[{"data":1,"prerenderedAt":1341},["ShallowReactive",2],{"lang-switch-post-\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab02-sigmoid-function":3,"post-pt-machine-learning-specialization-w3-lab02-sigmoid-function":4},"\u002Fen\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab02-sigmoid-function",{"id":5,"title":6,"body":7,"cover":1324,"date":1325,"description":1326,"extension":1327,"meta":1328,"navigation":1329,"order":1330,"path":1331,"playlist":1332,"seo":1333,"status":1334,"stem":1335,"tags":1336,"__hash__":1340},"posts\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab02-sigmoid-function.md","A Função Sigmoide: Botando um Teto na Regressão",{"type":8,"value":9,"toc":1317},"minimark",[10,32,37,291,335,363,439,525,529,533,644,1015,1142,1146,1149,1164,1183,1187,1230,1234,1246,1255,1266,1274,1289,1306,1313],[11,12,13,18,19,23,24,27,28,31],"p",{},[14,15,17],"a",{"href":16},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab01-classification","No lab passado",", a saída crua da regressão linear chegou a ",[20,21,22],"code",{},"1.4043"," num paciente real, um número que não significa nada como \"probabilidade de câncer\". Faltava um teto. É exatamente isso que a função sigmoide (também chamada de função logística) resolve: ela pega qualquer número, positivo, negativo, gigante, minúsculo, e devolve sempre algo entre ",[20,25,26],{},"0"," e ",[20,29,30],{},"1",".",[33,34,36],"h2",{"id":35},"a-fórmula-sem-drama","A fórmula, sem drama",[11,38,39],{},[40,41,44,107],"span",{"className":42},[43],"katex",[40,45,48],{"className":46},[47],"katex-mathml",[49,50,52],"math",{"xmlns":51},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[53,54,55,102],"semantics",{},[56,57,58,62,67,70,73,76],"mrow",{},[59,60,61],"mi",{},"g",[63,64,66],"mo",{"stretchy":65},"false","(",[59,68,69],{},"z",[63,71,72],{"stretchy":65},")",[63,74,75],{},"=",[77,78,79,82],"mfrac",{},[80,81,30],"mn",{},[56,83,84,86,89],{},[80,85,30],{},[63,87,88],{},"+",[90,91,92,95],"msup",{},[59,93,94],{},"e",[56,96,97,100],{},[63,98,99],{},"−",[59,101,69],{},[103,104,106],"annotation",{"encoding":105},"application\u002Fx-tex","g(z) = \\frac{1}{1+e^{-z}}",[40,108,112,151],{"className":109,"ariaHidden":111},[110],"katex-html","true",[40,113,116,121,127,131,135,139,144,148],{"className":114},[115],"base",[40,117],{"className":118,"style":120},[119],"strut","height:1em;vertical-align:-0.25em;",[40,122,61],{"className":123,"style":126},[124,125],"mord","mathnormal","margin-right:0.0359em;",[40,128,66],{"className":129},[130],"mopen",[40,132,69],{"className":133,"style":134},[124,125],"margin-right:0.044em;",[40,136,72],{"className":137},[138],"mclose",[40,140],{"className":141,"style":143},[142],"mspace","margin-right:0.2778em;",[40,145,75],{"className":146},[147],"mrel",[40,149],{"className":150,"style":143},[142],[40,152,154,158],{"className":153},[115],[40,155],{"className":156,"style":157},[119],"height:1.2484em;vertical-align:-0.4033em;",[40,159,161,165,288],{"className":160},[124],[40,162],{"className":163},[130,164],"nulldelimiter",[40,166,168],{"className":167},[77],[40,169,173,279],{"className":170},[171,172],"vlist-t","vlist-t2",[40,174,177,274],{"className":175},[176],"vlist-r",[40,178,182,248,259],{"className":179,"style":181},[180],"vlist","height:0.8451em;",[40,183,185,190],{"style":184