[{"data":1,"prerenderedAt":1787},["ShallowReactive",2],{"lang-switch-post-\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab03-decision-boundary":3,"post-pt-machine-learning-specialization-w3-lab03-decision-boundary":4},"\u002Fen\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab03-decision-boundary",{"id":5,"title":6,"body":7,"cover":1770,"date":1771,"description":1772,"extension":1773,"meta":1774,"navigation":1775,"order":1776,"path":1777,"playlist":1778,"seo":1779,"status":1780,"stem":1781,"tags":1782,"__hash__":1786},"posts\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab03-decision-boundary.md","Fronteira de Decisão: Onde a Sigmoide Muda de Ideia",{"type":8,"value":9,"toc":1763},"minimark",[10,33,38,61,80,84,97,365,379,752,1101,1109,1118,1122,1620,1624,1680,1684,1702,1717,1739,1742,1753,1759],[11,12,13,18,19,23,24,27,28,32],"p",{},[14,15,17],"a",{"href":16},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab02-sigmoid-function","Já vi a sigmoide"," espremer qualquer número pra dentro de ",[20,21,22],"code",{},"(0, 1)",", e o corte em ",[20,25,26],{},"0.5"," decidindo a classe final. Esse lab pega um exemplo com ",[29,30,31],"strong",{},"duas"," variáveis de entrada e mostra onde, geometricamente, esse corte acontece.",[34,35,37],"h2",{"id":36},"o-dado-dois-pacientes-duas-variáveis","O dado: dois pacientes, duas variáveis",[39,40,45],"pre",{"className":41,"code":42,"language":43,"meta":44,"style":44},"language-python shiki shiki-themes github-light github-dark","X = np.array([[0.5, 1.5], [1,1], [1.5, 0.5], [3, 0.5], [2, 2], [1, 2.5]])\ny = np.array([0, 0, 0, 1, 1, 1])\n","python","",[20,46,47,55],{"__ignoreMap":44},[48,49,52],"span",{"class":50,"line":51},"line",1,[48,53,54],{},"X = np.array([[0.5, 1.5], [1,1], [1.5, 0.5], [3, 0.5], [2, 2], [1, 2.5]])\n",[48,56,58],{"class":50,"line":57},2,[48,59,60],{},"y = np.array([0, 0, 0, 1, 1, 1])\n",[11,62,63,64,67,68,71,72,75,76,79],{},"Seis pacientes, cada um com duas variáveis (",[20,65,66],{},"x0",", ",[20,69,70],{},"x1","). Os três primeiros são ",[20,73,74],{},"y=0",", os três últimos são ",[20,77,78],{},"y=1",".",[34,81,83],{"id":82},"onde-fica-o-corte-em-05","Onde fica o corte em 0.5",[11,85,86,87,67,90,67,93,96],{},"Suponha que o modelo já foi treinado (o \"como treinar\" é assunto dos próximos dois labs) e chegou nesses parâmetros: ",[20,88,89],{},"b=-3",[20,91,92],{},"w0=1",[20,94,95],{},"w1=1",". O modelo é",[11,98,99],{},[48,100,103,173],{"className":101},[102],"katex",[48,104,107],{"className":105},[106],"katex-mathml",[108,109,111],"math",{"xmlns":110},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[112,113,114,168],"semantics",{},[115,116,117,121,126,130,133,136,139,141,150,153,160,163,166],"mrow",{},[118,119,120],"mi",{},"f",[122,123,125],"mo",{"stretchy":124},"false","(",[118,127,129],{"mathvariant":128},"bold","x",[122,131,132],{"stretchy":124},")",[122,134,135],{},"=",[118,137,138],{},"g",[122,140,125],{"stretchy":124},[142,143,144,146],"msub",{},[118,145,129],{},[147,148,149],"mn",{},"0",[122,151,152],{},"+",[142,154,155,157],{},[118,156,129],{},[147,158,159],{},"1",[122,161,162],{},"−",[147,164,165],{},"3",[122,167,132],{"stretchy":124},[169,170,172],"annotation",{"encoding":171},"application\u002Fx-tex","f(\\mathbf{x}) = g(x_0+x_1-3)",[48,174,178,217,297,353],{"className":175,"ariaHidden":177},[176],"katex-html","true",[48,179,182,187,193,197,201,205,210,214],{"className":180},[181],"base",[48,183],{"className":184,"style":186},[185],"strut","height:1em;vertical