"className":4955},[1482],[1113,4957],{"className":4958,"style":1478},[1477],[1113,4960,4962,4965,4968,4971,4974,4977],{"className":4961},[1147],[1113,4963],{"className":4964,"style":2845},[1151],[1113,4966,2127],{"className":4967},[2236],[1113,4969,1356],{"className":4970,"style":1372},[1156,1157],[1113,4972],{"className":4973,"style":1193},[1477],[1113,4975,2148],{"className":4976},[1556],[1113,4978],{"className":4979,"style":1193},[1477],[1113,4981,4983,4987,4990,4993,4996,4999],{"className":4982},[1147],[1113,4984],{"className":4985,"style":4986},[1151],"height:1.0641em;vertical-align:-0.25em;",[1113,4988,4274],{"className":4989,"style":4359},[1156,1157],[1113,4991,2127],{"className":4992},[2236],[1113,4994,1325],{"className":4995},[1156,1157],[1113,4997,2143],{"className":4998},[2277],[1113,5000,5002,5005],{"className":5001},[2277],[1113,5003,2143],{"className":5004},[2277],[1113,5006,5008],{"className":5007},[1503],[1113,5009,5011],{"className":5010},[1507],[1113,5012,5014],{"className":5013},[1512],[1113,5015,5017],{"className":5016,"style":2293},[1516],[1113,5018,5019,5022],{"style":2258},[1113,5020],{"className":5021,"style":1525},[1524],[1113,5023,5025],{"className":5024},[1529,1530,1531,1532],[1113,5026,1428],{"className":5027},[1156,1532],[1091,5029,5030,4854],{},[1095,5031,5032],{},"期望预测误差(EPE)",[1091,5034,5035],{},[1113,5036,5038,5091],{"className":5037},[1116],[1113,5039,5041],{"className":5040},[1120],[1122,5042,5043],{"xmlns":1124},[1126,5044,5045,5088],{},[1129,5046,5047,5050,5052,5054,5056,5058,5061,5065,5067,5069,5071,5073,5075,5077,5079,5085],{},[2366,5048,5049],{},"EPE",[1391,5051,2127],{"stretchy":2126},[1132,5053,4274],{},[1391,5055,2143],{"stretchy":2126},[1391,5057,1393],{},[1132,5059,5060],{},"E",[1391,5062,5064],{"fence":2126,"stretchy":1143,"minsize":5063,"maxsize":5063},"1.2em","[",[1391,5066,2127],{"stretchy":2126},[1132,5068,1356],{},[1391,5070,2148],{},[1132,5072,4274],{},[1391,5074,2127],{"stretchy":2126},[1132,5076,1325],{},[1391,5078,2143],{"stretchy":2126},[2129,5080,5081,5083],{},[1391,5082,2143],{"stretchy":2126},[1401,5084,1428],{},[1391,5086,5087],{"fence":2126,"stretchy":1143,"minsize":5063,"maxsize":5063},"]",[1136,5089,5090],{"encoding":1138},"\\text{EPE}(f) = E\\big[(y - f(x))^2\\big]",[1113,5092,5094,5124,5157],{"className":5093,"ariaHidden":1143},[1142],[1113,5095,5097,5100,5106,5109,5112,5115,5118,5121],{"className":5096},[1147],[1113,5098],{"className":5099,"style":2845},[1151],[1113,5101,5103],{"className":5102},[1156,2414],[1113,5104,5049],{"className":5105},[1156],[1113,5107,2127],{"className":5108},[2236],[1113,5110,4274],{"className":5111,"style":4359},[1156,1157],[1113,5113,2143],{"className":5114},[2277],[1113,5116],{"className":5117,"style":1478},[1477],[1113,5119,1393],{"className":5120},[1482],[1113,5122],{"className":5123,"style":1478},[1477],[1113,5125,5127,5131,5135,5142,5145,5148,5151,5154],{"className":5126},[1147],[1113,5128],{"className":5129,"style":5130},[1151],"height:1.2em;vertical-align:-0.35em;",[1113,5132,5060],{"className":5133,"style":5134},[1156,1157],"margin-right:0.0576em;",[1113,5136,5138],{"className":5137},[1156],[1113,5139,5064],{"className":5140},[5141,3160],"delimsizing",[1113,5143,2127],{"className":5144},[2236],[1113,5146,1356],{"className":5147,"style":1372},[1156,1157],[1113,5149],{"className":5150,"style":1193},[1477],[1113,5152,2148],{"className":5153},[1556],[1113,5155],{"className":5156,"style":1193},[1477],[1113,5158,5160,5163,5166,5169,5172,5175,5204],{"className":5159},[1147],[1113,5161],{"className":5162,"style":5130},[1151],[1113,5164,4274],{"className":5165,"style":4359},[1156,1157],[1113,5167,2127],{"className":5168},[2236],[1113,5170,1325],{"className":5171},[1156,1157],[1113,5173,2143],{"className":5174},[2277],[1113,5176,5178,5181],{"className":5177},[2277],[1113,5179,2143],{"className":5180},[2277],[1113,5182,5184],{"className":5183},[1503],[1113,5185,5187],{"className":5186},[1507],[1113,5188,5190],{"className":5189},[1512],[1113,5191,5193],{"className":5192,"style":2293},[1516],[1113,5194,5195,5198],{"style":2258},[1113,5196],{"className":5197,"style":1525},[1524],[1113,5199,5201],{"className":5200},[1529,1530,1531,1532],[1113,5202,1428],{"className":5203},[1156,1532],[1113,5205,5207],{"className":5206},[1156],[1113,5208,5087],{"className":5209},[5141,3160],[1091,5211,5212,5213,5216],{},"它可以分解成",[1095,5214,5215],{},"贝叶斯误差 + 模型误差","两部分。最小化 EPE,得到的最优预测函数是",[1091,5218,5219],{},[1113,5220,5222,5266],{"className":5221},[1116],[1113,5223,5225],{"className":5224},[1120],[1122,5226,5227],{"xmlns":1124},[1126,5228,5229,5263],{},[1129,5230,5231,5238,5240,5242,5244,5246,5248,5250,5253,5255,5257,5259,5261],{},[2129,5232,5233,5235],{},[1132,5234,4274],{},[1391,5236,5237],{},"∗",[1391,5239,2127],{"stretchy":2126},[1132,5241,1325],{},[1391,5243,2143],{"stretchy":2126},[1391,5245,1393],{},[1132,5247,5060],{},[1391,5249,5064],{"stretchy":2126},[2366,5251,5252],{}," ",[1132,5254,1356],{},[1391,5256,2942],{},[1132,5258,1325],{},[2366,5260,5252],{},[1391,5262,5087],{"stretchy":2126},[1136,5264,5265],{"encoding":1138},"f^*(x) = E[\\,y \\mid x\\,]",[1113,5267,5269,5323,5350],{"className":5268,"ariaHidden":1143},[1142],[1113,5270,5272,5275,5305,5308,5311,5314,5317,5320],{"className":5271},[1147],[1113,5273],{"className":5274,"style":2845},[1151],[1113,5276,5278,5281],{"className":5277},[1156],[1113,5279,4274],{"className":5280,"style":4359},[1156,1157],[1113,5282,5284],{"className":5283},[1503],[1113,5285,5287],{"className":5286},[1507],[1113,5288,5290],{"className":5289},[1512],[1113,5291,5294],{"className":5292,"style":5293},[1516],"height:0.6887em;",[1113,5295,5296,5299],{"style":2258},[1113,5297],{"className":5298,"style":1525},[1524],[1113,5300,5302],{"className":5301},[1529,1530,1531,1532],[1113,5303,5237],{"className":5304},[1556,1532],[1113,5306,2127],{"className":5307},[2236],[1113,5309,1325],{"className":5310},[1156,1157],[1113,5312,2143],{"className":5313},[2277],[1113,5315],{"className":5316,"style":1478},[1477],[1113,5318,1393],{"className":5319},[1482],[1113,5321],{"className":5322,"style":1478},[1477],[1113,5324,5326,5329,5332,5335,5338,5341,5344,5347],{"className":5325},[1147],[1113,5327],{"className":5328,"style":2845},[1151],[1113,5330,5060],{"className":5331,"style":5134},[1156,1157],[1113,5333,5064],{"className":5334},[2236],[1113,5336],{"className":5337,"style":3546},[1477],[1113,5339,1356],{"className":5340,"style":1372},[1156,1157],[1113,5342],{"className":5343,"style":1478},[1477],[1113,5345,2942],{"className":5346},[1482],[1113,5348],{"className":5349,"style":1478},[1477],[1113,5351,5353,5356,5359,5362],{"className":5352},[1147],[1113,5354],{"className":5355,"style":2845},[1151],[1113,5357,1325],{"className":5358},[1156,1157],[1113,5360],{"className":5361,"style":3546},[1477],[1113,5363,5087],{"className":5364},[2277],[1091,5366,5367,5368,5396,5397,1980,5425,5428,5429,5495,5496,5498,5499,5502],{},"也就是给定 ",[1113,5369,5371,5384],{"className":5370},[1116],[1113,5372,5374],{"className":5373},[1120],[1122,5375,5376],{"xmlns":1124},[1126,5377,5378,5382],{},[1129,5379,5380],{},[1132,5381,1325],{},[1136,5383,1325],{"encoding":1138},[1113,5385,5387],{"className":5386,"ariaHidden":1143},[1142],[1113,5388,5390,5393],{"className":5389},[1147],[1113,5391],{"className":5392,"style":1337},[1151],[1113,5394,1325],{"className":5395},[1156,1157]," 时,",[1113,5398,5400,5413],{"className":5399},[1116],[1113,5401,5403],{"className":5402},[1120],[1122,5404,5405],{"xmlns":1124},[1126,5406,5407,5411],{},[1129,5408,5409],{},[1132,5410,1356],{},[1136,5412,1356],{"encoding":1138},[1113,5414,5416],{"className":5415,"ariaHidden":1143},[1142],[1113,5417,5419,5422],{"className":5418},[1147],[1113,5420],{"className":5421,"style":1368},[1151],[1113,5423,1356],{"className":5424,"style":1372},[1156,1157],[1095,5426,5427],{},"条件期望","。在平方损失下,这个条件期望 ",[1113,5430,5432,5456],{"className":5431},[1116],[1113,5433,5435],{"className":5434},[1120],[1122,5436,5437],{"xmlns":1124},[1126,5438,5439,5453],{},[1129,5440,5441,5443,5445,5447,5449,5451],{},[1132,5442,5060],{},[1391,5444,5064],{"stretchy":2126},[1132,5446,1356],{},[1391,5448,2942],{},[1132,5450,1325],{},[1391,5452,5087],{"stretchy":2126},[1136,5454,5455],{"encoding":1138},"E[y\\mid x]",[1113,5457,5459,5483],{"className":5458,"ariaHidden":1143},[1142],[1113,5460,5462,5465,5468,5471,5474,5477,5480],{"className":5461},[1147],[1113,5463],{"className":5464,"style":2845},[1151],[1113,5466,5060],{"className":5467,"style":5134},[1156,1157],[1113,5469,5064],{"className":5470},[2236],[1113,5472,1356],{"className":5473,"style":1372},[1156,1157],[1113,5475],{"className":5476,"style":1478},[1477],[1113,5478,2942],{"className":5479},[1482],[1113,5481],{"className":5482,"style":1478},[1477],[1113,5484,5486,5489,5492],{"className":5485},[1147],[1113,5487],{"className":5488,"style":2845},[1151],[1113,5490,1325],{"className":5491},[1156,1157],[1113,5493,5087],{"className":5494},[2277]," 就是",[1095,5497,4840],{},",它带来的误差就是",[1095,5500,5501],{},"贝叶斯误差",",即任何模型所能达到的最小误差。",[1107,5504,5506],{"id":5505},"_0-1-损失函数下","0-1 损失函数下",[1091,5508,5509,5512,5513,3717],{},[1095,5510,5511],{},"0-1 损失",":预测对了损失为 0,预测错了损失为 1,即 ",[1113,5514,5516,5571],{"className":5515},[1116],[1113,5517,5519],{"className":5518},[1120],[1122,5520,5521],{"xmlns":1124},[1126,5522,5523,5568],{},[1129,5524,5525,5527,5529,5531,5533,5535,5537,5539,5541,5543,5545,5547,5549,5551,5553,5556,5558,5560,5562,5564,5566],{},[1132,5526,4869],{},[1391,5528,2127],{"stretchy":2126},[1132,5530,1356],{},[1391,5532,4876],{"separator":1143},[1132,5534,4274],{},[1391,5536,2127],{"stretchy":2126},[1132,5538,1325],{},[1391,5540,2143],{"stretchy":2126},[1391,5542,2143],{"stretchy":2126},[1391,5544,1393],{},[1401,5546,1413],{"mathvariant":1209},[1391,5548,5064],{"stretchy":2126},[2366,5550,5252],{},[1132,5552,1356],{},[1391,5554,5555],{"mathvariant":2135},"≠",[1132,5557,4274],{},[1391,5559,2127],{"stretchy":2126},[1132,5561,1325],{},[1391,5563,2143],{"stretchy":2126},[2366,5565,5252],{},[1391,5567,5087],{"stretchy":2126},[1136,5569,5570],{"encoding":1138},"L(y, f(x)) = \\mathbb{1}[\\,y \\ne