[{"data":1,"prerenderedAt":2806},["ShallowReactive",2],{"lang-switch-post-\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab04-logistic-loss":3,"post-pt-machine-learning-specialization-w3-lab04-logistic-loss":4},"\u002Fen\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab04-logistic-loss",{"id":5,"title":6,"body":7,"cover":2789,"date":2790,"description":2791,"extension":2792,"meta":2793,"navigation":2794,"order":2795,"path":2796,"playlist":2797,"seo":2798,"status":2799,"stem":2800,"tags":2801,"__hash__":2805},"posts\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab04-logistic-loss.md","Erro Quadrático Não Serve Aqui: a Perda Logística",{"type":8,"value":9,"toc":2782},"minimark",[10,20,25,863,877,987,1020,1027,1037,1040,1044,1053,1954,1961,1990,1994,2016,2559,2582,2586,2637,2641,2657,2691,2768,2778],[11,12,13,14,19],"p",{},"Toda a base de regressão linear até aqui usou o erro quadrático como função de custo, ",[15,16,18],"a",{"href":17},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab03-cost-function","uma tigela lisa e bem-comportada"," onde gradiente descendente sempre acha o fundo. A tentação óbvia é reaproveitar a mesma ideia pra regressão logística: pega a saída da sigmoide e mede o erro quadrático dela contra o rótulo. Esse lab mostra, com número real, por que essa tentação é uma armadilha.",[21,22,24],"h2",{"id":23},"reaproveitando-o-erro-quadrático-e-uma-pista-de-que-vai-dar-ruim","Reaproveitando o erro quadrático (e uma pista de que vai dar ruim)",[11,26,27],{},[28,29,32,236],"span",{"className":30},[31],"katex",[28,33,36],{"className":34},[35],"katex-mathml",[37,38,40],"math",{"xmlns":39},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[41,42,43,231],"semantics",{},[44,45,46,50,55,58,62,65,68,71,86,111,168,170,174,186,188,200,202,204,208,210,212,224,227,229],"mrow",{},[47,48,49],"mi",{},"J",[51,52,54],"mo",{"stretchy":53},"false","(",[47,56,57],{},"w",[51,59,61],{"separator":60},"true",",",[47,63,64],{},"b",[51,66,67],{"stretchy":53},")",[51,69,70],{},"=",[72,73,74,78],"mfrac",{},[75,76,77],"mn",{},"1",[44,79,80,83],{},[75,81,82],{},"2",[47,84,85],{},"m",[87,88,89,92,102],"msubsup",{},[51,90,91],{},"∑",[44,93,94,97,99],{},[47,95,96],{},"i",[51,98,70],{},[75,100,101],{},"0",[44,103,104,106,109],{},[47,105,85],{},[51,107,108],{},"−",[75,110,77],{},[112,113,114,166],"msup",{},[44,115,116,118,132,134,147,149,151,164],{},[51,117,54],{"fence":60},[119,120,121,124],"msub",{},[47,122,123],{},"f",[44,125,126,128,130],{},[47,127,57],{},[51,129,61],{"separator":60},[47,131,64],{},[51,133,54],{"stretchy":53},[112,135,136,139],{},[47,137,138],{},"x",[44,140,141,143,145],{},[51,142,54],{"stretchy":53},[47,144,96],{},[51,146,67],{"stretchy":53},[51,148,67],{"stretchy":53},[51,150,108],{},[112,152,153,156],{},[47,154,155],{},"y",[44,157,158,160,162],{},[51,159,54],{"stretchy":53},[47,161,96],{},[51,163,67],{"stretchy":53},[51,165,67],{"fence":60},[75,167,82],{},[51,169,61],{"separator":60},[171,172],"mspace",{"width":173},"1em",[119,175,176,178],{},[47,177,123],{},[44,179,180,182,184],{},[47,181,57],{},[51,183,61],{"separator":60},[47,185,64],{},[51,187,54],{"stretchy":53},[112,189,190,192],{},[47,191,138],{},[44,193,194,196,198],{},[51,195,54],{"stretchy":53},[47,197,96],{},[51,199,67],{"stretchy":53},[51,201,67],{"stretchy":53},[51,203,70],{},[205,206,207],"mtext",{},"sigmoid",[51,209,54],{"stretchy":53},[47,211,57],{},[112,213,214,216],{},[47,215,138],{},[44,217,218,220,222],{},[51,219,54],{"stretchy":53},[47,221,96],{},[51,223,67],{"stretchy":53},[51,225,226],{},"+",[47,228,64],{},[51,230,67],{"stretchy":53},[232,233,235],"annotation",{"encoding":234},"application\u002Fx-tex","J(w,b) 