-align:-0.25em;",[48,188,120],{"className":189,"style":192},[190,191],"mord","mathnormal","margin-right:0.1076em;",[48,194,125],{"className":195},[196],"mopen",[48,198,129],{"className":199},[190,200],"mathbf",[48,202,132],{"className":203},[204],"mclose",[48,206],{"className":207,"style":209},[208],"mspace","margin-right:0.2778em;",[48,211,135],{"className":212},[213],"mrel",[48,215],{"className":216,"style":209},[208],[48,218,220,223,227,230,286,290,294],{"className":219},[181],[48,221],{"className":222,"style":186},[185],[48,224,138],{"className":225,"style":226},[190,191],"margin-right:0.0359em;",[48,228,125],{"className":229},[196],[48,231,233,236],{"className":232},[190],[48,234,129],{"className":235},[190,191],[48,237,240],{"className":238},[239],"msupsub",[48,241,245,277],{"className":242},[243,244],"vlist-t","vlist-t2",[48,246,249,272],{"className":247},[248],"vlist-r",[48,250,254],{"className":251,"style":253},[252],"vlist","height:0.3011em;",[48,255,257,262],{"style":256},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[48,258],{"className":259,"style":261},[260],"pstrut","height:2.7em;",[48,263,269],{"className":264},[265,266,267,268],"sizing","reset-size6","size3","mtight",[48,270,149],{"className":271},[190,268],[48,273,276],{"className":274},[275],"vlist-s","​",[48,278,280],{"className":279},[248],[48,281,284],{"className":282,"style":283},[252],"height:0.15em;",[48,285],{},[48,287],{"className":288,"style":289},[208],"margin-right:0.2222em;",[48,291,152],{"className":292},[293],"mbin",[48,295],{"className":296,"style":289},[208],[48,298,300,304,344,347,350],{"className":299},[181],[48,301],{"className":302,"style":303},[185],"height:0.7333em;vertical-align:-0.15em;",[48,305,307,310],{"className":306},[190],[48,308,129],{"className":309},[190,191],[48,311,313],{"className":312},[239],[48,314,316,336],{"className":315},[243,244],[48,317,319,333],{"className":318},[248],[48,320,322],{"className":321,"style":253},[252],[48,323,324,327],{"style":256},[48,325],{"className":326,"style":261},[260],[48,328,330],{"className":329},[265,266,267,268],[48,331,159],{"className":332},[190,268],[48,334,276],{"className":335},[275],[48,337,339],{"className":338},[248],[48,340,342],{"className":341,"style":283},[252],[48,343],{},[48,345],{"className":346,"style":289},[208],[48,348,162],{"className":349},[293],[48,351],{"className":352,"style":289},[208],[48,354,356,359,362],{"className":355},[181],[48,357],{"className":358,"style":186},[185],[48,360,165],{"className":361},[190],[48,363,132],{"className":364},[204],[11,366,367,370,371,374,375,378],{},[14,368,369],{"href":16},"Já vi que"," ",[20,372,373],{},"sigmoid(z) >= 0.5"," exatamente quando ",[20,376,377],{},"z >= 0",". Então:",[380,381,382,569],"ul",{},[383,384,385,386,388,389],"li",{},"prevê ",[20,387,78],{}," quando ",[48,390,392,427],{"className":391},[102],[48,393,395],{"className":394},[106],[108,396,397],{"xmlns":110},[112,398,399,424],{},[115,400,401,407,409,415,417,419,422],{},[142,402,403,405],{},[118,404,129],{},[147,406,149],{},[122,408,152],{},[142,410,411,413],{},[118,412,129],{},[147,414,159],{},[122,416,162],{},[147,418,165],{},[122,420,421],{},"≥",[147,423,149],{},[169,425,426],{"encoding":171},"x_0+x_1-3 \\geq 