f(x)\\,]",[1113,5572,5574,5616,5683],{"className":5573,"ariaHidden":1143},[1142],[1113,5575,5577,5580,5583,5586,5589,5592,5595,5598,5601,5604,5607,5610,5613],{"className":5576},[1147],[1113,5578],{"className":5579,"style":2845},[1151],[1113,5581,4869],{"className":5582},[1156,1157],[1113,5584,2127],{"className":5585},[2236],[1113,5587,1356],{"className":5588,"style":1372},[1156,1157],[1113,5590,4876],{"className":5591},[4933],[1113,5593],{"className":5594,"style":3546},[1477],[1113,5596,4274],{"className":5597,"style":4359},[1156,1157],[1113,5599,2127],{"className":5600},[2236],[1113,5602,1325],{"className":5603},[1156,1157],[1113,5605,4949],{"className":5606},[2277],[1113,5608],{"className":5609,"style":1478},[1477],[1113,5611,1393],{"className":5612},[1482],[1113,5614],{"className":5615,"style":1478},[1477],[1113,5617,5619,5622,5625,5628,5631,5634,5637,5680],{"className":5618},[1147],[1113,5620],{"className":5621,"style":2845},[1151],[1113,5623,1413],{"className":5624},[1156],[1113,5626,5064],{"className":5627},[2236],[1113,5629],{"className":5630,"style":3546},[1477],[1113,5632,1356],{"className":5633,"style":1372},[1156,1157],[1113,5635],{"className":5636,"style":1478},[1477],[1113,5638,5640,5673,5677],{"className":5639},[1482],[1113,5641,5643],{"className":5642},[1482],[1113,5644,5647],{"className":5645},[1156,5646],"vbox",[1113,5648,5651],{"className":5649},[5650],"thinbox",[1113,5652,5655,5658,5669],{"className":5653},[5654],"rlap",[1113,5656],{"className":5657,"style":1492},[1151],[1113,5659,5662],{"className":5660},[5661],"inner",[1113,5663,5665],{"className":5664},[1156],[1113,5666,5668],{"className":5667},[1482],"",[1113,5670],{"className":5671},[5672],"fix",[1113,5674],{"className":5675},[1477,5676],"nobreak",[1113,5678,1393],{"className":5679},[1482],[1113,5681],{"className":5682,"style":1478},[1477],[1113,5684,5686,5689,5692,5695,5698,5701,5704],{"className":5685},[1147],[1113,5687],{"className":5688,"style":2845},[1151],[1113,5690,4274],{"className":5691,"style":4359},[1156,1157],[1113,5693,2127],{"className":5694},[2236],[1113,5696,1325],{"className":5697},[1156,1157],[1113,5699,2143],{"className":5700},[2277],[1113,5702],{"className":5703,"style":3546},[1477],[1113,5705,5087],{"className":5706},[2277],[1091,5708,5709,5712],{},[1095,5710,5711],{},"泛化误差"," 就是分类错误率。最小化它,得到的最优分类器是选后验概率最大的类:",[1091,5714,5715],{},[1113,5716,5718,5777],{"className":5717},[1116],[1113,5719,5721],{"className":5720},[1120],[1122,5722,5723],{"xmlns":1124},[1126,5724,5725,5774],{},[1129,5726,5727,5733,5735,5737,5739,5741,5744,5746,5758,5760,5762,5764,5766,5768,5770,5772],{},[2129,5728,5729,5731],{},[1132,5730,4274],{},[1391,5732,5237],{},[1391,5734,2127],{"stretchy":2126},[1132,5736,1325],{},[1391,5738,2143],{"stretchy":2126},[1391,5740,1393],{},[1132,5742,5743],{},"arg",[1391,5745,3477],{},[1395,5747,5748,5755],{},[1129,5749,5750,5753],{},[1132,5751,5752],{},"max",[1391,5754,3477],{},[1132,5756,5757],{},"c",[1132,5759,2931],{},[1391,5761,2127],{"stretchy":2126},[1132,5763,1356],{},[1391,5765,1393],{},[1132,5767,5757],{},[1391,5769,2942],{},[1132,5771,1325],{},[1391,5773,2143],{"stretchy":2126},[1136,5775,5776],{"encoding":1138},"f^*(x) = \\arg\\max_{c} P(y = c \\mid x)",[1113,5778,5780,5833,5914,5932],{"className":5779,"ariaHidden":1143},[1142],[1113,5781,5783,5786,5815,5818,5821,5824,5827,5830],{"className":5782},[1147],[1113,5784],{"className":5785,"style":2845},[1151],[1113,5787,5789,5792],{"className":5788},[1156],[1113,5790,4274],{"className":5791,"style":4359},[1156,1157],[1113,5793,5795],{"className":5794},[1503],[1113,5796,5798],{"className":5797},[1507],[1113,5799,5801],{"className":5800},[1512],[1113,5802,5804],{"className":5803,"style":5293},[1516],[1113,5805,5806,5809],{"style":2258},[1113,5807],{"className":5808,"style":1525},[1524],[1113,5810,5812],{"className":5811},[1529,1530,1531,1532],[1113,5813,5237],{"className":5814},[1556,1532],[1113,5816,2127],{"className":5817},[2236],[1113,5819,1325],{"className":5820},[1156,1157],[1113,5822,2143],{"className":5823},[2277],[1113,5825],{"className":5826,"style":1478},[1477],[1113,5828,1393],{"className":5829},[1482],[1113,5831],{"className":5832,"style":1478},[1477],[1113,5834,5836,5839,5846,5849,5893,5896,5899,5902,5905,5908,5911],{"className":5835},[1147],[1113,5837],{"className":5838,"style":2845},[1151],[1113,5840,5842,5843],{"className":5841},[3542],"ar",[1113,5844,2716],{"style":5845},"margin-right:0.0139em;",[1113,5847],{"className":5848,"style":3546},[1477],[1113,5850,5852,5855],{"className":5851},[3542],[1113,5853,5752],{"className":5854},[3542],[1113,5856,5858],{"className":5857},[1503],[1113,5859,5861,5885],{"className":5860},[1507,1508],[1113,5862,5864,5882],{"className":5863},[1512],[1113,5865,5867],{"className":5866,"style":1796},[1516],[1113,5868,5870,5873],{"style":5869},"top:-2.55em;margin-right:0.05em;",[1113,5871],{"className":5872,"style":1525},[1524],[1113,5874,5876],{"className":5875},[1529,1530,1531,1532],[1113,5877,5879],{"className":5878},[1156,1532],[1113,5880,5757],{"className":5881},[1156,1157,1532],[1113,5883,1540],{"className":5884},[1539],[1113,5886,5888],{"className":5887},[1512],[1113,5889,5891],{"className":5890,"style":1547},[1516],[1113,5892],{},[1113,5894],{"className":5895,"style":3546},[1477],[1113,5897,2931],{"className":5898,"style":3030},[1156,1157],[1113,5900,2127],{"className":5901},[2236],[1113,5903,1356],{"className":5904,"style":1372},[1156,1157],[1113,5906],{"className":5907,"style":1478},[1477],[1113,5909,1393],{"className":5910},[1482],[1113,5912],{"className":5913,"style":1478},[1477],[1113,5915,5917,5920,5923,5926,5929],{"className":5916},[1147],[1113,5918],{"className":5919,"style":2845},[1151],[1113,5921,5757],{"className":5922},[1156,1157],[1113,5924],{"className":5925,"style":1478},[1477],[1113,5927,2942],{"className":5928},[1482],[1113,5930],{"className":5931,"style":1478},[1477],[1113,5933,5935,5938,5941],{"className":5934},[1147],[1113,5936],{"className":5937,"style":2845},[1151],[1113,5939,1325],{"className":5940},[1156,1157],[1113,5942,2143],{"className":5943},[2277],[1107,5945,5947],{"id":5946},"_0-1-损失下的二分类问题","0-1 损失下的二分类问题",[1091,5949,5950,5951,6028],{},"在二分类(",[1113,5952,5954,5982],{"className":5953},[1116],[1113,5955,5957],{"className":5956},[1120],[1122,5958,5959],{"xmlns":1124},[1126,5960,5961,5979],{},[1129,5962,5963,5965,5967,5970,5972,5974,5976],{},[1132,5964,1356],{},[1391,5966,4307],{},[1391,5968,5969],{"stretchy":2126},"{",[1401,5971,1403],{},[1391,5973,4876],{"separator":1143},[1401,5975,1413],{},[1391,5977,5978],{"stretchy":2126},"}",[1136,5980,5981],{"encoding":1138},"y \\in \\{0,1\\}",[1113,5983,5985,6004],{"className":5984,"ariaHidden":1143},[1142],[1113,5986,5988,5992,5995,5998,6001],{"className":5987},[1147],[1113,5989],{"className":5990,"style":5991},[1151],"height:0.7335em;vertical-align:-0.1944em;",[1113,5993,1356],{"className":5994,"style":1372},[1156,1157],[1113,5996],{"className":5997,"style":1478},[1477],[1113,5999,4307],{"className":6000},[1482],[1113,6002],{"className":6003,"style":1478},[1477],[1113,6005,6007,6010,6013,6016,6019,6022,6025],{"className":6006},[1147],[1113,6008],{"className":6009,"style":2845},[1151],[1113,6011,5969],{"className":6012},[2236],[1113,6014,1403],{"className":6015},[1156],[1113,6017,4876],{"className":6018},[4933],[1113,6020],{"className":6021,"style":3546},[1477],[1113,6023,1413],{"className":6024},[1156],[1113,6026,5978],{"className":6027},[2277],")下,期望预测误差的最小化归结为一个简单的比较:",[6030,6031,6032,6235],"ol",{},[4057,6033,6034,6035,6205,6206,6234],{},"如果 ",[1113,6036,6038,6085],{"className":6037},[1116],[1113,6039,6041],{"className":6040},[1120],[1122,6042,6043],{"xmlns":1124},[1126,6044,6045,6082],{},[1129,6046,6047,6049,6051,6053,6055,6057,6059,6061,6063,6066,6068,6070,6072,6074,6076,6078,6080],{},[1132,6048,2931],{},[1391,6050,2127],{"stretchy":2126},[1132,6052,1356],{},[1391,6054,1393],{},[1401,6056,1413],{},[1391,6058,2942],{},[1132,6060,1325],{},[1391,6062,2143],{"stretchy":2126},[1391,6064,6065],{},">",[1132,6067,2931],{},[1391,6069,2127],{"stretchy":2126},[1132,6071,1356],{},[1391,6073,1393],{},[1401,6075,1403],{},[1391,6077,2942],{},[1132,6079,1325],{},[1391,6081,2143],{"stretchy":2126},[1136,6083,6084],{"encoding":1138},"P(y=1\\mid x) > P(y=0\\mid x)",[1113,6086,6088,6112,6130,6151,6175,6193],{"className":6087,"ariaHidden":1143},[1142],[1113,6089,6091,6094,6097,6100,6103,6106,6109],{"className":6090},[1147],[1113,6092],{"className":6093,"style":2845},[1151],[1113,6095,2931],{"className":6096,"style":3030},[1156,1157],[1113,6098,2127],{"className":6099},[2236],[1113,6101,1356],{"className":6102,"style":1372},[1156,1157],[1113,6104],{"className":6105,"style":1478},[1477],[1113,6107,1393],{"className":6108},[1482],[1113,6110],{"className":6111,"style":1478},[1477],[1113,6113,6115,6118,6121,6124,6127],{"className":6114},[1147],[1113,6116],{"className":6117,"style":2845},[1151],[1113,6119,1413],{"className":6120},[1156],[1113,6122],{"className":6123,"style":1478},[1477],[1113,6125,2942],{"className":6126},[1482],[1113,6128],{"className":6129,"style":1478},[1477],[1113,6131,6133,6136,6139,6142,6145,6148],{"className":6132},[1147],[1113,6134],{"className":6135,"style":2845},[1151],[1113,6137,1325],{"className":6138},[1156,1157],[1113,6140,2143],{"className":6141},[2277],[1113,6143],{"className":6144,"style":1478},[1477],[1113,6146,6065],{"className":6147},[1482],[1113,6149],{"className":6150,"style":1478},[1477],[1113,6152,6154,6157,6160,6163,6166,6169,6172],{"className":6153},[1147],[1113,6155],{"className":6156,"style":2845},[1151],[1113,6158,2931],{"className":6159,"style":3030},[1156,1157],[1113,6161,2127],{"className":6162},[2236],[1113,6164,1356],{"className":6165,"style":1372},[1156,1157],[1113,6167],{"className":6168,"style":1478},[1477],[1113,6170,1393],{"className":6171},[1482],[1113,6173],{"className":6174,"style":1478},[1477],[1113,6176,6178,6181,6184,6187,6190],{"className":6177},[1147],[1113,6179],{"className":6180,"style":2845},[1151],[1113,6182,1403],{"className":6183},[1156],[1113,6185],{"className":6186,"style":1478},[1477],[1113,6188,2942],{"className":6189},[1482],[1113,6191],{"className":6192,"style":1478},[1477],[1113,6194,6196,6199,6202],{"className":6195},[1147],[1113,6197],{"className":6198,"style":2845},[1151],[1113,6200,1325],{"className":6201},[1156,1157],[1113,6203,2143],{"className":6204},[2277],",则判 ",[1113,6207,6209,6222],{"className":6208},[1116],[1113,6210,6212],{"className":6211},[1120],[1122,6213,6214],{"xmlns":1124},[1126,6215,6216,6220],{},[1129,6217,6218],{},[1132,6219,1325],{},[1136,6221,1325],{"encoding":1138},[1113,6223,6225],{"className":6224,"ariaHidden":1143},[1142],[1113,6226,6228,6231],{"className":6227},[1147],[1113,6229],{"className":6230,"style":1337},[1151],[1113,6232,1325],{"className":6233},[1156,1157]," 为第 1 类;",[4057,6236,6034,6237,6205,6407,6435],{},[1113,6238,6240,6287],{"className":6239},[1116],[1113,6241,6243],{"className":6242},[1120],[1122,6244,6245],{"xmlns":1124},[1126,6246,6247,6284],{},[1129,6248,6249,6251,6253,6255,6257,6259,6261,6263,6265,6268,6270,6272,6274,6276,6278,6280,6282],{},[1132,6250,2931],{},[1391,6252,2127],{"stretchy":2126},[1132,6254,1356],{},[1391,6256,1393],{},[1401,6258,1413],{},[1391,6260,2942],{},[1132,6262,1325],{},[1391,6264,2143],{"stretchy":2126},[1391,6266,6267],{},"\u003C",[1132,6269,2931],{},[1391,6271,2127],{"stretchy":2126},[1132,6273,1356],{},[1391,6275,1393],{},[1401,6277,1403],{},[1391,6279,2942],{},[1132,6281,1325],{},[1391,6283,2143],{"stretchy":2126},[1136,6285,6286],{"encoding":1138},"P(y=1\\mid x) \u003C P(y=0\\mid x)",[1113,6288,6290,6314,6332,6353,6377,6395],{"className":6289,"ariaHidden":1143},[1142],[1113,6291,6293,6296,6299,6302,6305,6308,6311],{"className":6292},[1147],[1113,6294],{"className":6295,"style":2845},[1151],[1113,6297,2931],{"className":6298,"style":3030},[1156,1157],[1113,6300,2127],{"className":6301},[2236],[1113,6303,1356],{"className":6304,"style":1372},[1156,1157],[1113,6306],{"className":6307,"style":1478},[1477],[1113,6309,1393],{"className":6310},[1482],[1113,6312],{"className":6313,"style":1478},[1477],[1113,6315,6317,6320,6323,6326,6329],{"className":6316},[1147],[1113,6318],{"className":6319,"style":2845},[1151],[1113,6321,1413],{"className":6322},[1156],[1113,6324],{"className":6325,"style":1478},[1477],[1113,6327,2942],{"className":6328},[1482],[1113,6330],{"className":6331,"style":1478},[1477],[1113,6333,6335,6338,6341,6344,6347,6350],{"className":6334},[1147],[1113,6336],{"className":6337,"style":2845},[1151],[1113,6339,1325],{"className":6340},[1156,1157],[1113,6342,2143],{"className":6343},[2277],[1113,6345],{"className":6346,"style":1478},[1477],[1113,6348,6267],{"className":6349},[1482],[1113,6351],{"className":6352,"style":1478},[1477],[1113,6354,6356,6359,6362,6365,6368,6371,6374],{"className":6355},[1147],[1113,6357],{"className":6358,"style":2845},[1151],[1113,6360,2931],{"className":6361,"style":3030},[1156,1157],[1113,6363,2127],{"className":6364},[2236],[1113,6366,1356],{"className":6367,"style":1372},[1156,1157],[1113,6369],{"className":6370,"style":1478},[1477],[1113,6372,1393],{"className":6373},[1482],[1113,6375],{"className":6376,"style":1478},[1477],[1113,6378,6380,6383,6386,6389,6392],{"className":6379},[1147],[1113,6381],{"className":6382,"style":2845},[1151],[1113,6384,1403],{"className":6385},[1156],[1113,6387],{"className":6388,"style":1478},[1477],[1113,6390,2942],{"className":6391},[1482],[1113,6393],{"className":6394,"style":1478},[1477],[1113,6396,6398,6401,6404],{"className":6397},[1147],[1113,6399],{"className":6400,"style":2845},[1151],[1113,6402,1325],{"className":6403},[1156,1157],[1113,6405,2143],{"className":6406},[2277],[1113,6408,6410,6423],{"className":6409},[1116],[1113,6411,6413],{"className":6412},[1120],[1122,6414,6415],{"xmlns":1124},[1126,6416,6417,6421],{},[1129,6418,6419],{},[1132,6420,1325],{},[1136,6422,1325],{"encoding":1138},[1113,6424,6426],{"className":6425,"ariaHidden":1143},[1142],[1113,6427,6429,6432],{"className":6428},[1147],[1113,6430],{"className":6431,"style":1337},[1151],[1113,6433,1325],{"className":6434},[1156,1157]," 为第 0 类。",[1091,6437,6438,6439,6549,6550,6552,6553,3717],{},"于是最优判别就是\"哪个后验概率大就判哪类\",等价于以 ",[1113,6440,6442,6474],{"className":6441},[1116],[1113,6443,6445],{"className":6444},[1120],[1122,6446,6447],{"xmlns":1124},[1126,6448,6449,6471],{},[1129,6450,6451,6453,6455,6457,6459,6461,6463,6465,6467,6469],{},[1132,6452,2931],{},[1391,6454,2127],{"stretchy":2126},[1132,6456,1356],{},[1391,6458,1393],{},[1401,6460,1413],{},[1391,6462,2942],{},[1132,6464,1325],{},[1391,6466,2143],{"stretchy":2126},[1391,6468,1393],{},[1401,6470,3828],{},[1136,6472,6473],{"encoding":1138},"P(y=1\\mid x)=0.5",[1113,6475,6477,6501,6519,6540],{"className":6476,"ariaHidden":1143},[1142],[1113,6478,6480,6483,6486,6489,6492,6495,6498],{"className":6479},[1147],[1113,6481],{"className":6482,"style":2845},[1151],[1113,6484,2931],{"className":6485,"style":3030},[1156,1157],[1113,6487,2127],{"className":6488},[2236],[1113,6490,1356],{"className":6491,"style":1372},[1156,1157],[1113,6493],{"className":6494,"style":1478},[1477],[1113,6496,1393],{"className":6497},[1482],[1113,6499],{"className":6500,"style":1478},[1477],[1113,6502,6504,6507,6510,6513,6516],{"className":6503},[1147],[1113,6505],{"className":6506,"style":2845},[1151],[1113,6508,1413],{"className":6509},[1156],[1113,6511],{"className":6512,"style":1478},[1477],[1113,6514,2942],{"className":6515},[1482],[1113,6517],{"className":6518,"style":1478},[1477],[1113,6520,6522,6525,6528,6531,6534,6537],{"className":6521},[1147],[1113,6523],{"className":6524,"style":2845},[1151],[1113,6526,1325],{"className":6527},[1156,1157],[1113,6529,2143],{"className":6530},[2277],[1113,6532],{"className":6533,"style":1478},[1477],[1113,6535,1393],{"className":6536},[1482],[1113,6538],{"className":6539,"style":1478},[1477],[1113,6541,6543,6546],{"className":6542},[1147],[1113,6544],{"className":6545,"style":3840},[1151],[1113,6547,3828],{"className":6548},[1156]," 为界。这里的最优规则又叫",[1095,6551,4840],{},",它对应的最小错误率被称为",[1095,6554,6555],{},"贝叶斯风险",[2689,6557],{},[1304,6559,6561],{"id":6560},"五支持向量机svm","五、支持向量机(SVM)",[1091,6563,6564],{},"SVM（支持向量机）是一种追求最大间隔的几何分类器，它不仅要求将不同类别的样本正确分开，更致力于在所有可能的分界超平面中，找到一个距离两侧最近样本（即“支持向量”）最远的那一个；当数据线性不可分时，它通过引入Hinge损失和正则系数 C 构建“软间隔”来容忍部分违规，并借助拉格朗日对偶求解，使得最终的模型仅由少数关键的支持向量线性组合决定，从而在保证强泛化能力的同时实现了极其高效的稀疏表达。",[1107,6566,6568],{"id":6567},"标准-svm硬间隔","标准 SVM(硬间隔)",[1091,6570,6571,6572,6575],{},"SVM 的核心思想是找一个",[1095,6573,6574],{},"间隔最大","的分隔超平面",[1091,6577,6578,4854,6581,3717],{},[1095,6579,6580],{},"分隔超平面",[1113,6582,6584,6614],{"className":6583},[1116],[1113,6585,6587],{"className":6586},[1120],[1122,6588,6589],{"xmlns":1124},[1126,6590,6591,6611],{},[1129,6592,6593,6600,6602,6604,6607,6609],{},[2129,6594,6595,6598],{},[1132,6596,6597],{},"w",[1132,6599,2136],{"mathvariant":2135},[1132,6601,1325],{},[1391,6603,1406],{},[1132,6605,6606],{},"b",[1391,6608,1393],{},[1401,6610,1403],{},[1136,6612,6613],{"encoding":1138},"w^{\\top}x + b = 0",[1113,6615,6617,6669,6687],{"className":6616,"ariaHidden":1143},[1142],[1113,6618,6620,6624,6657,6660,6663,6666],{"className":6619},[1147],[1113,6621],{"className":6622,"style":6623},[1151],"height:0.9324em;vertical-align:-0.0833em;",[1113,6625,6627,6631],{"className":6626},[1156],[1113,6628,6597],{"className":6629,"style":6630},[1156,1157],"margin-right:0.0269em;",[1113,6632,6634],{"className":6633},[1503],[1113,6635,6637],{"className":6636},[1507],[1113,6638,6640],{"className":6639},[1512],[1113,6641,6643],{"className":6642,"style":2255},[1516],[1113,6644,6645,6648],{"style":2258},[1113,6646],{"className":6647,"style":1525},[1524],[1113,6649,6651],{"className":6650},[1529,1530,1531,1532],[1113,6652,6654],{"className":6653},[1156,1532],[1113,6655,2136],{"className":6656},[1156,1532],[1113,6658,1325],{"className":6659},[1156,1157],[1113,6661],{"className":6662,"style":1193},[1477],[1113,6664,1406],{"className":6665},[1556],[1113,6667],{"className":6668,"style":1193},[1477],[1113,6670,6672,6675,6678,6681,6684],{"className":6671},[1147],[1113,6673],{"className":6674,"style":2038},[1151],[1113,6676,6606],{"className":6677},[1156,1157],[1113,6679],{"className":6680,"style":1478},[1477],[1113,6682,1393],{"className":6683},[1482],[1113,6685],{"className":6686,"style":1478},[1477],[1113,6688,6690,6693],{"className":6689},[1147],[1113,6691],{"className":6692,"style":3840},[1151],[1113,6694,1403],{"className":6695},[1156],[1091,6697,6698,4854,6701,3717],{},[1095,6699,6700],{},"决策函数",[1113,6702,6704,6745],{"className":6703},[1116],[1113,6705,6707],{"className":6706},[1120],[1122,6708,6709],{"xmlns":1124},[1126,6710,6711,6742],{},[1129,6712,6713,6715,6717,6719,6721,6723,6726,6728,6734,6736,6738,6740],{},[1132,6714,4274],{},[1391,6716,2127],{"stretchy":2126},[1132,6718,1325],{},[1391,6720,2143],{"stretchy":2126},[1391,6722,1393],{},[2366,6724,6725],{},"sign",[1391,6727,2127],{"stretchy":2126},[2129,6729,6730,6732],{},[1132,6731,6597],{},[1132,6733,2136],{"mathvariant":2135},[1132,6735,1325],{},[1391,6737,1406],{},[1132,6739,6606],{},[1391,6741,2143],{"stretchy":2126},[1136,6743,6744],{"encoding":1138},"f(x) = \\text{sign}(w^{\\top}x + b)",[1113,6746,6748,6775,6834],{"className":6747,"ariaHidden":1143},[1142],[1113,6749,6751,6754,6757,6760,6763,6766,6769,6772],{"className":6750},[1147],[1113,6752],{"className":6753,"style":2845},[1151],[1113,6755,4274],{"className":6756,"style":4359},[1156,1157],[1113,6758,2127],{"className":6759},[2236],[1113,6761,1325],{"className":6762},[1156,1157],[1113,6764,2143],{"className":6765},[2277],[1113,6767],{"className":6768,"style":1478},[1477],[1113,6770,1393],{"className":6771},[1482],[1113,6773],{"className":6774,"style":1478},[1477],[1113,6776,6778,6781,6787,6790,6822,6825,6828,6831],{"className":6777},[1147],[1113,6779],{"className":6780,"style":2232},[1151],[1113,6782,6784],{"className":6783},[1156,2414],[1113,6785,6725],{"className":6786},[1156],[1113,6788,2127],{"className":6789},[2236],[1113,6791,6793,6796],{"className":6792},[1156],[1113,6794,6597],{"className":6795,"style":6630},[1156,1157],[1113,6797,6799],{"className":6798},[1503],[1113,6800,6802],{"className":6801},[1507],[1113,6803,6805],{"className":6804},[1512],[1113,6806,6808],{"className":6807,"style":2255},[1516],[1113,6809,6810,6813],{"style":2258},[1113,6811],{"className":6812,"style":1525},[1524],[1113,6814,6816],{"className":6815},[1529,1530,1531,1532],[1113,6817,6819],{"className":6818},[1156,1532],[1113,6820,2136],{"className":6821},[1156,1532],[1113,6823,1325],{"className":6824},[1156,1157],[1113,6826],{"className":6827,"style":1193},[1477],[1113,6829,1406],{"className":6830},[1556],[1113,6832],{"className":6833,"style":1193},[1477],[1113,6835,6837,6840,6843],{"className":6836},[1147],[1113,6838],{"className":6839,"style":2845},[1151],[1113,6841,6606],{"className":6842},[1156,1157],[1113,6844,2143],{"className":6845},[2277],[1091,6847,6848,6851,6852,6892],{},[1095,6849,6850],{},"优化问题","(最大化间隔,等价于在正确分类约束下最小化 ",[1113,6853,6855,6874],{"className":6854},[1116],[1113,6856,6858],{"className":6857},[1120],[1122,6859,6860],{"xmlns":1124},[1126,6861,6862,6871],{},[1129,6863,6864,6867,6869],{},[1132,6865,6866],{"mathvariant":2135},"∥",[1132,6868,6597],{},[1132,6870,6866],{"mathvariant":2135},[1136,6872,6873],{"encoding":1138},"\\|w\\|",[1113,6875,6877],{"className":6876,"ariaHidden":1143},[1142],[1113,6878,6880,6883,6886,6889],{"className":6879},[1147],[1113,6881],{"className":6882,"style":2845},[1151],[1113,6884,6866],{"className":6885},[1156],[1113,6887,6597],{"className":6888,"style":6630},[1156,1157],[1113,6890,6866],{"className":6891},[1156],"):",[1091,6894,6895],{},[1113,6896,6898,7031],{"className":6897},[1116],[1113,6899,6901],{"className":6900},[1120],[1122,6902,6903],{"xmlns":1124},[1126,6904,6905,7028],{},[1129,6906,6907,6923,6926,6938,6941,6944,6946,6963,6965,6971,6973,6975,6981,6983,6986,6988,6994,6996,7002,7008,7010,7012,7014,7017,7019,7021,7023,7026],{},[1395,6908,6909,6915],{},[1129,6910,6911,6913],{},[1132,6912,5752],{},[1391,6914,3477],{},[1129,6916,6917,6919,6921],{},[1132,6918,6597],{},[1391,6920,4876],{"separator":1143},[1132,6922,6606],{},[2366,6924,6925],{}," ",[2950,6927,6928,6930],{},[1401,6929,1428],{},[1129,6931,6932,6934,6936],{},[1132,6933,6866],{"mathvariant":2135},[1132,6935,6597],{},[1132,6937,6866],{"mathvariant":2135},[1477,6939],{"width":6940},"1em",[1391,6942,6943],{},"⟺",[1477,6945],{"width":6940},[1395,6947,6948,6955],{},[1129,6949,6950,6953],{},[1132,6951,6952],{},"min",[1391,6954,3477],{},[1129,6956,6957,6959,6961],{},[1132,6958,6597],{},[1391,6960,4876],{"separator":1143},[1132,6962,6606],{},[2366,6964,6925],{},[2950,6966,6967,6969],{},[1401,6968,1413],{},[1401,6970,1428],{},[1132,6972,6866],{"mathvariant":2135},[1132,6974,6597],{},[2129,6976,6977,6979],{},[1132,6978,6866],{"mathvariant":2135},[1401,6980,1428],{},[1477,6982],{"width":6940},[2366,6984,6985],{},"s.t.",[1477,6987],{"width":6940},[1395,6989,6990,6992],{},[1132,6991,1356],{},[1132,6993,4304],{},[1391,6995,2127],{"stretchy":2126},[2129,6997,6998,7000],{},[1132,6999,6597],{},[1132,7001,2136],{"mathvariant":2135},[1395,7003,7004,7006],{},[1132,7005,1325],{},[1132,7007,4304],{},[1391,7009,1406],{},[1132,7011,6606],{},[1391,7013,2143],{"stretchy":2126},[1391,7015,7016],{},"≥",[1401,7018,1413],{},[1391,7020,4876],{"separator":1143},[2366,7022,6925],{},[1132,7024,7025],{"mathvariant":2135},"∀",[1132,7027,4304],{},[1136,7029,7030],{"encoding":1138},"\\max_{w,b}\\ \\frac{2}{\\|w\\|} \\quad\\Longleftrightarrow\\quad \\min_{w,b}\\ \\frac{1}{2}\\|w\\|^2 \\quad \\text{s.t.}\\quad y_i(w^{\\top}x_i + b) \\ge 1,\\ \\forall 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损失","来度量违反程度:",[1091,7760,7761],{},[1113,7762,7764,7831],{"className":7763},[1116],[1113,7765,7767],{"className":7766},[1120],[1122,7768,7769],{"xmlns":1124},[1126,7770,7771,7828],{},[1129,7772,7773,7780,7782,7784,7786,7788,7790,7792,7794,7796,7798,7800,7802,7804,7806,7808,7810,7812,7814,7816,7818,7820,7822,7824,7826],{},[1395,7774,7775,7777],{},[1132,7776,4869],{},[2366,7778,7779],{},"hinge",[1391,7781,2127],{"stretchy":2126},[1132,7783,1356],{},[1391,7785,4876],{"separator":1143},[1132,7787,4274],{},[1391,7789,2127],{"stretchy":2126},[1132,7791,1325],{},[1391,7793,2143],{"stretchy":2126},[1391,7795,2143],{"stretchy":2126},[1391,7797,1393],{},[1132,7799,5752],{},[1391,7801,3477],{},[1391,7803,2127],{"fence":2126,"stretchy":1143,"minsize":5063,"maxsize":5063},[1401,7805,1403],{},[1391,7807,4876],{"separator":1143},[2366,7809,6925],{},[1401,7811,1413],{},[1391,7813,2148],{},[1132,7815,1356],{},[2366,7817,5252],{},[1132,7819,4274],{},[1391,7821,2127],{"stretchy":2126},[1132,7823,1325],{},[1391,7825,2143],{"stretchy":2126},[1391,7827,2143],{"fence":2126,"stretchy":1143,"minsize":5063,"maxsize":5063},[1136,7829,7830],{"encoding":1138},"L_{\\text{hinge}}(y, f(x)) = \\max\\big(0,\\ 1 - y\\,f(x)\\big)",[1113,7832,7834,7920,7962],{"className":7833,"ariaHidden":1143},[1142],[1113,7835,7837,7841,7887,7890,7893,7896,7899,7902,7905,7908,7911,7914,7917],{"className":7836},[1147],[1113,7838],{"className":7839,"style":7840},[1151],"height:1.0361em;vertical-align:-0.2861em;",[1113,7842,7844,7847],{"className":7843},[1156],[1113,7845,4869],{"className":7846},[1156,1157],[1113,7848,7850],{"className":7849},[1503],[1113,7851,7853,7879],{"className":7852},[1507,1508],[1113,7854,7856,7876],{"className":7855},[1512],[1113,7857,7859],{"className":7858,"style":4222},[1516],[1113,7860,7861,7864],{"style":1626},[1113,7862],{"className":7863,"style":1525},[1524],[1113,7865,7867],{"className":7866},[1529,1530,1531,1532],[1113,7868,7870],{"className":7869},[1156,1532],[1113,7871,7873],{"className":7872},[1156,2414,1532],[1113,7874,7779],{"className":7875},[1156,1532],[1113,7877,1540],{"className":7878},[1539],[1113,7880,7882],{"className":7881},[1512],[1113,7883,7885],{"className":7884,"style":1817},[1516],[1113,7886],{},[1113,7888,2127],{"className":7889},[2236],[1113,7891,1356],{"className":7892,"style":1372},[1156,1157],[1113,7894,4876],{"className":7895},[4933],[1113,7897],{"className":7898,"style":3546},[1477],[1113,7900,4274],{"className":7901,"style":4359},[1156,1157],[1113,7903,2127],{"className":7904},[2236],[1113,7906,1325],{"className":7907},[1156,1157],[1113,7909,4949],{"className":7910},[2277],[1113,7912],{"className":7913,"style":1478},[1477],[1113,7915,1393],{"className":7916},[1482],[1113,7918],{"className":7919,"style":1478},[1477],[1113,7921,7923,7926,7929,7932,7938,7941,7944,7947,7950,7953,7956,7959],{"className":7922},[1147],[1113,7924],{"className":7925,"style":5130},[1151],[1113,7927,5752],{"className":7928},[3542],[1113,7930],{"className":7931,"style":3546},[1477],[1113,7933,7935],{"className":7934},[1156],[1113,7936,2127],{"className":7937},[5141,3160],[1113,7939,1403],{"className":7940},[1156],[1113,7942,4876],{"className":7943},[4933],[1113,7945,6925],{"className":7946},[1477],[1113,7948],{"className":7949,"style":3546},[1477],[1113,7951,1413],{"className":7952},[1156],[1113,7954],{"className":7955,"style":1193},[1477],[1113,7957,2148],{"className":7958},[1556],[1113,7960],{"className":7961,"style":1193},[1477],[1113,7963,7965,7968,7971,7974,7977,7980,7983,7986],{"className":7964},[1147],[1113,7966],{"className":7967,"style":5130},[1151],[1113,7969,1356],{"className":7970,"style":1372},[1156,1157],[1113,7972],{"className":7973,"style":3546},[1477],[1113,7975,4274],{"className":7976,"style":4359},[1156,1157],[1113,7978,2127],{"className":7979},[2236],[1113,7981,1325],{"className":7982},[1156,1157],[1113,7984,2143],{"className":7985},[2277],[1113,7987,7989],{"className":7988},[1156],[1113,7990,2143],{"className":7991},[5141,3160],[1091,7993,7994,7996,7997,8068],{},[1095,7995,6850],{},"在 Hinge 损失基础上加一个控制复杂度的正则项。若采用线性分隔超平面、正则项用 ",[1113,7998,8000,8018],{"className":7999},[1116],[1113,8001,8003],{"className":8002},[1120],[1122,8004,8005],{"xmlns":1124},[1126,8006,8007,8015],{},[1129,8008,8009],{},[1395,8010,8011,8013],{},[1132,8012,4869],{},[1401,8014,1428],{},[1136,8016,8017],{"encoding":1138},"L_2",[1113,8019,8021],{"className":8020,"ariaHidden":1143},[1142],[1113,8022,8024,8028],{"className":8023},[1147],[1113,8025],{"className":8026,"style":8027},[1151],"height:0.8333em;vertical-align:-0.15em;",[1113,8029,8031,8034],{"className":8030},[1156],[1113,8032,4869],{"className":8033},[1156,1157],[1113,8035,8037],{"className":8036},[1503],[1113,8038,8040,8060],{"className":8039},[1507,1508],[1113,8041,8043,8057],{"className":8042},[1512],[1113,8044,8046],{"className":8045,"style":1517},[1516],[1113,8047,8048,8051],{"style":1626},[1113,8049],{"className":8050,"style":1525},[1524],[1113,8052,8054],{"className":8053},[1529,1530,1531,1532],[1113,8055,1428],{"className":8056},[1156,1532],[1113,8058,1540],{"className":8059},[1539],[1113,8061,8063],{"className":8062},[1512],[1113,8064,8066],{"className":8065,"style":1547},[1516],[1113,8067],{}," 正则,优化问题可写成",[1091,8070,8071],{},[1113,8072,8074,8183],{"className":8073},[1116],[1113,8075,8077],{"className":8076},[1120],[1122,8078,8079],{"xmlns":1124},[1126,8080,8081,8180],{},[1129,8082,8083,8099,8101,8107,8109,8111,8117,8119,8121,8136,8138,8140,8142,8144,8146,8148,8150,8152,8158,8160,8166,8172,8174,8176,8178],{},[1395,8084,8085,8091],{},[1129,8086,8087,8089],{},[1132,8088,6952],{},[1391,8090,3477],{},[1129,8092,8093,8095,8097],{},[1132,8094,6597],{},[1391,8096,4876],{"separator":1143},[1132,8098,6606],{},[2366,8100,6925],{},[2950,8102,8103,8105],{},[1401,8104,1413],{},[1401,8106,1428],{},[1132,8108,6866],{"mathvariant":2135},[1132,8110,6597],{},[2129,8112,8113,8115],{},[1132,8114,6866],{"mathvariant":2135},[1401,8116,1428],{},[1391,8118,1406],{},[1132,8120,1279],{},[2455,8122,8123,8125,8133],{},[1391,8124,4295],{},[1129,8126,8127,8129,8131],{},[1132,8128,4304],{},[1391,8130,1393],{},[1401,8132,1413],{},[1132,8134,8135],{},"n",[1132,8137,5752],{},[1391,8139,3477],{},[1391,8141,2127],{"fence":2126,"stretchy":1143,"minsize":5063,"maxsize":5063},[1401,8143,1403],{},[1391,8145,4876],{"separator":1143},[2366,8147,6925],{},[1401,8149,1413],{},[1391,8151,2148],{},[1395,8153,8154,8156],{},[1132,8155,1356],{},[1132,8157,4304],{},[1391,8159,2127],{"stretchy":2126},[2129,8161,8162,8164],{},[1132,8163,6597],{},[1132,8165,2136],{"mathvariant":2135},[1395,8167,8168,8170],{},[1132,8169,1325],{},[1132,8171,4304],{},[1391,8173,1406],{},[1132,8175,6606],{},[1391,8177,2143],{"stretchy":2126},[1391,8179,2143],{"fence":2126,"stretchy":1143,"minsize":5063,"maxsize":5063},[1136,8181,8182],{"encoding":1138},"\\min_{w,b}\\ \\frac{1}{2}\\|w\\|^2 + C\\sum_{i=1}^{n}\\max\\big(0,\\ 1 - y_i(w^{\\top}x_i + b)\\big)",[1113,8184,8186,8360,8477,8607],{"className":8185,"ariaHidden":1143},[1142],[1113,8187,8189,8193,8242,8245,8248,8316,8319,8322,8351,8354,8357],{"className":8188},[1147],[1113,8190],{"className":8191,"style":8192},[1151],"height:1.1901em;vertical-align:-0.345em;",[1113,8194,8196,8199],{"className":8195},[3542],[1113,8197,6952],{"className":8198},[3542],[1113,8200,8202],{"className":8201},[1503],[1113,8203,8205,8234],{"className":8204},[1507,1508],[1113,8206,8208,8231],{"className":8207},[1512],[1113,8209,8211],{"className":8210,"style":4222},[1516],[1113,8212,8213,8216],{"style":5869},[1113,8214],{"className":8215,"style":1525},[1524],[1113,8217,8219],{"className":8218},[1529,1530,1531,1532],[1113,8220,8222,8225,8228],{"className":8221},[1156,1532],[1113,8223,6597],{"className":8224,"style":6630},[1156,1157,1532],[1113,8226,4876],{"className":8227},[4933,1532],[1113,8229,6606],{"className":8230},[1156,1157,1532],[1113,8232,1540],{"className":8233},[1539],[1113,8235,8237],{"className":8236},[1512],[1113,8238,8240],{"className":8239,"style":1817},[1516],[1113,8241],{},[1113,8243,6925],{"className":8244},[1477],[1113,8246],{"className":8247,"style":3546},[1477],[1113,8249,8251,8254,8313],{"className":8250},[1156],[1113,8252],{"className":8253},[2236,3098],[1113,8255,8257],{"className":8256},[2950],[1113,8258,8260,8305],{"className":8259},[1507,1508],[1113,8261,8263,8302],{"className":8262},[1512],[1113,8264,8266,8280,8288],{"className":8265,"style":3111},[1516],[1113,8267,8268,8271],{"style":3568},[1113,8269],{"className":8270,"style":2045},[1524],[1113,8272,8274],{"className":8273},[1529,1530,1531,1532],[1113,8275,8277],{"className":8276},[1156,1532],[1113,8278,1428],{"className":8279},[1156,1532],[1113,8281,8282,8285],{"style":3204},[1113,8283],{"className":8284,"style":2045},[1524],[1113,8286],{"className":8287,"style":3212},[3211],[1113,8289,8290,8293],{"style":3215},[1113,8291],{"className":8292,"style":2045},[1524],[1113,8294,8296],{"className":8295},[1529,1530,1531,1532],[1113,8297,8299],{"className":8298},[1156,1532],[1113,8300,1413],{"className":8301},[1156,1532],[1113,8303,1540],{"className":8304},[1539],[1113,8306,8308],{"className":8307},[1512],[1113,8309,8311],{"className":8310,"style":4471},[1516],[1113,8312],{},[1113,8314],{"className":8315},[2277,3098],[1113,8317,6866],{"className":8318},[1156],[1113,8320,6597],{"className":8321,"style":6630},[1156,1157],[1113,8323,8325,8328],{"className":8324},[1156],[1113,8326,6866],{"className":8327},[1156],[1113,8329,8331],{"className":8330},[1503],[1113,8332,8334],{"className":8333},[1507],[1113,8335,8337],{"className":8336},[1512],[1113,8338,8340],{"className":8339,"style":2293},[1516],[1113,8341,8342,8345],{"style":2258},[1113,8343],{"className":8344,"style":1525},[1524],[1113,8346,8348],{"className":8347},[1529,1530,1531,1532],[1113,8349,1428],{"className":8350},[1156,1532],[1113,8352],{"className":8353,"style":1193},[1477],[1113,8355,1406],{"className":8356},[1556],[1113,8358],{"className":8359,"style":1193},[1477],[1113,8361,8363,8366,8369,8372,8438,8441,8444,8447,8453,8456,8459,8462,8465,8468,8471,8474],{"className":8362},[1147],[1113,8364],{"className":8365,"style":5130},[1151],[1113,8367,1279],{"className":8368,"style":1294},[1156,1157],[1113,8370],{"className":8371,"style":3546},[1477],[1113,8373,8375,8378],{"className":8374},[3542],[1113,8376,4295],{"className":8377,"style":4488},[3542,4486,4487],[1113,8379,8381],{"className":8380},[1503],[1113,8382,8384,8429],{"className":8383},[1507,1508],[1113,8385,8387,8426],{"className":8386},[1512],[1113,8388,8391,8411],{"className":8389,"style":8390},[1516],"height:0.8043em;",[1113,8392,8393,8396],{"style":4504},[1113,8394],{"className":8395,"style":1525},[1524],[1113,8397,8399],{"className":8398},[1529,1530,1531,1532],[1113,8400,8402,8405,8408],{"className":8401},[1156,1532],[1113,8403,4304],{"className":8404},[1156,1157,1532],[1113,8406,1393],{"className":8407},[1482,1532],[1113,8409,1413],{"className":8410},[1156,1532],[1113,8412,8414,8417],{"style":8413},"top:-3.2029em;margin-right:0.05em;",[1113,8415],{"className":8416,"style":1525},[1524],[1113,8418,8420],{"className":8419},[1529,1530,1531,1532],[1113,8421,8423],{"className":8422},[1156,1532],[1113,8424,8135],{"className":8425},[1156,1157,1532],[1113,8427,1540],{"className":8428},[1539],[1113,8430,8432],{"className":8431},[1512],[1113,8433,8436],{"className":8434,"style":8435},[1516],"height:0.2997em;",[1113,8437],{},[1113,8439],{"className":8440,"style":3546},[1477],[1113,8442,5752],{"className":8443},[3542],[1113,8445],{"className":8446,"style":3546},[1477],[1113,8448,8450],{"className":8449},[1156],[1113,8451,2127],{"className":8452},[5141,3160],[1113,8454,1403],{"className":8455},[1156],[1113,8457,4876],{"className":8458},[4933],[1113,8460,6925],{"className":8461},[1477],[1113,8463],{"className":8464,"style":3546},[1477],[1113,8466,1413],{"className":8467},[1156],[1113,8469],{"className":8470,"style":1193},[1477],[1113,8472,2148],{"class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",[1113,8629,8631,8644],{"className":8630},[1116],[1113,8632,8634],{"className":8633},[1120],[1122,8635,8636],{"xmlns":1124},[1126,8637,8638,8642],{},[1129,8639,8640],{},[1132,8641,1279],{},[1136,8643,1279],{"encoding":1138},[1113,8645,8647],{"className":8646,"ariaHidden":1143},[1142],[1113,8648,8650,8653],{"className":8649},[1147],[1113,8651],{"className":8652,"style":1152},[1151],[1113,8654,1279],{"className":8655,"style":1294},[1156,1157]," 是正则系数,权衡\"间隔大小\"与\"分类错误\"。",[1091,8658,8659,8660,6892],{},"把这个无约束问题转化为标准型(引入松弛变量 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,[1113,9911,2148],{"className":9912},[1556],[1113,9914],{"className":9915,"style":1193},[1477],[1113,9917,9919,9922,9962,9965,10006,10012,10052,10055,10087,10127,10130,10133],{"className":9918},[1147],[1113,9920],{"className":9921,"style":5130},[1151],[1113,9923,9925,9928],{"className":9924},[3542],[1113,9926,4295],{"className":9927,"style":4488},[3542,4486,4487],[1113,9929,9931],{"className":9930},[1503],[1113,9932,9934,9954],{"className":9933},[1507,1508],[1113,9935,9937,9951],{"className":9936},[1512],[1113,9938,9940],{"className":9939,"style":9841},[1516],[1113,9941,9942,9945],{"style":4504},[1113,9943],{"className":9944,"style":1525},[1524],[1113,9946,9948],{"className":9947},[1529,1530,1531,1532],[1113,9949,4304],{"className":9950},[1156,1157,1532],[1113,9952,1540],{"className":9953},[1539],[1113,9955,9957],{"className":9956},[1512],[1113,9958,9960],{"className":9959,"style":8435},[1516],[1113,9961],{},[1113,9963],{"className":9964,"style":3546},[1477],[1113,9966,9968,9971],{"className":9967},[1156],[1113,9969,9503],{"className":9970,"style":9670},[1156,1157],[1113,9972,9974],{"className":9973},[1503],[1113,9975,9977,9998],{"className":9976},[1507,1508],[1113,9978,9980,9995],{"className":9979},[1512],[1113,9981,9983],{"className":9982,"style":4646},[1516],[1113,9984,9986,9989],{"style":9985},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[1113,9987],{"className":9988,"style":1525},[1524],[1113,9990,9992],{"className":9991},[1529,1530,1531,1532],[1113,9993,4304],{"className":9994},[1156,1157,1532],[1113,9996,1540],{"className":9997},[1539],[1113,9999,10001],{"className":10000},[1512],[1113,10002,10004],{"className":10003,"style":1547},[1516],[1113,10005],{},[1113,10007,10009],{"className":10008},[1156],[1113,10010,5064],{"className":10011},[5141,3160],[1113,10013,10015,10018],{"className":10014},[1156],[1113,10016,1356],{"className":10017,"style":1372},[1156,1157],[1113,10019,10021],{"className":10020},[1503],[1113,10022,10024,10044],{"className":10023},[1507,1508],[1113,10025,10027,10041],{"className":10026},[1512],[1113,10028,10030],{"className":10029,"style":4646},[1516],[1113,10031,10032,10035],{"style":2540},[1113,10033],{"className":10034,"style":1525},[1524],[1113,10036,10038],{"className":10037},[1529,1530,1531,1532],[1113,10039,4304],{"className":10040},[1156,1157,1532],[1113,10042,1540],{"className":10043},[1539],[1113,10045,10047],{"className":10046},[1512],[1113,10048,10050],{"className":10049,"style":1547},[1516],[1113,10051],{},[1113,10053,2127],{"className":10054},[2236],[1113,10056,10058,10061],{"className":10057},[1156],[1113,10059,6597],{"className":10060,"style":6630},[1156,1157],[1113,10062,10064],{"className":10063},[1503],[1113,10065,10067],{"className":10066},[1507],[1113,10068,10070],{"className":10069},[1512],[1113,10071,10073],{"className":10072,"style":2255},[1516],[1113,10074,10075,10078],{"style":2258},[1113,10076],{"className":10077,"style":1525},[1524],[1113,10079,10081],{"className":10080},[1529,1530,1531,1532],[1113,10082,10084],{"className":10083},[1156,1532],[1113,10085,2136],{"className":10086},[1156,1532],[1113,10088,10090,10093],{"className":10089},[1156],[1113,10091,1325],{"className":10092},[1156,1157],[1113,10094,10096],{"className":10095},[1503],[1113,10097,10099,10119],{"className":10098},[1507,1508],[1113,10100,10102,10116],{"className":10101},[1512],[1113,10103,10105],{"className":10104,"style":4646},[1516],[1113,10106,10107,10110],{"style":1626},[1113,10108],{"className":10109,"style":1525},[1524],[1113,10111,10113],{"className":10112},[1529,1530,1531,1532],[1113,10114,4304],{"className":10115},[1156,1157,1532],[1113,10117,1540],{"className":10118},[1539],[1113,10120,10122],{"className":10121},[1512],[1113,10123,10125],{"className":10124,"style":1547},[1516],[1113,10126],{},[1113,10128],{"className":10129,"style":1193},[1477],[1113,10131,1406],{"className":10132},[1556],[1113,10134],{"className":10135,"style":1193},[1477],[1113,10137,10139,10142,10145,10148,10151,10154],{"className":10138},[1147],[1113,10140],{"className":10141,"style":2845},[1151],[1113,10143,6606],{"className":10144},[1156,1157],[1113,10146,2143],{"className":10147},[2277],[1113,10149],{"className":10150,"style":1193},[1477],[1113,10152,2148],{"className":10153},[1556],[1113,10155],{"className":10156,"style":1193},[1477],[1113,10158,10160,10163,10166,10169,10172],{"className":10159},[1147],[1113,10161],{"className":10162,"style":9335},[1151],[1113,10164,1413],{"className":10165},[1156],[1113,10167],{"className":10168,"style":1193},[1477],[1113,10170,1406],{"className":10171},[1556],[1113,10173],{"className":10174,"style":1193},[1477],[1113,10176,10178,10181,10221,10227,10230,10233],{"className":10177},[1147],[1113,10179],{"className":10180,"style":5130},[1151],[1113,10182,10184,10187],{"className":10183},[1156],[1113,10185,8676],{"className":10186,"style