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fórmula de sempre, só que agora ",[867,868,123],"code",{}," já passou pela sigmoide antes de entrar na conta. Fixei ",[867,871,872],{},"b=-3"," (perto de onde um ajuste bom pra esse dado acaba caindo) e variei ",[867,875,57],{},":",[878,879,880,893],"table",{},[881,882,883],"thead",{},[884,885,886,890],"tr",{},[887,888,57],"th",{"align":889},"right",[887,891,892],{"align":889},"custo (erro quadrático + sigmoide)",[894,895,896,905,913,921,932,940,948,956,964,972,980],"tbody",{},[884,897,898,902],{},[899,900,901],"td",{"align":889},"1.0",[899,903,904],{"align":889},"0.0354",[884,906,907,910],{},[899,908,909],{"align":889},"1.1",[899,911,912],{"align":889},"0.0284",[884,914,915,918],{},[899,916,917],{"align":889},"1.2",[899,919,920],{"align":889},"0.0247",[884,922,923,926],{},[899,924,925],{"align":889},"1.3",[899,927,928],{"align":889},[929,930,931],"strong",{},"0.0235",[884,933,934,937],{},[899,935,936],{"align":889},"1.4",[899,938,939],{"align":889},"0.0243",[884,941,942,945],{},[899,943,944],{"align":889},"1.6",[899,946,947],{"align":889},"0.0304",[884,949,950,953],{},[899,951,952],{"align":889},"2.0",[899,954,955],{"align":889},"0.0509",[884,957,958,961],{},[899,959,960],{"align":889},"5.0",[899,962,963],{"align":889},"0.1480",[884,965,966,969],{},[899,967,968],{"align":889},"10.0",[899,970,971],{"align":889},"0.1667",[884,973,974,977],{},[899,975,976],{"align":889},"15.0",[899,978,979],{"align":889},"0.1669",[884,981,982,985],{},[899,983,984],{"align":889},"20.0",[899,986,979],{"align":889},[11,988,989,990,993,994,997,998,1000,1001,1003,1004,1006,1007,1010,1011,1013,1014,1016,1017,1019],{},"Repara nas últimas linhas: de ",[867,991,992],{},"w=10"," até ",[867,995,996],{},"w=20",", o custo praticamente não muda (",[867,999,971],{}," → ",[867,1002,979],{},"). Não é coincidência, é a sigmoide saturando: pra ",[867,1005,57],{}," grande, ",[867,1008,1009],{},"sigmoid(wx+b)"," já está tão perto de ",[867,1012,101],{}," ou ",[867,1015,77],{}," que aumentar ",[867,1018,57],{}," ainda mais quase não move a saída, e por tabela quase não move o custo. O gradiente nessa região é minúsculo. Gradiente descendente, se cair aí, mal se mexe.",[11,1021,1022,1023,1026],{},"Gira o gráfico abaixo e compara com ",[15,1024,1025],{"href":17},"a tigela lisa da regressão linear",": não é mais uma superfície simétrica com um fundo único e bem definido, tem dobras e um platô extenso onde a inclinação quase some.",[1028,1029],"cost-surface3d",{":b-max":82,":b-min":1030,":w-max":1031,":w-min":1032,":x-train":1033,":y-train":1034,"fn":1035,"height":1036},"-8","3","-2","[0,1,2,3,4,5]","[0,0,0,1,1,1]","sigmoid-squared-error","380px",[11,1038,1039],{},"Erro quadrático não é uma má ideia em si, ele só assume implicitamente que o ruído nos dados é bem-comportado (gaussiano), o que faz sentido pra prever um número contínuo. Colado numa sigmoide, essa suposição quebra, e a superfície de custo perde a garantia de ser uma tigela única. Precisa de uma função de perda pensada especificamente pra classificação.",[21,1041,1043],{"id":1042},"a-perda-logística-pune-forte-quando-erra-com-convicção","A