},"top:-2.655em;",[40,186],{"className":187,"style":189},[188],"pstrut","height:3em;",[40,191,197],{"className":192},[193,194,195,196],"sizing","reset-size6","size3","mtight",[40,198,200,203,207],{"className":199},[124,196],[40,201,30],{"className":202},[124,196],[40,204,88],{"className":205},[206,196],"mbin",[40,208,210,213],{"className":209},[124,196],[40,211,94],{"className":212},[124,125,196],[40,214,217],{"className":215},[216],"msupsub",[40,218,220],{"className":219},[171],[40,221,223],{"className":222},[176],[40,224,227],{"className":225,"style":226},[180],"height:0.7027em;",[40,228,230,234],{"style":229},"top:-2.786em;margin-right:0.0714em;",[40,231],{"className":232,"style":233},[188],"height:2.5em;",[40,235,239],{"className":236},[193,237,238,196],"reset-size3","size1",[40,240,242,245],{"className":241},[124,196],[40,243,99],{"className":244},[124,196],[40,246,69],{"className":247,"style":134},[124,125,196],[40,249,251,254],{"style":250},"top:-3.23em;",[40,252],{"className":253,"style":189},[188],[40,255],{"className":256,"style":258},[257],"frac-line","border-bottom-width:0.04em;",[40,260,262,265],{"style":261},"top:-3.394em;",[40,263],{"className":264,"style":189},[188],[40,266,268],{"className":267},[193,194,195,196],[40,269,271],{"className":270},[124,196],[40,272,30],{"className":273},[124,196],[40,275,278],{"className":276},[277],"vlist-s","​",[40,280,282],{"className":281},[176],[40,283,286],{"className":284,"style":285},[180],"height:0.4033em;",[40,287],{},[40,289],{"className":290},[138,164],[11,292,293,294,296,297,300,301,303,304,306,307,309,310,312,313,315,316,319,320,323,324,328,329,331,332,334],{},"Não precisa decorar essa fórmula de cor pra entender o que ela faz: quando ",[20,295,69],{}," é bem negativo, ",[20,298,299],{},"e^(-z)"," explode e a fração vira quase ",[20,302,26],{},". Quando ",[20,305,69],{}," é bem positivo, ",[20,308,299],{}," encolhe pra quase ",[20,311,26],{}," e a fração vira quase ",[20,314,30],{},". No meio, ",[20,317,318],{},"z=0",", dá exatamente ",[20,321,322],{},"0.5",". Ela nunca ",[325,326,327],"strong",{},"chega"," em ",[20,330,26],{}," ou ",[20,333,30],{}," de verdade, só se aproxima cada vez mais.",[336,337,342],"pre",{"className":338,"code":339,"language":340,"meta":341,"style":341},"language-python shiki shiki-themes github-light github-dark","def sigmoid(z):\n    g = 1\u002F(1+np.exp(-z))\n    return g\n","python","",[20,343,344,351,357],{"__ignoreMap":341},[40,345,348],{"class":346,"line":347},"line",1,[40,349,350],{},"def sigmoid(z):\n",[40,352,354],{"class":346,"line":353},2,[40,355,356],{},"    g = 1\u002F(1+np.exp(-z))\n",[40,358,360],{"class":346,"line":359},3,[40,361,362],{},"    return g\n",[11,364,365,366,369,370,432,433,438],{},"Quatro linhas. ",[20,367,368],{},"np.exp"," calcula ",[40,371,373,391],{"className":372},[43],[40,374,376],{"className":375},[47],[49,377,378],{"xmlns":51},[53,379,380,388],{},[56,381,382],{},[90,383,384,386],{},[59,385,94],{},[59,387,69],{},[103,389,390],{"encoding":105},"e^z",[40,392,394],{"className":393,"ariaHidden":111},[110],[40,395,397,401],{"className":396},[115],[40,398],{"className":399,"style":400},[119],"height:0.6644em;",[40,402,404,407],{"className":403},[124],[40,405,94],{"className":406},[124,125],[40,408,410],{"className":409},[216],[40,411,413],{"className":412},[171],[40,414,416],{"className":415},[176],[40,417,419],{"className":418,"style":400},[180],[40,420,422,426],{"style":421},"top:-3.063em;margin-right:0.05em;",[40,423],{"className":424,"style":425},[188],"height:2.7em;",[40,427,429],{"className":428},[193,194,195,196],[40,430,69],{"className":431,"style":134},[124,125,196]," elemento