":8697},[1156,1157],[1113,10188,10190],{"className":10189},[1503],[1113,10191,10193,10213],{"className":10192},[1507,1508],[1113,10194,10196,10210],{"className":10195},[1512],[1113,10197,10199],{"className":10198,"style":4646},[1516],[1113,10200,10201,10204],{"style":8712},[1113,10202],{"className":10203,"style":1525},[1524],[1113,10205,10207],{"className":10206},[1529,1530,1531,1532],[1113,10208,4304],{"className":10209},[1156,1157,1532],[1113,10211,1540],{"className":10212},[1539],[1113,10214,10216],{"className":10215},[1512],[1113,10217,10219],{"className":10218,"style":1547},[1516],[1113,10220],{},[1113,10222,10224],{"className":10223},[1156],[1113,10225,5087],{"className":10226},[5141,3160],[1113,10228],{"className":10229,"style":1193},[1477],[1113,10231,2148],{"className":10232},[1556],[1113,10234],{"className":10235,"style":1193},[1477],[1113,10237,10239,10242,10282,10285,10325],{"className":10238},[1147],[1113,10240],{"className":10241,"style":9816},[1151],[1113,10243,10245,10248],{"className":10244},[3542],[1113,10246,4295],{"className":10247,"style":4488},[3542,4486,4487],[1113,10249,10251],{"className":10250},[1503],[1113,10252,10254,10274],{"className":10253},[1507,1508],[1113,10255,10257,10271],{"className":10256},[1512],[1113,10258,10260],{"className":10259,"style":9841},[1516],[1113,10261,10262,10265],{"style":4504},[1113,10263],{"className":10264,"style":1525},[1524],[1113,10266,10268],{"className":10267},[1529,1530,1531,1532],[1113,10269,4304],{"className":10270},[1156,1157,1532],[1113,10272,1540],{"className":10273},[1539],[1113,10275,10277],{"className":10276},[1512],[1113,10278,10280],{"className":10279,"style":8435},[1516],[1113,10281],{},[1113,10283],{"className":10284,"style":3546},[1477],[1113,10286,10288,10291],{"className":10287},[1156],[1113,10289,9508],{"className":10290},[1156,1157],[1113,10292,10294],{"className":10293},[1503],[1113,10295,10297,10317],{"className":10296},[1507,1508],[1113,10298,10300,10314],{"className":10299},[1512],[1113,10301,10303],{"className":10302,"style":4646},[1516],[1113,10304,10305,10308],{"style":1626},[1113,10306],{"className":10307,"style":1525},[1524],[1113,10309,10311],{"className":10310},[1529,1530,1531,1532],[1113,10312,4304],{"className":10313},[1156,1157,1532],[1113,10315,1540],{"className":10316},[1539],[1113,10318,10320],{"className":10319},[1512],[1113,10321,10323],{"className":10322,"style":1547},[1516],[1113,10324],{},[1113,10326,10328,10331],{"className":10327},[1156],[1113,10329,8676],{"className":10330,"style":8697},[1156,1157],[1113,10332,10334],{"className":10333},[1503],[1113,10335,10337,10357],{"className":10336},[1507,1508],[1113,10338,10340,10354],{"className":10339},[1512],[1113,10341,10343],{"className":10342,"style":4646},[1516],[1113,10344,10345,10348],{"style":8712},[1113,10346],{"className":10347,"style":1525},[1524],[1113,10349,10351],{"className":10350},[1529,1530,1531,1532],[1113,10352,4304],{"className":10353},[1156,1157,1532],[1113,10355,1540],{"className":10356},[1539],[1113,10358,10360],{"className":10359},[1512],[1113,10361,10363],{"className":10362,"style":1547},[1516],[1113,10364],{},[1091,10366,10367,10368,10396,10397,10396,10425,10454],{},"对 ",[1113,10369,10371,10384],{"className":10370},[1116],[1113,10372,10374],{"className":10373},[1120],[1122,10375,10376],{"xmlns":1124},[1126,10377,10378,10382],{},[1129,10379,10380],{},[1132,10381,6597],{},[1136,10383,6597],{"encoding":1138},[1113,10385,10387],{"className":10386,"ariaHidden":1143},[1142],[1113,10388,10390,10393],{"className":10389},[1147],[1113,10391],{"className":10392,"style":1337},[1151],[1113,10394,6597],{"className":10395,"style":6630},[1156,1157],"、",[1113,10398,10400,10413],{"className":10399},[1116],[1113,10401,10403],{"className":10402},[1120],[1122,10404,10405],{"xmlns":1124},[1126,10406,10407,10411],{},[1129,10408,10409],{},[1132,10410,6606],{},[1136,10412,6606],{"encoding":1138},[1113,10414,10416],{"className":10415,"ariaHidden":1143},[1142],[1113,10417,10419,10422],{"className":10418},[1147],[1113,10420],{"className":10421,"style":2038},[1151],[1113,10423,6606],{"className":10424},[1156,1157],[1113,10426,10428,10442],{"className":10427},[1116],[1113,10429,10431],{"className":10430},[1120],[1122,10432,10433],{"xmlns":1124},[1126,10434,10435,10439],{},[1129,10436,10437],{},[1132,10438,8676],{},[1136,10440,10441],{"encoding":1138},"\\xi",[1113,10443,10445],{"className":10444,"ariaHidden":1143},[1142],[1113,10446,10448,10451],{"className":10447},[1147],[1113,10449],{"className":10450,"style":1492},[1151],[1113,10452,8676],{"className":10453,"style":8697},[1156,1157]," 求偏导并令其为零,可以得到",[1091,10456,10457],{},[1113,10458,10460,10546],{"className":10459},[1116],[1113,10461,10463],{"className":10462},[1120],[1122,10464,10465],{"xmlns":1124},[1126,10466,10467,10543],{},[1129,10468,10469,10471,10473,10479,10485,10491,10497,10499,10502,10508,10514,10520,10522,10524,10526,10528,10530,10533,10539,10541],{},[1132,10470,6597],{},[1391,10472,1393],{},[1395,10474,10475,10477],{},[1391,10476,4295],{},[1132,10478,4304],{},[1395,10480,10481,10483],{},[1132,10482,9503],{},[1132,10484,4304],{},[1395,10486,10487,10489],{},[1132,10488,1356],{},[1132,10490,4304],{},[1395,10492,10493,10495],{},[1132,10494,1325],{},[1132,10496,4304],{},[1391,10498,4876],{"separator":1143},[1477,10500],{"width":10501},"2em",[1395,10503,10504,10506],{},[1391,10505,4295],{},[1132,10507,4304],{},[1395,10509,10510,10512],{},[1132,10511,9503],{},[1132,10513,4304],{},[1395,10515,10516,10518],{},[1132,10517,1356],{},[1132,10519,4304],{},[1391,10521,1393],{},[1401,10523,1403],{},[1391,10525,4876],{"separator":1143},[1477,10527],{"width":10501},[1401,10529,1403],{},[1391,10531,10532],{},"≤",[1395,10534,10535,10537],{},[1132,10536,9503],{},[1132,10538,4304],{},[1391,10540,10532],{},[1132,10542,1279],{},[1136,10544,10545],{"encoding":1138},"w = \\sum_{i}\\alpha_i y_i x_i, \\qquad \\sum_{i}\\alpha_i y_i = 0, \\qquad 0 \\le \\alpha_i \\le C",[1113,10547,10549,10567,10884,10915,10971],{"className":10548,"ariaHidden":1143},[1142],[1113,10550,10552,10555,10558,10561,10564],{"className":10551},[1147],[1113,10553],{"className":10554,"style":1337},[1151],[1113,10556,6597],{"className":10557,"style":6630},[1156,1157],[1113,10559],{"className":10560,"style":1478},[1477],[1113,10562,1393],{"className":10563},[1482],[1113,10565],{"className":10566,"style":1478},[1477],[1113,10568,10570,10573,10616,10619,10659,10699,10739,10742,10746,10749,10792,10795,10835,10875,10878,10881],{"className":10569},[1147],[1113,10571],{"className":10572,"style":9816},[1151],[1113,10574,10576,10579],{"className":10575},[3542],[1113,10577,4295],{"className":10578,"style":4488},[3542,4486,4487],[1113,10580,10582],{"className":10581},[1503],[1113,10583,10585,10608],{"className":10584},[1507,1508],[1113,10586,10588,10605],{"className":10587},[1512],[1113,10589,10591],{"className":10590,"style":9841},[1516],[1113,10592,10593,10596],{"style":4504},[1113,10594],{"className":10595,"style":1525},[1524],[1113,10597,10599],{"className":10598},[1529,1530,1531,1532],[1113,10600,10602],{"className":10601},[1156,1532],[1113,10603,4304],{"className":10604},[1156,1157,1532],[1113,10606,1540],{"className":10607},[1539],[1113,10609,10611],{"className":10610},[1512],[1113,10612,10614],{"className":10613,"style":8435},[1516],[1113,10615],{},[1113,10617],{"className":10618,"style":3546},[1477],[1113,10620,10622,10625],{"className":10621},[1156],[1113,10623,9503],{"className":10624,"style":9670},[1156,1157],[1113,10626,10628],{"className":10627},[1503],[1113,10629,10631,10651],{"className":10630},[1507,1508],[1113,10632,10634,10648],{"className":10633},[1512],[1113,10635,10637],{"className":10636,"style":4646},[1516],[1113,10638,10639,10642],{"style":9985},[1113,10640],{"className":10641,"style":1525},[1524],[1113,10643,10645],{"className":10644},[1529,1530,1531,1532],[1113,10646,4304],{"className":10647},[1156,1157,1532],[1113,10649,1540],{"className":10650},[1539],[1113,10652,10654],{"className":10653},[1512],[1113,10655,10657],{"className":10656,"style":1547},[1516],[1113,10658],{},[1113,10660,10662,10665],{"className":10661},[1156],[1113,10663,1356],{"className":10664,"style":1372},[1156,1157],[1113,10666,10668],{"className":10667},[1503],[1113,10669,10671,10691],{"className":10670},[1507,1508],[1113,10672,10674,10688],{"className":10673},[1512],[1113,10675,10677],{"className":10676,"style":4646},[1516],[1113,10678,10679,10682],{"style":2540},[1113,10680],{"className":10681,"style":1525},[1524],[1113,10683,10685],{"className":10684},[1529,1530,1531,1532],[1113,10686,4304],{"className":10687},[1156,1157,1532],[1113,10689,1540],{"className":10690},[1539],[1113,10692,10694],{"className":10693},[1512],[1113,10695,10697],{"className":10696,"style":1547},[1516],[1113,10698],{},[1113,10700,10702,10705],{"className":10701},[1156],[1113,10703,1325],{"className":10704},[1156,1157],[1113,10706,10708],{"className":10707},[1503],[1113,10709,10711,10731],{"className":10710},[1507,1508],[1113,10712,10714,10728],{"className":10713},[1512],[1113,10715,10717],{"className":10716,"style":4646},[1516],[1113,10718,10719,10722],{"style":1626},[1113,10720],{"className":10721,"style":1525},[1524],[1113,10723,10725],{"className":10724},[1529,1530,1531,1532],[1113,10726,4304],{"className":10727},[1156,1157,1532],[1113,10729,1540],{"className":10730},[1539],[1113,10732,10734],{"className":10733},[1512],[1113,10735,10737],{"className":10736,"style":1547},[1516],[1113,10738],{},[1113,10740,4876],{"className":10741},[4933],[1113,10743],{"className":10744,"style":10745},[1477],"margin-right:2em;",[1113,10747],{"className":10748,"style":3546},[1477],[1113,10750,10752,10755],{"className":10751},[3542],[1113,10753,4295],{"className":10754,"style":4488},[3542,4486,4487],[1113,10756,10758],{"className":10757},[1503],[1113,10759,10761,10784],{"className":10760},[1507,1508],[1113,10762,10764,10781],{"className":10763},[1512],[1113,10765,10767],{"className":10766,"style":9841},[1516],[1113,10768,10769,10772],{"style":4504},[1113,10770],{"className":10771,"style":1525},[1524],[1113,10773,10775],{"className":10774},[1529,1530,1531,1532],[1113,10776,10778],{"className":10777},[1156,1532],[1113,10779,4304],{"className":10780},[1156,1157,1532],[1113