perda logística: pune forte quando erra com convicção",[11,1045,1046,1047,1049,1050,1052],{},"A ideia por trás da perda logística é simples de explicar sem fórmula nenhuma primeiro: se o rótulo certo é ",[867,1048,77],{},", eu quero punir pesado quando o modelo disse \"quase certeza que é 0\", e quase não punir quando ele disse \"quase certeza que é 1\". E vice-versa pro rótulo ",[867,1051,101],{},". A fórmula, em duas 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y^{(i)}) = \\begin{cases}\n-\\log\\left(f_{w,b}(x^{(i)})\\right) & \\text{se } y^{(i)}=1 \\\\\n-\\log\\left(1-f_{w,b}(x^{(i)})\\right) & \\text{se } y^{(i)}=0\n\\end{cases}",[28,1297,1299,1468],{"className":1298,"ariaHidden":60},[239],[28,1300,1302,1306,1310,1314,1317,1366,1369,1409,1412,1415,1418,1456,1459,1462,1465],{"className":1301},[243],[28,1303],{"className":1304,"style":1305},[247],"height:1.2241em;vertical-align:-0.2861em;",[28,1307,1072],{"className":1308,"style":1309},[252,253],"margin-right:0.0197em;",[28,1311,1313],{"className":1312},[252,253],"oss",[28,1315,54],{"className":1316},[258],[28,1318,1320,1323],{"className":1319},[252],[28,1321,123],{"className":1322,"style":496},[252,253],[28,1324,1326],{"className":1325},[403],[28,1327,1329,1358],{"className":1328},[309,310],[28,1330,1332,1355],{"className":1331},[314],[28,1333,1335],{"className":1334,"style":509},[318],[28,1336,1337,1340],{"style":512},[28,1338],{"className":1339,"style":420},[326],[28,1341,1343],{"className":1342},[331,332,333,334],[28,1344,1346,1349,1352],{"className":1345},[252,334],[28,1347,57],{"className":1348,"style":262},[252,253,334],[28,1350,61],{"className":1351},[266,334],[28,1353,64],{"className":1354},[252,253,334],[28,1356,374],{"className":1357},[373],[28,1359,1361],{"className":1360},[314],[28,1362,1364],{"className":1363,"style":540},[318],[28,1365],{},[28,1367,54],{"className":1368},[258],[28,1370,1372,1375],{"className":1371},[252],[28,1373,138],{"className":1374},[252,253],[28,1376,1378],{"className":1377},[403],[28,1379,1381],{"className":1380},[309],[28,1382,1384],{"className":1383},[314],[28,1385,1388],{"className":1386,"style":1387},[318],"height:0.938em;",[28,1389,1391,1394],{"style":1390},"top:-3.113em;margin-right:0.05em;",[28,1392],{"className":1393,"style":420},[326],[28,1395,1397],{"className":1396},[331,332,333,334],[28,1398,1400,1403,1406],{"className":1399},[252,334],[28,1401,54],{"className":1402},[258,334],[28,1404,96],{"className":1405},[252,253,334],[28,1407,67],{"className":1408},[277,334],[28,1410,67],{"className":1411},[277],[28,1413,61],{"className":1414},[266],[28,1416],{"className":1417,"style":270},[171],[28,1419,1421,1424],{"className":1420},[252],[28,1422,155],{"className":1423,"style":605},[252,253],[28,1425,1427],{"className":1426},[403],[28,1428,1430],{"className":1429},[309],[28,1431,1433],{"className":1432},[314],[28,1434,1436],{"className":1435,"style":1387},[318],[28,1437,1438,1441],{"style":1390},[28,1439],{"className":1440,"style":420},[326],[28,1442,1444],{"className":1443},[331,332,333,334],[28,1445,1447,1450,1453],{"className":1446},[252,334],[28,1448,54],{"className":1449},[258,334],[28,1451,96],{"className":1452},[252,253,334],[28,1454,67],{"className":1455},[277,334],[28,1457,67],{"className":1458},[277],[28,1460],{"className":1461,"style":281},[171],[28,1463,70],{"className":1464},[285],[28,1466],{"className":1467,"style":281},[171],[28,1469,1471