a elemento, então essa mesma função funciona tanto pra um número só quanto pra um array inteiro de uma vez (",[434,435,437],"glossary-term",{"definition":436},"fazer a conta em cima do array inteiro de uma vez, sem passar item por item","vetorização",").",[440,441,442,451],"blockquote",{},[11,443,444,447,448,450],{},[325,445,446],{},"Saída"," (",[20,449,69],{}," de -10 a 10, alguns valores):",[452,453,454,467],"table",{},[455,456,457],"thead",{},[458,459,460,464],"tr",{},[461,462,69],"th",{"align":463},"right",[461,465,466],{"align":463},"sigmoid(z)",[468,469,470,479,487,495,502,509,517],"tbody",{},[458,471,472,476],{},[473,474,475],"td",{"align":463},"-10",[473,477,478],{"align":463},"0.0000",[458,480,481,484],{},[473,482,483],{"align":463},"-2",[473,485,486],{"align":463},"0.1192",[458,488,489,492],{},[473,490,491],{"align":463},"-1",[473,493,494],{"align":463},"0.2689",[458,496,497,499],{},[473,498,26],{"align":463},[473,500,501],{"align":463},"0.5000",[458,503,504,506],{},[473,505,30],{"align":463},[473,507,508],{"align":463},"0.7311",[458,510,511,514],{},[473,512,513],{"align":463},"2",[473,515,516],{"align":463},"0.8808",[458,518,519,522],{},[473,520,521],{"align":463},"10",[473,523,524],{"align":463},"1.0000",[526,527],"sigmoid-curve-chart",{"curve-label":466,"threshold-label":528,"x-label":69,"y-label":466},"limiar (z=0, sigmoid=0.5)",[33,530,532],{"id":531},"regressão-logística-regressão-linear-com-um-teto-embutido","Regressão logística: regressão linear com um teto embutido",[11,534,535,536,643],{},"Regressão logística é só isso: pega o modelo linear de sempre, ",[40,537,539,570],{"className":538},[43],[40,540,542],{"className":541},[47],[49,543,544],{"xmlns":51},[53,545,546,567],{},[56,547,548,550,552,556,559,562,564],{},[59,549,69],{},[63,551,75],{},[59,553,555],{"mathvariant":554},"bold","w",[63,557,558],{},"⋅",[59,560,561],{"mathvariant":554},"x",[63,563,88],{},[59,565,566],{},"b",[103,568,569],{"encoding":105},"z = \\mathbf{w}\\cdot\\mathbf{x}+b",[40,571,573,592,614,633],{"className":572,"ariaHidden":111},[110],[40,574,576,580,583,586,589],{"className":575},[115],[40,577],{"className":578,"style":579},[119],"height:0.4306em;",[40,581,69],{"className":582,"style":134},[124,125],[40,584],{"className":585,"style":143},[142],[40,587,75],{"className":588},[147],[40,590],{"className":591,"style":143},[142],[40,593,595,599,604,608,611],{"className":594},[115],[40,596],{"className":597,"style":598},[119],"height:0.4445em;",[40,600,555],{"className":601,"style":603},[124,602],"mathbf","margin-right:0.016em;",[40,605],{"className":606,"style":607},[142],"margin-right:0.2222em;",[40,609,558],{"className":610},[206],[40,612],{"className":613,"style":607},[142],[40,615,617,621,624,627,630],{"className":616},[115],[40,618],{"className":619,"style":620},[119],"height:0.6667em;vertical-align:-0.0833em;",[40,622,561],{"className":623},[124,602],[40,625],{"className":626,"style":607},[142],[40,628,88],{"className":629},[206],[40,631],{"className":632,"style":607},[142],[40,634,636,640],{"className":635},[115],[40,637],{"className":638,"style":639},[119],"height:0.6944em;",[40,641,566],{"className":642},[124,125],", e