0",[48,428,430,485,540,559],{"className":429,"ariaHidden":177},[176],[48,431,433,436,476,479,482],{"className":432},[181],[48,434],{"className":435,"style":303},[185],[48,437,439,442],{"className":438},[190],[48,440,129],{"className":441},[190,191],[48,443,445],{"className":444},[239],[48,446,448,468],{"className":447},[243,244],[48,449,451,465],{"className":450},[248],[48,452,454],{"className":453,"style":253},[252],[48,455,456,459],{"style":256},[48,457],{"className":458,"style":261},[260],[48,460,462],{"className":461},[265,266,267,268],[48,463,149],{"className":464},[190,268],[48,466,276],{"className":467},[275],[48,469,471],{"className":470},[248],[48,472,474],{"className":473,"style":283},[252],[48,475],{},[48,477],{"className":478,"style":289},[208],[48,480,152],{"className":481},[293],[48,483],{"className":484,"style":289},[208],[48,486,488,491,531,534,537],{"className":487},[181],[48,489],{"className":490,"style":303},[185],[48,492,494,497],{"className":493},[190],[48,495,129],{"className":496},[190,191],[48,498,500],{"className":499},[239],[48,501,503,523],{"className":502},[243,244],[48,504,506,520],{"className":505},[248],[48,507,509],{"className":508,"style":253},[252],[48,510,511,514],{"style":256},[48,512],{"className":513,"style":261},[260],[48,515,517],{"className":516},[265,266,267,268],[48,518,159],{"className":519},[190,268],[48,521,276],{"className":522},[275],[48,524,526],{"className":525},[248],[48,527,529],{"className":528,"style":283},[252],[48,530],{},[48,532],{"className":533,"style":289},[208],[48,535,162],{"className":536},[293],[48,538],{"className":539,"style":289},[208],[48,541,543,547,550,553,556],{"className":542},[181],[48,544],{"className":545,"style":546},[185],"height:0.7804em;vertical-align:-0.136em;",[48,548,165],{"className":549},[190],[48,551],{"className":552,"style":209},[208],[48,554,421],{"className":555},[213],[48,557],{"className":558,"style":209},[208],[48,560,562,566],{"className":561},[181],[48,563],{"className":564,"style":565},[185],"height:0.6444em;",[48,567,149],{"className":568},[190],[383,570,385,571,388,573],{},[20,572,74],{},[48,574,576,611],{"className":575},[102],[48,577,579],{"className":578},[106],[108,580,581],{"xmlns":110},[112,582,583,608],{},[115,584,585,591,593,599,601,603,606],{},[142,586,587,589],{},[118,588,129],{},[147,590,149],{},[122,592,152],{},[142,594,595,597],{},[118,596,129],{},[147,598,159],{},[122,600,162],{},[147,602,165],{},[122,604,605],{},"\u003C",[147,607,149],{},[169,609,610],{"encoding":171},"x_0+x_1-3 \u003C 0",[48,612,614,669,724,743],{"className":613,"ariaHidden":177},[176],[48,615,617,620,660,663,666],{"className":616},[181],[48,618],{"className":619,"style":303},[185],[48,621,623,626],{"className":622},[190],[48,624,129],{"className":625},[190,191],[48,627,629],{"className":628},[239],[48,630,632,652],{"className":631},[243,244],[48,633,635,649],{"className":634},[248],[48,636,638],{"className":637,"style":253},[252],[48,639,640,643],{"style":256},[48,641],{"className":642,"style":261},[260],[48,644,646],{"className":645},[265,266,267,268],[48,647,149],{"className":648},[190,268],[48,650,276],{"className":651},[275],[48,653,655],{"className":654},[248],[48,656,658],{"className":657,"style":283},[252],[48,659],{},[48,661],{"className":662,"style":289},[208],[48,664,152],{"className":665},[293],[48,667],{"className":668,"style":289},[208],[48,670,672,675,715,718,721],{"className":671},[181],[48,673],{"className":674,"style":303},[185],[48,676,678,681],{"className":677},[190],[48,679,129],{"className":680},[190,191],[48,682,684],{"className":683},[239],[48,685,687,707],{"className":686},[243,244],[48,688,690,704],{"className":689},[248],[48,691,693],{"className":692,"style":253},[252],[48,694,695,698],{"style":256},[48,696],{"className":697,