,1475],{"className":1470},[243],[28,1472],{"className":1473,"style":1474},[247],"height:3em;vertical-align:-1.25em;",[28,1476,1478,1485,1951],{"className":1477},[476],[28,1479,1481],{"className":1480,"style":484},[258,483],[28,1482,1133],{"className":1483},[488,1484],"size4",[28,1486,1488],{"className":1487},[252],[28,1489,1491,1795,1800],{"className":1490},[1135],[28,1492,1495],{"className":1493},[1494],"col-align-l",[28,1496,1498,1786],{"className":1497},[309,310],[28,1499,1501,1783],{"className":1500},[314],[28,1502,1505,1640],{"className":1503,"style":1504},[318],"height:1.69em;",[28,1506,1508,1512],{"style":1507},"top:-3.69em;",[28,1509],{"className":1510,"style":1511},[326],"height:3.008em;",[28,1513,1515,1518,1521,1529,1532],{"className":1514},[252],[28,1516,108],{"className":1517},[252],[28,1519],{"className":1520,"style":270},[171],[28,1522,1524,1525],{"className":1523},[393],"lo",[28,1526,1528],{"style":1527},"margin-right:0.0139em;","g",[28,1530],{"className":1531,"style":270},[171],[28,1533,1535,1541,1590,1593,1631,1634],{"className":1534},[476],[28,1536,1538],{"className":1537,"style":484},[258,483],[28,1539,54],{"className":1540},[488,489],[28,1542,1544,1547],{"className":1543},[252],[28,1545,123],{"className":1546,"style":496},[252,253],[28,1548,1550],{"className":1549},[403],[28,1551,1553,1582],{"className":1552},[309,310],[28,1554,1556,1579],{"className":1555},[314],[28,1557,1559],{"className":1558,"style":509},[318],[28,1560,1561,1564],{"style":512},[28,1562],{"className":1563,"style":420},[326],[28,1565,1567],{"className":1566},[331,332,333,334],[28,1568,1570,1573,1576],{"className":1569},[252,334],[28,1571,57],{"className":1572,"style":262},[252,253,334],[28,1574,61],{"className":1575},[266,334],[28,1577,64],{"className":1578},[252,253,334],[28,1580,374],{"className":1581},[373],[28,1583,1585],{"className":1584},[314],[28,1586,1588],{"className":1587,"style":540},[318],[28,1589],{},[28,1591,54],{"className":1592},[258],[28,1594,1596,1599],{"className":1595},[252],[28,1597,138],{"className":1598},[252,253],[28,1600,1602],{"className":1601},[403],[28,1603,1605],{"className":1604},[309],[28,1606,1608],{"className":1607},[314],[28,1609,1611],{"className":16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(previsão do modelo)","perda","y=0 (−log(1−f))","y=1 (−log f)",[11,1962,1963,1964,1967,1968,1970,1971,1973,1974,1976,1977,1970,1979,1981,1982,1985,1986,1989],{},"Olha a curva azul (",[867,1965,1966],{},"y=1","): quando ",[867,1969,123],{}," está perto de ",[867,1972,77],{}," (modelo acertou com confiança), a perda cai pra quase ",[867,1975,101],{},". Quando ",[867,1978,123],{},[867,1980,101],{}," (modelo errou feio, disse \"quase certeza que não\" pro caso que era sim), a perda ",[929,1983,1984],{},"explode",", tende a infinito. A curva vermelha (",[867,1987,1988],{},"y=0",") é o espelho exato, virada ao contrário. Diferente da parábola do erro quadrático, essas curvas nunca ficam achatadas: sempre têm inclinação, então gradiente descendente sempre tem uma direção clara pra seguir, por pior que a previsão esteja.",[21,1991,1993],{"id":1992},"uma-linha-só-pra-programar","Uma linha só, pra programar",[11,1995,1996,1997,2000,2001,2003,2004,1013,2006,2008,2009,2011,2012,2015],{},"Duas fórmulas separadas por ",[867,1998,1999],{},"if"," são chatas de programar. Como ",[867,2002,155],{}," só vale ",[867,2005,101],{},[867,2007,77],{},", dá pra