passa o resultado pela sigmoide.",[11,645,646],{},[40,647,649,734],{"className":648},[43],[40,650,652],{"className":651},[47],[49,653,654],{"xmlns":51},[53,655,656,731],{},[56,657,658,673,675,677,679,681,683,685,687,689,691,693,695,697,699],{},[659,660,661,664],"msub",{},[59,662,663],{},"f",[56,665,666,668,671],{},[59,667,555],{"mathvariant":554},[63,669,670],{"separator":111},",",[59,672,566],{},[63,674,66],{"stretchy":65},[59,676,561],{"mathvariant":554},[63,678,72],{"stretchy":65},[63,680,75],{},[59,682,61],{},[63,684,66],{"stretchy":65},[59,686,555],{"mathvariant":554},[63,688,558],{},[59,690,561],{"mathvariant":554},[63,692,88],{},[59,694,566],{},[63,696,72],{"stretchy":65},[63,698,75],{},[77,700,701,703],{},[80,702,30],{},[56,704,705,707,709],{},[80,706,30],{},[63,708,88],{},[90,710,711,713],{},[59,712,94],{},[56,714,715,717,719,721,723,725,727,729],{},[63,716,99],{},[63,718,66],{"stretchy":65},[59,720,555],{"mathvariant":554},[63,722,558],{},[59,724,561],{"mathvariant":554},[63,726,88],{},[59,728,566],{},[63,730,72],{"stretchy":65},[103,732,733],{"encoding":105},"f_{\\mathbf{w},b}(\\mathbf{x}) = g(\\mathbf{w}\\cdot\\mathbf{x}+b) = \\frac{1}{1+e^{-(\\mathbf{w}\\cdot\\mathbf{x}+b)}}",[40,735,737,816,840,858,879],{"className":736,"ariaHidden":111},[110],[40,738,740,744,798,801,804,807,810,813],{"className":739},[115],[40,741],{"className":742,"style":743},[119],"height:1.0361em;vertical-align:-0.2861em;",[40,745,747,751],{"className":746},[124],[40,748,663],{"className":749,"style":750},[124,125],"margin-right:0.1076em;",[40,752,754],{"className":753},[216],[40,755,757,789],{"className":756},[171,172],[40,758,760,786],{"className":759},[176],[40,761,764],{"className":762,"style":763},[180],"height:0.3361em;",[40,765,767,770],{"style":766},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[40,768],{"className":769,"style":425},[188],[40,771,773],{"className":772},[193,194,195,196],[40,774,776,779,783],{"className":775},[124,196],[40,777,555],{"className":778,"style":603},[124,602,196],[40,780,670],{"className":781},[782,196],"mpunct",[40,784,566],{"className":785},[124,125,196],[40,787,278],{"className":788},[277],[40,790,792],{"className":791},[176],[40,793,796],{"className":794,"style":795},[180],"height:0.2861em;",[40,797],{},[40,799,66],{"className":800},[130],[40,802,561],{"className":803},[124,602],[40,805,72],{"className":806},[138],[40,808],{"className":809,"style":143},[142],[40,811,75],{"className":812},[147],[40,814],{"className":815,"style":143},[142],[40,817,819,822,825,828,831,834,837],{"className":818},[115],[40,820],{"className":821,"style":120},[119],[40,823,61],{"className":824,"style":126},[124,125],[40,826,66],{"className":827},[130],[40,829,555],{"className":830,"style":603},[124,602],[40,832],{"className":833,"style":607},[142],[40,835,558],{"className":836},[206],[40,838],{"className":839,"style":607},[142],[40,841,843,846,849,852,855],{"className":842},[115],[40,844],{"className":845,"style":620},[119],[40,847,561],{"className":848},[124,602],[40,850],{"className":851,"style":607},[142],[40,853,88],{"className":854},[206],[40,856],{"className