"style":261},[260],[48,699,701],{"className":700},[265,266,267,268],[48,702,159],{"className":703},[190,268],[48,705,276],{"className":706},[275],[48,708,710],{"className":709},[248],[48,711,713],{"className":712,"style":283},[252],[48,714],{},[48,716],{"className":717,"style":289},[208],[48,719,162],{"className":720},[293],[48,722],{"className":723,"style":289},[208],[48,725,727,731,734,737,740],{"className":726},[181],[48,728],{"className":729,"style":730},[185],"height:0.6835em;vertical-align:-0.0391em;",[48,732,165],{"className":733},[190],[48,735],{"className":736,"style":209},[208],[48,738,605],{"className":739},[213],[48,741],{"className":742,"style":209},[208],[48,744,746,749],{"className":745},[181],[48,747],{"className":748,"style":565},[185],[48,750,149],{"className":751},[190],[11,753,754,755,932,933,1090,1091,1094,1095,1097,1098,1100],{},"A fronteira entre as duas decisões é a linha onde a desigualdade vira igualdade: ",[48,756,758,792],{"className":757},[102],[48,759,761],{"className":760},[106],[108,762,763],{"xmlns":110},[112,764,765,789],{},[115,766,767,773,775,781,783,785,787],{},[142,768,769,771],{},[118,770,129],{},[147,772,149],{},[122,774,152],{},[142,776,777,779],{},[118,778,129],{},[147,780,159],{},[122,782,162],{},[147,784,165],{},[122,786,135],{},[147,788,149],{},[169,790,791],{"encoding":171},"x_0+x_1-3=0",[48,793,795,850,905,923],{"className":794,"ariaHidden":177},[176],[48,796,798,801,841,844,847],{"className":797},[181],[48,799],{"className":800,"style":303},[185],[48,802,804,807],{"className":803},[190],[48,805,129],{"className":806},[190,191],[48,808,810],{"className":809},[239],[48,811,813,833],{"className":812},[243,244],[48,814,816,830],{"className":815},[248],[48,817,819],{"className":818,"style":253},[252],[48,820,821,824],{"style":256},[48,822],{"className":823,"style":261},[260],[48,825,827],{"className":826},[265,266,267,268],[48,828,149],{"className":829},[190,268],[48,831,276],{"className":832},[275],[48,834,836],{"className":835},[248],[48,837,839],{"className":838,"style":283},[252],[48,840],{},[48,842],{"className":843,"style":289},[208],[48,845,152],{"className":846},[293],[48,848],{"className":849,"style":289},[208],[48,851,853,856,896,899,902],{"className":852},[181],[48,854],{"className":855,"style":303},[185],[48,857,859,862],{"className":858},[190],[48,860,129],{"className":861},[190,191],[48,863,865],{"className":864},[239],[48,866,868,888],{"className":867},[243,244],[48,869,871,885],{"className":870},[248],[48,872,874],{"className":873,"style":253},[252],[48,875,876,879],{"style":256},[48,877],{"className":878,"style":261},[260],[48,880,882],{"className":881},[265,266,267,268],[48,883,159],{"className":884},[190,268],[48,886,276],{"className":887},[275],[48,889,891],{"className":890},[248],[48,892,894],{"className":893,"style":283},[252],[48,895],{},[48,897],{"className":898,"style":289},[208],[48,900,162],{"className":901},[293],[48,903],{"className":904,"style":289},[208],[48,906,908,911,914,917,920],{"className":907},[181],[48,909],{"className":910,"style":565},[185],[48,912,165],{"className":913},[190],[48,915],{"className":916,"style":209},[208],[48,918,135],{"className":919},[213],[48,921],{"className":922,"style":209},[208],[48,924,926,929],{"className":925},[181],[48,927],{"className":928,"style":565},[185],[48,930,149],{"className":931},[190],", ou