combinar as duas num único código, usando ",[867,2010,155],{}," e ",[867,2013,2014],{},"(1-y)"," como interruptores que ligam e desligam cada termo:",[11,2017,2018],{},[28,2019,2021,2159],{"className":2020},[31],[28,2022,2024],{"className":2023},[35],[37,2025,2026],{"xmlns":39},[41,2027,2028,2156],{},[44,2029,2030,2032,2034,2036,2038,2040,2042,2054,2056,2058,2092,2094,2096,2098,2100,2112,2114,2116,2118],{},[47,2031,1072],{},[47,2033,1075],{},[47,2035,1078],{},[47,2037,1078],{},[51,2039,70],{},[51,2041,108],{},[112,2043,2044,2046],{},[47,2045,155],{},[44,2047,2048,2050,2052],{},[51,2049,54],{"stretchy":53},[47,2051,96],{},[51,2053,67],{"stretchy":53},[47,2055,1154],{},[51,2057,1157],{},[44,2059,2060,2062,2074,2076,2088,2090],{},[51,2061,54],{"fence":60},[119,2063,2064,2066],{},[47,2065,123],{},[44,2067,2068,2070,2072],{},[47,2069,57],{},[51,2071,61],{"separator":60},[47,2073,64],{},[51,2075,54],{"stretchy":53},[112,2077,2078,2080],{},[47,2079,138],{},[44,2081,2082,2084,2086],{},[51,2083,54],{"stretchy":53},[47,2085,96],{},[51,2087,67],{"stretchy":53},[51,2089,67],{"stretchy":53},[51,2091,67],{"fence":60},[51,2093,108],{},[51,2095,54],{"stretchy":53},[75,2097,77],{},[51,2099,108],{},[112,2101,2102,2104],{},[47,2103,155],{},[44,2105,2106,2108,2110],{},[51,2107,54],{"stretchy":53},[47,2109,96],{},[51,2111,67],{"stretchy":53},[51,2113,67],{"stretchy":53},[47,2115,1154],{},[51,2117,1157],{},[44,2119,2120,2122,2124,2126,2138,2140,2152,2154],{},[51,2121,54],{"fence":60},[75,2123,77],{},[51,2125,108],{},[119,2127,2128,2130],{},[47,2129,123],{},[44,2131,2132,2134,2136],{},[47,2133,57],{},[51,2135,61],{"separator":60},[47,2137,64],{},[51,2139,54],{"stretchy":53},[112,2141,2142,2144],{},[47,2143,138],{},[44,2145,2146,2148,2150],{},[51,2147,54],{"stretchy":53},[47,2149,96],{},[51,2151,67],{"stretchy":53},[51,2153,67],{"stretchy":53},[51,2155,67],{"fence":60},[232,2157,2158],{"encoding":234},"loss = -y^{(i)}\\log\\left(f_{w,b}(x^{(i)})\\right) - (1-y^{(i)})\\log\\left(1-f_{w,b}(x^{(i)})\\right)",[28,2160,2162,2184,2360,2381],{"className":2161,"ariaHidden":60},[239],[28,2163,2165,2169,2172,2175,2178,2181],{"className":2164},[243],[28,2166],{"className":2167,"style":2168},[247],"height:0.6944em;",[28,2170,1072],{"className":2171,"style":1309},[252,253],[28,2173,1313],{"className":2174},[252,253],[28,2176],{"className":2177,"style":281},[171],[28,2179,70],{"className":2180},[285],[28,2182],{"className":2183,"style":281},[171],[28,2185,2187,2191,2194,2232,2235,2240,2243,2351,2354,2357],{"className":2186},[243],[28,2188],{"className":2189,"style":2190},[247],"height:1.238em;vertical-align:-0.35em;",[28,2192,108],{"className":2193},[252],[28,2195,2197,2200],{"className":2196},[252],[28,2198,155],{"className":2199,"style":605},[252,253],[28,2201,2203],{"className":2202},[403],[28,2204,2206],{"className":2205},[309],[28,2207,2209],{"className":2208},[314],[28,2210,2212],{"className":2211,"style":564},[318],[28,2213,2214,2217],{"style":567},[28,2215],{"className":2216,"style":420},[326],[28,2218,2220],{"className":2219},[331,332,333,334],[28,2221,2223,2226,2229],{"className":2222},[252,334],[28,2224,54],{"className":2225},[258,334],[28,2227,96],{"className":2228},[252,253,334],[28,2230,67],{"className":2231},[277,334],[28,2233],{"className":2234,"style":270},[171],[28,2236,1524,2238],{"className":2237},[393],[28,2239,1528],{"style":1527},[28,2241],{"className":2242,"style":270},