":857,"style":607},[142],[40,859,861,864,867,870,873,876],{"className":860},[115],[40,862],{"className":863,"style":120},[119],[40,865,566],{"className":866},[124,125],[40,868,72],{"className":869},[138],[40,871],{"className":872,"style":143},[142],[40,874,75],{"className":875},[147],[40,877],{"className":878,"style":143},[142],[40,880,882,886],{"className":881},[115],[40,883],{"className":884,"style":885},[119],"height:1.2889em;vertical-align:-0.4438em;",[40,887,889,892,1012],{"className":888},[124],[40,890],{"className":891},[130,164],[40,893,895],{"className":894},[77],[40,896,898,1003],{"className":897},[171,172],[40,899,901,1000],{"className":900},[176],[40,902,904,978,986],{"className":903,"style":181},[180],[40,905,907,910],{"style":906},"top:-2.6146em;",[40,908],{"className":909,"style":189},[188],[40,911,913],{"className":912},[193,194,195,196],[40,914,916,919,922],{"className":915},[124,196],[40,917,30],{"className":918},[124,196],[40,920,88],{"className":921},[206,196],[40,923,925,928],{"className":924},[124,196],[40,926,94],{"className":927},[124,125,196],[40,929,931],{"className":930},[216],[40,932,934],{"className":933},[171],[40,935,937],{"className":936},[176],[40,938,941],{"className":939,"style":940},[180],"height:0.822em;",[40,942,944,948],{"style":943},"top:-2.822em;margin-right:0.0714em;",[40,945],{"className":946,"style":947},[188],"height:2.5357em;",[40,949,951],{"className":950},[193,237,238,196],[40,952,954,957,960,963,966,969,972,975],{"className":953},[124,196],[40,955,99],{"className":956},[124,196],[40,958,66],{"className":959},[130,196],[40,961,555],{"className":962,"style":603},[124,602,196],[40,964,558],{"className":965},[206,196],[40,967,561],{"className":968},[124,602,196],[40,970,88],{"className":971},[206,196],[40,973,566],{"className":974},[124,125,196],[40,976,72],{"className":977},[138,196],[40,979,980,983],{"style":250},[40,981],{"className":982,"style":189},[188],[40,984],{"className":985,"style":258},[257],[40,987,988,991],{"style":261},[40,989],{"className":990,"style":189},[188],[40,992,994],{"className":993},[193,194,195,196],[40,995,997],{"className":996},[124,196],[40,998,30],{"className":999},[124,196],[40,1001,278],{"className":1002},[277],[40,1004,1006],{"className":1005},[176],[40,1007,1010],{"className":1008,"style":1009},[180],"height:0.4438em;",[40,1011],{},[40,1013],{"className":1014},[138,164],[11,1016,1017,1018,1118,1119,1122,1123,1126,1127,1129,1130,1132,1133,1136,1137,1139,1140,31],{},"A saída ",[40,1019,1021,1051],{"className":1020},[43],[40,1022,1024],{"className":1023},[47],[49,1025,1026],{"xmlns":51},[53,1027,1028,1048],{},[56,1029,1030,1042,1044,1046],{},[659,1031,1032,1034],{},[59,1033,663],{},[56,1035,1036,1038,1040],{},[59,1037,555],{"mathvariant":554},[63,1039,670],{"separator":111},[59,1041,566],{},[63,1043,66],{"stretchy":65},[59,1045,561],{"mathvariant":554},[63,1047,72],{"stretchy":65},[103,1049,1050],{"encoding":105},"f_{\\mathbf{w},b}(\\mathbf{x})",[40,1052,1054],{"className":1053,"ariaHidden":111},[110],[40,1055,1057,1060,1109,1112,1115],{"className":1056},[115],[40,1058],{"className":1059,"style":743},[119],[40,1061,1063,1066],{"className":1062},[124],[40,1064,663],{"className":1065,"style":750},[124,125],[40,1067,1069],{"className":1068},[216],[40,1070,1072,1101],{"className":1