,10782,1540],{"className":10783},[1539],[1113,10785,10787],{"className":10786},[1512],[1113,10788,10790],{"className":10789,"style":8435},[1516],[1113,10791],{},[1113,10793],{"className":10794,"style":3546},[1477],[1113,10796,10798,10801],{"className":10797},[1156],[1113,10799,9503],{"className":10800,"style":9670},[1156,1157],[1113,10802,10804],{"className":10803},[1503],[1113,10805,10807,10827],{"className":10806},[1507,1508],[1113,10808,10810,10824],{"className":10809},[1512],[1113,10811,10813],{"className":10812,"style":4646},[1516],[1113,10814,10815,10818],{"style":9985},[1113,10816],{"className":10817,"style":1525},[1524],[1113,10819,10821],{"className":10820},[1529,1530,1531,1532],[1113,10822,4304],{"className":10823},[1156,1157,1532],[1113,10825,1540],{"className":10826},[1539],[1113,10828,10830],{"className":10829},[1512],[1113,10831,10833],{"className":10832,"style":1547},[1516],[1113,10834],{},[1113,10836,10838,10841],{"className":10837},[1156],[1113,10839,1356],{"className":10840,"style":1372},[1156,1157],[1113,10842,10844],{"className":10843},[1503],[1113,10845,10847,10867],{"className":10846},[1507,1508],[1113,10848,10850,10864],{"className":10849},[1512],[1113,10851,10853],{"className":10852,"style":4646},[1516],[1113,10854,10855,10858],{"style":2540},[1113,10856],{"className":10857,"style":1525},[1524],[1113,10859,10861],{"className":10860},[1529,1530,1531,1532],[1113,10862,4304],{"className":10863},[1156,1157,1532],[1113,10865,1540],{"className":10866},[1539],[1113,10868,10870],{"className":10869},[1512],[1113,10871,10873],{"className":10872,"style":1547},[1516],[1113,10874],{},[1113,10876],{"className":10877,"style":1478},[1477],[1113,10879,1393],{"className":10880},[1482],[1113,10882],{"className":10883,"style":1478},[1477],[1113,10885,10887,10891,10894,10897,10900,10903,10906,10909,10912],{"className":10886},[1147],[1113,10888],{"className":10889,"style":10890},[1151],"height:0.8389em;vertical-align:-0.1944em;",[1113,10892,1403],{"className":10893},[1156],[1113,10895,4876],{"className":10896},[4933],[1113,10898],{"className":10899,"style":10745},[1477],[1113,10901],{"className":10902,"style":3546},[1477],[1113,10904,1403],{"className":10905},[1156],[1113,10907],{"className":10908,"style":1478},[1477],[1113,10910,10532],{"className":10911},[1482],[1113,10913],{"className":10914,"style":1478},[1477],[1113,10916,10918,10922,10962,10965,10968],{"className":10917},[1147],[1113,10919],{"className":10920,"style":10921},[1151],"height:0.786em;vertical-align:-0.15em;",[1113,10923,10925,10928],{"className":10924},[1156],[1113,10926,9503],{"className":10927,"style":9670},[1156,1157],[1113,10929,10931],{"className":10930},[1503],[1113,10932,10934,10954],{"className":10933},[1507,1508],[1113,10935,10937,10951],{"className":10936},[1512],[1113,10938,10940],{"className":10939,"style":4646},[1516],[1113,10941,10942,10945],{"style":9985},[1113,10943],{"className":10944,"style":1525},[1524],[1113,10946,10948],{"className":10947},[1529,1530,1531,1532],[1113,10949,4304],{"className":10950},[1156,1157,1532],[1113,10952,1540],{"className":10953},[1539],[1113,10955,10957],{"className":10956},[1512],[1113,10958,10960],{"className":10959,"style":1547},[1516],[1113,10961],{},[1113,10963],{"className":10964,"style":1478},[1477],[1113,10966,10532],{"className":10967},[1482],[1113,10969],{"className":10970,"style":1478},[1477],[1113,10972,10974,10977],{"className":10973},[1147],[1113,10975],{"className":10976,"style":1152},[1151],[1113,10978,1279],{"className":10979,"style":1294},[1156,1157],[1091,10981,10982,10983,11011,11012,1980,11105,11108],{},"代回即得对偶问题,求解后 ",[1113,10984,10986,10999],{"className":10985},[1116],[1113,10987,10989],{"className":10988},[1120],[1122,10990,10991],{"xmlns":1124},[1126,10992,10993,10997],{},[1129,10994,10995],{},[1132,10996,6597],{},[1136,10998,6597],{"encoding":1138},[1113,11000,11002],{"className":11001,"ariaHidden":1143},[1142],[1113,11003,11005,11008],{"className":11004},[1147],[1113,11006],{"className":11007,"style":1337},[1151],[1113,11009,6597],{"className":11010,"style":6630},[1156,1157]," 只由 ",[1113,11013,11015,11037],{"className":11014},[1116],[1113,11016,11018],{"className":11017},[1120],[1122,11019,11020],{"xmlns":1124},[1126,11021,11022,11034],{},[1129,11023,11024,11030,11032],{},[1395,11025,11026,11028],{},[1132,11027,9503],{},[1132,11029,4304],{},[1391,11031,6065],{},[1401,11033,1403],{},[1136,11035,11036],{"encoding":1138},"\\alpha_i > 0",[1113,11038,11040,11096],{"className":11039,"ariaHidden":1143},[1142],[1113,11041,11043,11047,11087,11090,11093],{"className":11042},[1147],[1113,11044],{"className":11045,"style":11046},[1151],"height:0.6891em;vertical-align:-0.15em;",[1113,11048,11050,11053],{"className":11049},[1156],[1113,11051,9503],{"className":11052,"style":9670},[1156,1157],[1113,11054,11056],{"className":11055},[1503],[1113,11057,11059,11079],{"className":11058},[1507,1508],[1113,11060,11062,11076],{"className":11061},[1512],[1113,11063,11065],{"className":11064,"style":4646},[1516],[1113,11066,11067,11070],{"style":9985},[1113,11068],{"className":11069,"style":1525},[1524],[1113,11071,11073],{"className":11072},[1529,1530,1531,1532],[1113,11074,4304],{"className":11075},[1156,1157,1532],[1113,11077,1540],{"className":11078},[1539],[1113,11080,11082],{"className":11081},[1512],[1113,11083,11085],{"className":11084,"style":1547},[1516],[1113,11086],{},[1113,11088],{"className":11089,"style":1478},[1477],[1113,11091,6065],{"className":11092},[1482],[1113,11094],{"className":11095,"style":1478},[1477],[1113,11097,11099,11102],{"className":11098},[1147],[1113,11100],{"className":11101,"style":3840},[1151],[1113,11103,1403],{"className":11104},[1156],[1095,11106,11107],{},"支持向量","决定。",[2689,11110],{},[1304,11112,11113],{"id":11113},"总结",[4054,11115,11116,11346,11629,11635,11727,11952],{},[4057,11117,11118,11120,11121,11345],{},[1095,11119,329],{},":加一列全 1 吸收截距,最小二乘闭式解 ",[1113,11122,11124,11171],{"className":11123},[1116],[1113,11125,11127],{"className":11126},[1120],[1122,11128,11129],{"xmlns":1124},[1126,11130,11131,11169],{},[1129,11132,11133,11139,11141,11143,11149,11151,11161,11167],{},[2000,11134,11135,11137],{"accent":1143},[1132,11136,1399],{},[1391,11138,2006],{},[1391,11140,1393],{},[1391,11142,2127],{"stretchy":2126},[2129,11144,11145,11147],{},[1132,11146,1134],{},[1132,11148,2136],{"mathvariant":2135},[1132,11150,1134],{},[2129,11152,11153,11155],{},[1391,11154,2143],{"stretchy":2126},[1129,11156,11157,11159],{},[1391,11158,2148],{},[1401,11160,1413],{},[2129,11162,11163,11165],{},[1132,11164,1134],{},[1132,11166,2136],{"mathvariant":2135},[1132,11168,1356],{},[1136,11170,2161],{"encoding":1138},[1113,11172,11174,11231],{"className":11173,"ariaHidden":1143},[1142],[1113,11175,11177,11180,11222,11225,11228],{"className":11176},[1147],[1113,11178],{"className":11179,"style":2171},[1151],[1113,11181,11183],{"className":11182},[1156,2028],[1113,11184,11186,11214],{"className":11185},[1507,1508],[1113,11187,11189,11211],{"className":11188},[1512],[1113,11190,11192,11200],{"className":11191,"style":2184},[1516],[1113,11193,11194,11197],{"style":2041},[1113,11195],{"className":11196,"style":2045},[1524],[1113,11198,1399],{"className":11199,"style":1499},[1156,1157],[1113,11201,11202,11205],{"style":2195},[1113,11203],{"className":11204,"style":2045},[1524],[1113,11206,11208],{"className":11207,"style":2202},[2057],[1113,11209,2006],{"className":11210},[1156],[1113,11212,1540],{"className":11213},[1539],[1113,11215,11217],{"className":11216},[1512],[1113,11218,11220],{"className":11219,"style":2071},[1516],[1113,11221],{},[1113,11223],{"className":11224,"style":1478},[1477],[1113,11226,1393],{"className":11227},[1482],[1113,11229],{"className":11230,"style":1478},[1477],[1113,11232,11234,11237,11240,11272,11275,11310,11342],{"className":11233},[1147],[1113,11235],{"className":11236,"style":2232},[1151],[1113,11238,2127],{"className":11239},[2236],[1113,11241,11243,11246],{"className":11242},[1156],[1113,11244,1134],{"className":11245,"style":1158},[1156,1157],[1113,11247,11249],{"className":11248},[1503],[1113,11250,11252],{"className":11251},[1507],[1113,11253,11255],{"className":11254},[1512],[1113,11256,11258],{"className":11257,"style":2255},[1516],[1113,11259,11260,11263],{"style":2258},[1113,11261],{"className":11262,"style":1525},[1524],[1113,11264,11266],{"className":11265},[1529,1530,1531,1532],[1113,11267,11269],{"className":11268},[1156,1532],[1113,11270,2136],{"className":11271},[1156,1532],[1113,11273,1134],{"className":11274,"style":1158},[1156,1157],[1113,11276,11278,11281],{"className":11277},[2277],[1113,11279,2143],{"className":11280},[2277],[1113,11282,11284],{"className":11283},[1503],[1113,11285,11287],{"className":11286},[1507],[1113,11288,11290],{"className":11289},[1512],[1113,11291,11293],{"className":11292,"style":2293},[1516],[1113,11294,11295,11298],{"style":2258},[1113,11296],{"className":11297,"style":1525},[1524],[1113,11299,11301],{"className":11300},[1529,1530,1531,1532],[1113,11302,11304,11307],{"className":11303},[1156,1532],[1113,11305,2148],{"className":11306},[1156,1532],[1113,11308,1413],{"className":11309},[1156,1532],[1113,11311,11313,11316],{"className":11312},[1156],[1113,11314,1134],{"className":11315,"style":1158},[1156,1157],[1113,11317,11319],{"className":11318},[1503],[1113,11320,11322],{"className":11321},[1507],[1113,11323,11325],{"className":11324},[1512],[1113,11326,11328],{"className":11327,"style":2255},[1516],[1113,11329,11330,11333],{"style":2258},[1113,11331],{"className":11332,"style":1525},[1524],[1113,11334,11336],{"className":11335},[1529,1530,1531,1532],[1113,11337,11339],{"className":11338},[1156,1532],[1113,11340,2136],{"className":11341},[1156,1532],[1113,11343,1356],{"className":11344,"style":1372},[1156,1157],";有闭式解。",[4057,11347,11348,11350,11351,11535,11536,11539,11540,3717],{},[1095,11349,330],{},":广义线性模型 + logit 联系函数;用线性结果逼近对数几率 ",[1113,11352,11354,11392],{"className":11353},[1116],[1113,11355,11357],{"className":11356},[1120],[1122,11358,11359],{"xmlns":1124},[1126,11360,11361,11389],{},[1129,11362,11363,11365,11367,11379,11381,11387],{},[1132,11364,3474],{},[1391,11366,3477],{},[2950,11368,11369,11371],{},[1132,11370,1091],{},[1129,11372,11373,11375,11377],{},[1401,11374,1413],{},[1391,11376,2148],{},[1132,11378,1091],{},[1391,11380,1393],{},[2129,11382,11383,11385],{},[1132,11384,1325],{},[1132,11386,2136],{"mathvariant":2135},[1132,11388,1399],{},[1136,11390,11391],{"encoding":1138},"\\ln\\frac{p}{1-p}=x^{\\top}\\beta",[1113,11393,11395,11494],{"className":11394,"ariaHidden":1143},[1142],[1113,11396,11398,11402,11405,11408,11485,11488,11491],{"className":11397},[1147],[1113,11399],{"className":11400,"style":11401},[1151],"height:1.2286em;vertical-align:-0.4811em;",[1113,11403,3474],{"className":11404},[3542],[1113,11406],{"className":11407,"style":3546},[1477],[1113,11409,11411,11414,11482],{"className":11410},[1156],[1113,11412],{"className":11413},[2236,3098],[1113,11415,11417],{"className":11416},[2950],[1113,11418,11420,11473],{"className":11419},[1507,1508],[1113,11421,11423,11470],{"className":11422},[1512],[1113,11424,11427,11447,11455],{"className":11425,"style":11426},[1516],"height:0.7475em;",[1113,11428,11429,11432],{"style":3568},[1113,11430],{"className":11431,"style":2045},[1524],[1113,11433,11435],{"className":11434},[1529,1530,1531,1532],[1113,11436,11438,11441,11444],{"className":11437},[1156,1532],[1113,11439,1413],{"className":11440},[1156,1532],[1113,11442,2148],{"className":11443},[1556,1532],[1113,11445,1091],{"className":11446},[1156,1157,1532],[1113,11448,11449,11452],{"style":3204},[1113,11450],{"className":11451,"style":2045},[1524],[1113,11453],{"className":11454,"style":3212},[3211],[1113,11456,11458,11461],{"style":11457},"top:-3.4461em;",[1113,11459],{"className":11460,"style":2045},[1524],[1113,11462,11464],{"className":11463},[1529,1530,1531,1532],[1113,11465,11467],{"className":11466},[1156,1532],[1113,11468,1091],{"className":11469},[1156,1157,1532],[1113,11471,1540],{"className":11472},[1539],[1113,11474,11476],{"className":11475},[1512],[1113,11477,11480],{"className":11478,"style":11479},[1516],"height:0.4811em;",[1113,11481],{},[1113,11483],{"className":11484},[2277,3098],[1113,11486],{"className":11487,"style":1478},[1477],[1113,11489,1393],{"className":11490},[1482],[1113,11492],{"className":11493,"style":1478},[1477],[1113,11495,11497,11500,11532],{"className":11496},[1147],[1113,11498],{"className":11499,"style":2764},[1151],[1113,11501,11503,11506],{"className":11502},[1156],[1113,11504,1325],{"className":11505},[1156,1157],[1113,11507,11509],{"className":11508},[1503],[1113,11510,11512],{"className":11511},[1507],[1113,11513,11515],{"className":11514},[1512],[1113,11516,11518],{"className":11517,"style":2255},[1516],[1113,11519,11520,11523],{"style":2258},[1113,11521],{"className":11522,"style":1525},[1524],[1113,11524,11526],{"className":11525},[1529,1530,1531,1532],[1113,11527,11529],{"className":11528},[1156,1532],[1113,11530,2136],{"className":11531},[1156,1532],[1113,11533,1399],{"className":11534,"style":1499},[1156,1157],";",[1095,11537,11538],{},"无闭式解,需迭代",";判别线 ",[1113,11541,11543,11567],{"className":11542},[1116],[1113,11544,11546],{"className":11545},[1120],[1122,11547,11548],{"xmlns":1124},[1126,11549,11550,11564],{},[1129,11551,11552,11558,11560,11562],{},[2129,11553,11554,11556],{},[1132,11555,1325],{},[1132,11557,2136],{"mathvariant":2135},[1132,11559,1399],{},[1391,11561,1393],{},[1401,11563,1403],{},[1136,11565,11566],{"encoding":1138},"x^{\\top}\\beta=0",[1113,11568,11570,11620],{"className":11569,"ariaHidden":1143},[1142],[1113,11571,11573,11576,11608,11611,11614,11617],{"className":11572},[1147],[1113,11574],{"className":11575,"style":2764},[1151],[1113,11577,11579,11582],{"className":11578},[1156],[1113,11580,1325],{"className":11581},[1156,1157],[1113,11583,11585],{"className":11584},[1503],[1113,11586,11588],{"className":11587},[1507],[1113,11589,11591],{"className":11590},[1512],[1113,11592,11594],{"className":11593,"style":2255},[1516],[1113,11595,11596,11599],{"style":2258},[1113,11597],{"className":11598,"style":1525},[1524],[1113,11600,11602],{"className":11601},[1529,1530,1531,1532],[1113,11603,11605],{"className":11604},[1156,1532],[1113,11606,2136],{"className":11607},[1156,1532],[1113,11609,1399],{"className":11610,"style":1499},[1156,1157],[1113,11612],{"className":11613,"style":1478},[1477],[1113,11615,1393],{"className":11616},[1482],[1113,11618],{"className":11619,"style":1478},[1477],[1113,11621,11623,11626],{"className":11622},[1147],[1113,11624],{"className":11625,"style":3840},[1151],[1113,11627,1403],{"className":11628},[1156],[4057,11630,11631,11634],{},[1095,11632,11633],{},"线性判别何时够",":两类同方差异均值高斯 → 线性最优;10 个高斯混合 → 线性远远不够。",[4057,11636,11637,4854,11640,11668,11669,11697,11698,11726],{},[1095,11638,11639],{},"最近邻",[1113,11641,11643,11656],{"className":11642},[1116],[1113,11644,11646],{"className":11645},[1120],[1122,11647,11648],{"xmlns":1124},[1126,11649,11650,11654],{},[1129,11651,11652],{},[1132,11653,4149],{},[1136,11655,4149],{"encoding":1138},[1113,11657,11659],{"className":11658,"ariaHidden":1143},[1142],[1113,11660,11662,11665],{"className":11661},[1147],[1113,11663],{"className":11664,"style":2038},[1151],[1113,11666,4149],{"className":11667,"style":4164},[1156,1157]," 个近邻多数表决;",[1113,11670,11672,11685],{"className":11671},[1116],[1113,11673,11675],{"className":11674},[1120],[1122,11676,11677],{"xmlns":1124},[1126,11678,11679,11683],{},[1129,11680,11681],{},[1132,11682,4149],{},[1136,11684,4149],{"encoding":1138},[1113,11686,11688],{"className":11687,"ariaHidden":1143},[1142],[1113,11689,11691,11694],{"className":11690},[1147],[1113,11692],{"className":11693,"style":2038},[1151],[1113,11695,4149],{"className":11696,"style":4164},[1156,1157]," 小边界弯(过拟合),",[1113,11699,11701,11714],{"className":11700},[1116],[1113,11702,11704],{"className":11703},[1120],[1122,11705,11706],{"xmlns":1124},[1126,11707,11708,11712],{},[1129,11709,11710],{},[1132,11711,4149],{},[1136,11713,4149],{"encoding":1138},[1113,11715,11717],{"className":11716,"ariaHidden":1143},[1142],[1113,11718,11720,11723],{"className":11719},[1147],[1113,11721],{"className":11722,"style":2038},[1151],[1113,11724,4149],{"className":11725,"style":4164},[1156,1157]," 大边界平滑。",[4057,11728,11729,11731,11732,11797,11798,11951],{},[1095,11730,4840],{},":平方损失下最优预测是条件期望 ",[1113,11733,11735,11758],{"className":11734},[1116],[1113,11736,11738],{"className":11737},[1120],[1122,11739,11740],{"xmlns":1124},[1126,11741,11742,11756],{},[1129,11743,11744,11746,11748,11750,11752,11754],{},[1132,11745,5060],{},[1391,11747,5064],{"stretchy":2126},[1132,11749,1356],{},[1391,11751,2942],{},[1132,11753,1325],{},[1391,11755,5087],{"stretchy":2126},[1136,11757,5455],{"encoding":1138},[1113,11759,11761,11785],{"className":11760,"ariaHidden":1143},[1142],[1113,11762,11764,11767,11770,11773,11776,11779,11782],{"className":11763},[1147],[1113,11765],{"className":11766,"style":2845},[1151],[1113,11768,5060],{"className":11769,"style":5134},[1156,1157],[1113,11771,5064],{"className":11772},[2236],[1113,11774,1356],{"className":11775,"style":1372},[1156,1157],[1113,11777],{"className":11778,"style":1478},[1477],[1113,11780,2942],{"className":11781},[1482],[1113,11783],{"className":11784,"style":1478},[1477],[1113,11786,11788,11791,11794],{"className":11787},[1147],[1113,11789],{"className":11790,"style":2845},[1151],[1113,11792,1325],{"className":11793},[1156,1157],[1113,11795,5087],{"className":11796},[2277],";0-1 损失下最优是最大后验 ",[1113,11799,11801,11843],{"className":11800},[1116],[1113,11802,11804],{"className":11803},[1120],[1122,11805,11806],{"xmlns":1124},[1126,11807,11808,11840],{},[1129,11809,11810,11812,11814,11824,11826,11828,11830,11832,11834,11836,11838],{},[1132,11811,5743],{},[1391,11813,3477],{},[1395,11815,11816,11822],{},[1129,11817,11818,11820],{},[1132,11819,5752],{},[1391,11821,3477],{},[1132,11823,5757],{},[1132,11825,2931],{},[1391,11827,2127],{"stretchy":2126},[1132,11829,1356],{},[1391,11831,1393],{},[1132,11833,5757],{},[1391,11835,2942],{},[1132,11837,1325],{},[1391,11839,2143],{"stretchy":2126},[1136,11841,11842],{"encoding":1138},"\\arg\\max_c P(y=c\\mid x)",[1113,11844,11846,11921,11939],{"className":11845,"ariaHidden":1143},[1142],[1113,11847,11849,11852,11857,11860,11900,11903,11906,11909,11912,11915,11918],{"className":11848},[1147],[1113,11850],{"className":11851,"style":2845},[1151],[1113,11853,5842,11855],{"className":11854},[3542],[1113,11856,2716],{"style":5845},[1113,11858],{"className":11859,"style":3546},[1477],[1113,11861,11863,11866],{"className":11862},[3542],[1113,11864,5752],{"className":11865},[3542],[1113,11867,11869],{"className":11868},[1503],[1113,11870,11872,11892],{"className":11871},[1507,1508],[1113,11873,11875,11889],{"className":11874},[1512],[1113,11876,11878],{"className":11877,"style":1796},[1516],[1113,11879,11880,11883],{"style":5869},[1113,11881],{"className":11882,"style":1525},[1524],[1113,11884,11886],{"className":11885},[1529,1530,1531,1532],[1113,11887,5757],{"className":11888},[1156,1157,1532],[1113,11890,1540],{"className":11891},[1539],[1113,11893,11895],{"className":11894},[1512],[1113,11896,11898],{"className":11897,"style":1547},[1516],[1113,11899],{},[1113,11901],{"className":11902,"style":3546},[1477],[1113,11904,2931],{"className":11905,"style":3030},[1156,1157],[1113,11907,2127],{"className":11908},[2236],[1113,11910,1356],{"className":11911,"style":1372},[1156,1157],[1113,11913],{"className":11914,"style":1478},[1477],[1113,11916,1393],{"className":11917},[1482],[1113,11919],{"className":11920,"style":1478},[1477],[1113,11922,11924,11927,11930,11933,11936],{"className":11923},[1147],[1113,11925],{"className":11926,"style":2845},[1151],[1113,11928,5757],{"className":11929},[1156,1157],[1113,11931],{"className":11932,"style":1478},[1477],[1113,11934,2942],{"className":11935},[1482],[1113,11937],{"className":11938,"style":1478},[1477],[1113,11940,11942,11945,11948],{"className":11941},[1147],[1113,11943],{"className":11944,"style":2845},[1151],[1113,11946,1325],{"className":11947},[1156,1157],[1113,11949,2143],{"className":11950},[2277],";对应最小误差叫贝叶斯误差\u002F风险。",[4057,11953,11954,11957,11958,12111,12112,12320,12321,12390,12391,12419,12420,10396,12612,10396,12758,3717],{},[1095,11955,11956],{},"SVM",":硬间隔 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s.t. 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