[171],[28,2244,2246,2252,2301,2304,2342,2345],{"className":2245},[476],[28,2247,2249],{"className":2248,"style":484},[258,483],[28,2250,54],{"className":2251},[488,489],[28,2253,2255,2258],{"className":2254},[252],[28,2256,123],{"className":2257,"style":496},[252,253],[28,2259,2261],{"className":2260},[403],[28,2262,2264,2293],{"className":2263},[309,310],[28,2265,2267,2290],{"className":2266},[314],[28,2268,2270],{"className":2269,"style":509},[318],[28,2271,2272,2275],{"style":512},[28,2273],{"className":2274,"style":420},[326],[28,2276,2278],{"className":2277},[331,332,333,334],[28,2279,2281,2284,2287],{"className":2280},[252,334],[28,2282,57],{"className":2283,"style":262},[252,253,334],[28,2285,61],{"className":2286},[266,334],[28,2288,64],{"className":2289},[252,253,334],[28,2291,374],{"className":2292},[373],[28,2294,2296],{"className":2295},[314],[28,2297,2299],{"className":2298,"style":540},[318],[28,2300],{},[28,2302,54],{"className":2303},[258],[28,2305,2307,2310],{"className":2306},[252],[28,2308,138],{"className":2309},[252,253],[28,2311,2313],{"className":2312},[403],[28,2314,2316],{"className":2315},[309],[28,2317,2319],{"className":2318},[314],[28,2320,2322],{"className":2321,"style":564},[318],[28,2323,2324,2327],{"style":567},[28,2325],{"className":2326,"style":420},[326],[28,2328,2330],{"className":2329},[331,332,333,334],[28,2331,2333,2336,2339],{"className":2332},[252,334],[28,2334,54],{"className":2335},[258,334],[28,2337,96],{"className":2338},[252,253,334],[28,2340,67],{"className":2341},[277,334],[28,2343,67],{"className":2344},[277],[28,2346,2348],{"className":2347,"style":484},[277,483],[28,2349,67],{"className":2350},[488,489],[28,2352],{"className":2353,"style":592},[171],[28,2355,108],{"className":2356},[454],[28,2358],{"className":2359,"style":592},[171],[28,2361,2363,2366,2369,2372,2375,2378],{"className":2362},[243],[28,2364],{"className":2365,"style":248},[247],[28,2367,54],{"className":2368},[258],[28,2370,77],{"className":2371},[252],[28,2373],{"className":2374,"style":592},[171],[28,2376,108],{"className":2377},[454],[28,2379],{"className":2380,"style":592},[171],[28,2382,2384,2387,2425,2428,2431,2436,2439],{"className":2383},[243],[28,2385],{"className":2386,"style":2190},[247],[28,2388,2390,2393],{"className":2389},[252],[28,2391,155],{"className":2392,"style":605},[252,253],[28,2394,2396],{"className":2395},[403],[28,2397,2399],{"className":2398},[309],[28,2400,2402],{"className":2401},[314],[28,2403,2405],{"className":2404,"style":564},[318],[28,2406,2407,2410],{"style":567},[28,2408],{"className":2409,"style":420},[326],[28,2411,2413],{"className":2412},[331,332,333,334],[28,2414,2416,2419,2422],{"className":2415},[252,334],[28,2417,54],{"className":2418},[258,334],[28,2420,96],{"className":2421},[252,253,334],[28,2423,67],{"className":2424},[277,334],[28,2426,67],{"className":2427},[277],[28,2429],{"className":2430,"style":270},[171],[28,2432,1524,2434],{"className":2433},[393],[28,2435,1528],{"style":1527},[28,2437],{"className":2438,"style":270},[171],[28,2440,2442,2448,2451,2454,2457,2460,2509,2512,2550,2553],{"className":2441},[476],[28,2443,2445],{"className":2444,"style":484},[258,483],[28,2446,54],{"className":2447},[488,489],[28,2449,77],{"className":2450},[252],[28,2452],{"className":2453,"style":592},[171],[28,2455,108],{"className":2456},[454],[28,2458],{"className":2459,"style":592},[171],[28,2461,2463