071},[171,172],[40,1073,1075,1098],{"className":1074},[176],[40,1076,1078],{"className":1077,"style":763},[180],[40,1079,1080,1083],{"style":766},[40,1081],{"className":1082,"style":425},[188],[40,1084,1086],{"className":1085},[193,194,195,196],[40,1087,1089,1092,1095],{"className":1088},[124,196],[40,1090,555],{"className":1091,"style":603},[124,602,196],[40,1093,670],{"className":1094},[782,196],[40,1096,566],{"className":1097},[124,125,196],[40,1099,278],{"className":1100},[277],[40,1102,1104],{"className":1103},[176],[40,1105,1107],{"className":1106,"style":795},[180],[40,1108],{},[40,1110,66],{"className":1111},[130],[40,1113,561],{"className":1114},[124,602],[40,1116,72],{"className":1117},[138]," agora é interpretada como uma ",[325,1120,1121],{},"probabilidade",": a chance estimada de ",[20,1124,1125],{},"y=1"," dado ",[20,1128,561],{},". Pra virar decisão final, o mesmo corte em ",[20,1131,322],{}," de antes: ",[20,1134,1135],{},"f >= 0.5"," prevê ",[20,1138,30],{},", senão prevê ",[20,1141,26],{},[33,1143,1145],{"id":1144},"o-mesmo-teste-do-lab-passado-agora-com-teto","O mesmo teste do lab passado, agora com teto",[11,1147,1148],{},"Volto pro mesmo exemplo do tumor, só que agora com a caixinha pra trocar entre regressão linear e logística:",[1150,1151],"threshold-fit-explorer",{":allow-logistic-toggle":111,":base-points":1152,":outlier-points":1153,"accuracy-label":1154,"add-outlier-label":1155,"class0-label":1156,"class1-label":1157,"correct-label":1158,"logistic-toggle-label":1159,"remove-outlier-label":1160,"threshold-label":1161,"wrong-label":1162,"x-label":1163},"[[0,0],[1,0],[2,0],[3,1],[4,1],[5,1]]","[[10,1],[11,1]]","acurácia","Adicionar tumores grandes (malignos)","Benigno","Maligno","Acertou","usar regressão logística (sigmoide) em vez de linear","Remover tumores grandes","Fronteira de decisão","Errou","tamanho do tumor",[11,1165,1166,1167,1170,1171,1174,1175,27,1177,1179,1180,1182],{},"Adiciona os tumores grandes de novo (igual no lab passado): com regressão linear, ",[20,1168,1169],{},"x=3"," continua sendo classificado errado. Marca \"usar regressão logística\": a curva sigmoide, diferente da reta, ",[325,1172,1173],{},"acha um jeito de acomodar os novos pontos extremos sem se distorcer no meio",", porque ela já satura perto de ",[20,1176,26],{},[20,1178,30],{}," em vez de continuar crescendo pra sempre. ",[20,1181,1169],{}," volta a ser classificado certo. Nenhum ponto mudou de lugar, só o formato do modelo que aprende os dados mudou.",[33,1184,1186],{"id":1185},"fechando","Fechando",[452,1188,1189,1200],{},[455,1190,1191],{},[458,1192,1193,1197],{},[461,1194,1196],{"align":1195},"left","O que eu já sabia",[461,1198,1199],{"align":1195},"O que essa aula assentou",[468,1201,1202,1210,1222],{},[458,1203,1204,1207],{},[473,1205,1206],{"align":1195},"Regressão linear não tem teto na saída",[473,1208,1209],{"align":1195},"A sigmoide espreme qualquer número real pro intervalo (0, 1)",[458,1211,1212,1219],{},[473,1213,1214,1215,1218],{"align":1195},"Um ",[20,1216,1217],{},"> 0.5"," transforma número em decisão",[473,1220,1221],{"align":1195},"Isso continua valendo, só que agora o número que passa pelo corte é uma probabilidade de verdade, nunca maior que 1",[458,1223,1224,1227],{},[473,1225,1226],{"align":1195},"Regressão linear se distorce com ponto extremo",[473,1228,1229],{"align":1195},"Regressão logística (linear + sigmoide) resiste ao mesmo ponto extremo, porque a curva satura em vez de continuar subindo",[33,1231,1233],{"id":1232},"aplicação-prática","Aplicação Prática",[11,1235,1236,1238,1239,1242,1243,1245],{},[14,1237,17],{"href":16},", a regressão linear crua no dataset real de câncer de mama (",[20,1240,1241],{},"worst concave points",", 569 pacientes) chegou a devolver ",[20,1244,22],{}," pra um paciente, um número sem sentido como probabilidade. Aplico a sigmoide direto nesse mesmo número:",[336,1247,1249],{"className":338,"code":1248,"language":340,"meta":341,"style":341},"print(sigmoid(1.4043))\n",[20,1250,1251],{"__ignoreMap":341},[40,1252,1253],{"class":346,"line":347},[40,1254,1248],{},[440,1256,1257],{},[11,1258,1259,1262,1263,31],{},[325,1260,1261],{},"Saída:"," ",[20,1264,1265],{},"0.8028",[11,1267,1268,1270,1271,1273],{},[20,1269,1265],{}," já é uma resposta que faz sentido: \"80% de chance de ser maligno\". Ajusto a regressão logística de verdade nesse dataset (gradiente descendente, a mesma variável ",[20,1272,1241],{},", normalizada):",[336,1275,1277],{"className":338,"code":1276,"language":340,"meta":341,"style":341},"w, b = fit_logistic_1d(X_train_z, y_train)\nprint(f\"w={w:.4f} b={b:.4f}\")\n",[20,1278,1279,1284],{"__ignoreMap":341},[40,1280,1281],{"class":346,"line":347},[40,1282,1283],{},"w, b = fit_logistic_1d(X_train_z, y_train)\n",[40,1285,1286],{"class":346,"line":353},[40,1287,1288],{},"print(f\"w={w:.4f} b={b:.4f}\")\n",[440,1290,1291],{},[11,1292,1293,1262,1295,1298,1299,1302,1303,31],{},[325,1294,1261],{},[20,1296,1297],{},"w=3.9565 b=-1.1326",", acurácia de treino ",[325,1300,1301],{},"0.9055",", acurácia de teste ",[325,1304,1305],{},"0.9211",[11,1307,1308,1309,1312],{},"Nesse dataset em particular, sem outlier chamativo, a acurácia da versão logística fica bem próxima da versão linear do lab passado (0.9099\u002F0.9298 lá, 0.9055\u002F0.9211 aqui), porque os pacientes reais não têm um \"tumor de tamanho 10\" absurdo puxando a reta. A diferença que importa não é a acurácia nesse dataset específico, é a ",[325,1310,1311],{},"saída",": toda previsão da versão logística já nasce entre 0 e 1, pronta pra ser lida como probabilidade, sem precisar confiar que nenhum paciente futuro vai ter um valor extremo o bastante pra fazer a conta explodir.",[1314,1315,1316],"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":341,"searchDepth":353,"depth":353,"links":1318},[1319,1320,1321,1322,1323],{"id":35,"depth":353,"text":36},{"id":531,"depth":353,"text":532},{"id":1144,"depth":353,"text":1145},{"id":1185,"depth":353,"text":1186},{"id":1232,"depth":353,"text":1233},null,"2026-09-04","Semana 3, Lab 2: a saída da regressão linear não tinha teto, então o curso enfia ela dentro de uma função que sempre devolve algo entre 0 e 1. A sigmoide é isso: um jeito de espremer qualquer número numa probabilidade.","md",{},true,13,"\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab02-sigmoid-function","machine-learning-specialization",{"title":6,"description":1326},"published","pt\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab02-sigmoid-function",[1337,1338,1339],"classificacao","regressao-logistica","sigmoide","_1zvbhlxwYUXCU6PizJBGxzizUQmyMk_h0mEh8cU0OU",1788965098070]