,2466],{"className":2462},[252],[28,2464,123],{"className":2465,"style":496},[252,253],[28,2467,2469],{"className":2468},[403],[28,2470,2472,2501],{"className":2471},[309,310],[28,2473,2475,2498],{"className":2474},[314],[28,2476,2478],{"className":2477,"style":509},[318],[28,2479,2480,2483],{"style":512},[28,2481],{"className":2482,"style":420},[326],[28,2484,2486],{"className":2485},[331,332,333,334],[28,2487,2489,2492,2495],{"className":2488},[252,334],[28,2490,57],{"className":2491,"style":262},[252,253,334],[28,2493,61],{"className":2494},[266,334],[28,2496,64],{"className":2497},[252,253,334],[28,2499,374],{"className":2500},[373],[28,2502,2504],{"className":2503},[314],[28,2505,2507],{"className":2506,"style":540},[318],[28,2508],{},[28,2510,54],{"className":2511},[258],[28,2513,2515,2518],{"className":2514},[252],[28,2516,138],{"className":2517},[252,253],[28,2519,2521],{"className":2520},[403],[28,2522,2524],{"className":2523},[309],[28,2525,2527],{"className":2526},[314],[28,2528,2530],{"className":2529,"style":564},[318],[28,2531,2532,2535],{"style":567},[28,2533],{"className":2534,"style":420},[326],[28,2536,2538],{"className":2537},[331,332,333,334],[28,2539,2541,2544,2547],{"className":2540},[252,334],[28,2542,54],{"className":2543},[258,334],[28,2545,96],{"className":2546},[252,253,334],[28,2548,67],{"className":2549},[277,334],[28,2551,67],{"className":2552},[277],[28,2554,2556],{"className":2555,"style":484},[277,483],[28,2557,67],{"className":2558},[488,489],[11,2560,2561,2562,2564,2565,2568,2569,1976,2572,2574,2575,2578,2579,2581],{},"Quando ",[867,2563,1966],{},", o segundo termo zera (",[867,2566,2567],{},"1-1=0",") e sobra só ",[867,2570,2571],{},"-log(f)",[867,2573,1988],{},", o primeiro termo zera e sobra só ",[867,2576,2577],{},"-log(1-f)",". A mesma linha de código cobre os dois casos, sem ",[867,2580,1999],{}," nenhum.",[21,2583,2585],{"id":2584},"fechando","Fechando",[878,2587,2588,2599],{},[881,2589,2590],{},[884,2591,2592,2596],{},[887,2593,2595],{"align":2594},"left","O que eu já sabia",[887,2597,2598],{"align":2594},"O que essa aula assentou",[894,2600,2601,2609,2617],{},[884,2602,2603,2606],{},[899,2604,2605],{"align":2594},"Erro quadrático dá uma tigela lisa pra regressão linear",[899,2607,2608],{"align":2594},"Erro quadrático + sigmoide não dá mais uma tigela, tem platôs onde o gradiente quase some",[884,2610,2611,2614],{},[899,2612,2613],{"align":2594},"Uma função de perda mede o erro de um exemplo só",[899,2615,2616],{"align":2594},"A perda logística pune forte erro confiante e quase nada acerto confiante, sem nunca ficar achatada",[884,2618,2619,2628],{},[899,2620,2621,2623,2624,2627],{"align":2594},[867,2622,1999],{},"\u002F",[867,2625,2626],{},"else"," separa casos",[899,2629,2630,2011,2632,2634,2635],{"align":2594},[867,2631,155],{},[867,2633,2014],{}," como interruptores combinam os dois casos numa fórmula só, sem ",[867,2636,1999],{},[21,2638,2640],{"id":2639},"aplicação-prática","Aplicação Prática",[11,2642,2643,2644,2648,2649,2652,2653,2656],{},"Usando o modelo logístico já ajustado ",[15,2645,2647],{"href":2646},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab02-sigmoid-function","no lab da sigmoide"," (",[867,2650,2651],{},"w=3.9565, b=-1.1326",", variável ",[867,2654,2655],{},"worst concave points","), calculo a perda de três pacientes reais do conjunto de teste, escolhidos pra mostrar os dois extremos e o meio:",[2658,2659,2664],"pre",{"className":2660,"code":2661,"language":2662,"meta":2663,"style":2663},"language-python shiki shiki-themes github-light github-dark","for nome, x, y_real in pacientes:\n    f = sigmoid(w*x + b)\n    loss = -y_real*np.log(f) - (1-y_real)*np.log(1-f)\n    print(f\"{nome}: f={f:.4f} loss={loss:.4f}\")\n","python","",[867,2665,2666,2673,2679,2685],{"__ignoreMap":2663},[28,2667,2670],{"class":2668,"line":2669},"line",1,[28,2671,2672],{},"for nome, x, y_real in pacientes:\n",[28,2674,2676],{"class":2668,"line":2675},2,[28,2677,2678],{},"    f = sigmoid(w*x + b)\n",[28,2680,2682],{"class":2668,"line":2681},3,[28,2683,2684],{},"    loss = -y_real*np.log(f) - (1-y_real)*np.log(1-f)\n",[28,2686,2688],{"class":2668,"line":2687},4,[28,2689,2690],{},"    print(f\"{nome}: f={f:.4f} loss={loss:.4f}\")\n",[2692,2693,2694,2699],"blockquote",{},[11,2695,2696],{},[929,2697,2698],{},"Saída:",[878,2700,2701,2719],{},[881,2702,2703],{},[884,2704,2705,2708,2710,2714,2717],{},[887,2706,2707],{"align":2594},"Paciente",[887,2709,2655],{"align":889},[887,2711,2713],{"align":2712},"center","y real",[887,2715,2716],{"align":889},"f(x)",[887,2718,1958],{"align":889},[894,2720,2721,2737,2752],{},[884,2722,2723,2726,2729,2731,2734],{},[899,2724,2725],{"align":2594},"Maligno claro",[899,2727,2728],{"align":889},"0.2867",[899,2730,77],{"align":2712},[899,2732,2733],{"align":889},"0.9999",[899,2735,2736],{"align":889},"0.0001",[884,2738,2739,2742,2745,2747,2750],{},[899,2740,2741],{"align":2594},"Benigno claro",[899,2743,2744],{"align":889},"0.0000",[899,2746,101],{"align":2712},[899,2748,2749],{"align":889},"0.0003",[899,2751,2749],{"align":889},[884,2753,2754,2757,2760,2762,2765],{},[899,2755,2756],{"align":2594},"Ambíguo",[899,2758,2759],{"align":889},"0.1335",[899,2761,101],{"align":2712},[899,2763,2764],{"align":889},"0.5097",[899,2766,2767],{"align":889},"0.7127",[11,2769,2770,2771,2774,2775,2777],{},"Os dois primeiros pacientes o modelo acerta com convicção total, a perda deles é praticamente zero. O terceiro é o caso ambíguo, bem em cima da fronteira de decisão (o modelo achou ",[867,2772,2773],{},"51%"," de chance de ser maligno, mas o paciente era benigno), e a perda dele sozinho (",[867,2776,2767],{},") já é maior que a soma dos outros dois juntos. É exatamente esse tipo de ponto, perto da fronteira e classificado errado, que mais empurra o ajuste durante o treino, porque é ele que carrega a perda alta.",[2779,2780,2781],"style",{},"html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":2663,"searchDepth":2675,"depth":2675,"links":2783},[2784,2785,2786,2787,2788],{"id":23,"depth":2675,"text":24},{"id":1042,"depth":2675,"text":1043},{"id":1992,"depth":2675,"text":1993},{"id":2584,"depth":2675,"text":2585},{"id":2639,"depth":2675,"text":2640},null,"2026-09-04","Semana 3, Lab 4: a mesma função de custo que funcionava tão bem pra regressão linear vira uma superfície cheia de platôs quando espremida atrás de uma sigmoide. A solução é trocar de função de perda, não de modelo.","md",{},true,15,"\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab04-logistic-loss","machine-learning-specialization",{"title":6,"description":2791},"published","pt\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab04-logistic-loss",[2802,2803,2804],"classificacao","regressao-logistica","funcao-de-custo","5HDnxtUNrGtQ1GTeqqfEdnN-PiqxcSsLDZx3mJqDXCg",1788965098423]