seja, ",[48,934,936,966],{"className":935},[102],[48,937,939],{"className":938},[106],[108,940,941],{"xmlns":110},[112,942,943,963],{},[115,944,945,951,953,955,957],{},[142,946,947,949],{},[118,948,129],{},[147,950,159],{},[122,952,135],{},[147,954,165],{},[122,956,162],{},[142,958,959,961],{},[118,960,129],{},[147,962,149],{},[169,964,965],{"encoding":171},"x_1 = 3-x_0",[48,967,969,1025,1044],{"className":968,"ariaHidden":177},[176],[48,970,972,976,1016,1019,1022],{"className":971},[181],[48,973],{"className":974,"style":975},[185],"height:0.5806em;vertical-align:-0.15em;",[48,977,979,982],{"className":978},[190],[48,980,129],{"className":981},[190,191],[48,983,985],{"className":984},[239],[48,986,988,1008],{"className":987},[243,244],[48,989,991,1005],{"className":990},[248],[48,992,994],{"className":993,"style":253},[252],[48,995,996,999],{"style":256},[48,997],{"className":998,"style":261},[260],[48,1000,1002],{"className":1001},[265,266,267,268],[48,1003,159],{"className":1004},[190,268],[48,1006,276],{"className":1007},[275],[48,1009,1011],{"className":1010},[248],[48,1012,1014],{"className":1013,"style":283},[252],[48,1015],{},[48,1017],{"className":1018,"style":209},[208],[48,1020,135],{"className":1021},[213],[48,1023],{"className":1024,"style":209},[208],[48,1026,1028,1032,1035,1038,1041],{"className":1027},[181],[48,1029],{"className":1030,"style":1031},[185],"height:0.7278em;vertical-align:-0.0833em;",[48,1033,165],{"className":1034},[190],[48,1036],{"className":1037,"style":289},[208],[48,1039,162],{"className":1040},[293],[48,1042],{"className":1043,"style":289},[208],[48,1045,1047,1050],{"className":1046},[181],[48,1048],{"className":1049,"style":975},[185],[48,1051,1053,1056],{"className":1052},[190],[48,1054,129],{"className":1055},[190,191],[48,1057,1059],{"className":1058},[239],[48,1060,1062,1082],{"className":1061},[243,244],[48,1063,1065,1079],{"className":1064},[248],[48,1066,1068],{"className":1067,"style":253},[252],[48,1069,1070,1073],{"style":256},[48,1071],{"className":1072,"style":261},[260],[48,1074,1076],{"className":1075},[265,266,267,268],[48,1077,149],{"className":1078},[190,268],[48,1080,276],{"className":1081},[275],[48,1083,1085],{"className":1084},[248],[48,1086,1088],{"className":1087,"style":283},[252],[48,1089],{},". Essa linha é a ",[29,1092,1093],{},"fronteira de decisão",": tudo o que a sigmoide faz depois é achatar a distância até essa linha numa probabilidade, mas a decisão binária final (",[20,1096,74],{}," ou ",[20,1099,78],{},") só depende de que lado da linha o ponto cai.",[1102,1103],"classification-boundary-comparison-chart",{":boundaries":1104,":classes":1105,":points":1106,":x-max":1107,":x-min":149,":y-max":1108,":y-min":149,"negative-label":74,"positive-label":78,"x-label":66,"y-label":70},"[{\"w\":[1,1],\"bias\":-3,\"label\":\"b=-3, w=[1,1]\"}]","[-1,-1,-1,1,1,1]","[[0.5,1.5],[1,1],[1.5,0.5],[3,0.5],[2,2],[1,2.5]]","4","3.5",[11,1110,1111,1112,1114,1115,1117],{},"Os três pacientes ",[20,1113,74],{}," caem todos abaixo da linha, os três ",[20,1116,78],{}," caem todos acima ou sobre ela. O modelo separa os seis perfeitamente, só olhando de que lado da reta cada um está.",[34,1119,1121],{"id":1120},"fronteiras-não-precisam-ser-retas","Fronteiras não precisam ser retas",[11,1123,1124,1125,1402,1403,1406,1407,1604,1605,1608,1609,1611,1612,1614,1615,1619],{},"Tudo isso partiu de ",[48,1126,1128,1177],{"className":1127},[102],[48,1129,1131],{"className":1130},[106],[108,1132,1133],{"xmlns":110},[112,1134,1135,1174],{},[115,1136,1137,1140,1142,1149,1155,1157,1163,1169,1171],{},[118,1138,1139],{},"z",[122,1141,135],{},[142,1143,1144,1147],{},[118,1145,1146],{},"w",[147,1148,149],{},[142,1150,1151,1153],{},[118,1152,129],{},[147,1154,149],{},[122,1156,152],{},[142,1158,1159,1161],{},[118,1160,1146],{},[147,1162,159],{},[142,1164,1165,1167],{},[118,1166,129],{},[147,1168,159],{},[122,1170,152],{},[118,1172,1173],{},"b",[169,1175,1176],{"encoding":171},"z = w_0x_0+w_1x_1+b",[48,1178,1180,1200,1297,1392],{"className":1179,"ariaHidden":177},[176],[48,1181,1183,1187,1191,1194,1197],{"className":1182},[181],[48,1184],{"className":1185,"style":1186},[185],"height:0.4306em;",[48,1188,1139],{"className":1189,"style":1190},[190,191],"margin-right:0.044em;",[48,1192],{"className":1193,"style":209},[208],[48,1195,135],{"className":1196},[213],[48,1198],{"className":1199,"style":209},[208],[48,1201,1203,1206,1248,1288,1291,1294],{"className":1202},[181],[48,1204],{"className":1205,"style":303},[185],[48,1207,1209,1213],{"className":1208},[190],[48,1210,1146],{"className":1211,"style":1212},[190,191],"margin-right:0.0269em;",[48,1214,1216],{"className":1215},[239],[48,1217,1219,1240],{"className":1218},[243,244],[48,1220,1222,1237],{"className":1221},[248],[48,1223,1225],{"className":1224,"style":253},[252],[48,1226,1228,1231],{"style":1227},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[48,1229],{"className":1230,"style":261},[260],[48,1232,1234],{"className":1233},[265,266,267,268],[48,1235,149],{"className":1236},[190,268],[48,1238,276],{"className":1239},[275],[48,1241,1243],{"className":1242},[248],[48,1244,1246],{"className":1245,"style":283},[252],[48,1247],{},[48,1249,1251,1254],{"className":1250},[190],[48,1252,129],{"className":1253},[190,191],[48,1255,1257],{"className":1256},[239],[48,1258,1260,1280],{"className":1259},[243,244],[48,1261,1263,1277],{"className":1262},[248],[48,1264,1266],{"className":1265,"style":253},[252],[48,1267,1268,1271],{"style":256},[48,1269],{"className":1270,"style":261},[260],[48,1272,1274],{"className":1273},[265,266,267,268],[48,1275,149],{"className":1276},[190,268],[48,1278,276],{"className":1279},[275],[48,1281,1283],{"className":1282},[248],[48,1284,1286],{"className":1285,"style":283},[252],[48,1287],{},[48,1289],{"className":1290,"style":289},[208],[48,1292,152],{"className":1293},[293],[48,1295],{"className":1296,"style":289},[208],[48,1298,1300,1303,1343,1383,1386,1389],{"className":1299},[181],[48,1301],{"className":1302,"style":303},[185],[48,1304,1306,1309],{"className":1305},[190],[48,1307,1146],{"className":1308,"style":1212},[190,191],[48,1310,1312],{"className":1311},[239],[48,1313,1315,1335],{"className":1314},[243,244],[48,1316,1318,1332],{"className":1317},[248],[48,1319,1321],{"className":1320,"style":253},[252],[48,1322,1323,1326],{"style":1227},[48,1324],{"className":1325,"style":261},[260],[48,1327,1329],{"className":1328},[265,266,267,268],[48,1330,159],{"className":1331},[190,268],[48,1333,276],{"className":1334},[275],[48,1336,1338],{"className":1337},[248],[48,1339,1341],{"className":1340,"style":283},[252],[48,1342],{},[48,1344,1346,1349],{"className":1345},[190],[48,1347,129],{"className":1348},[190,191],[48,1350,1352],{"className":1351},[239],[48,1353,1355,1375],{"className":1354},[243,244],[48,1356,1358,1372],{"className":1357},[248],[48,1359,1361],{"className":1360,"style":253},[252],[48,1362,1363,1366],{"style":256},[48,1364],{"className":1365,"style":261},[260],[48,1367,1369],{"className":1368},[265,266,267,268],[48,1370,159],{"className":1371},[190,268],[48,1373,276],{"className":1374},[275],[48,1376,1378],{"className":1377},[248],[48,1379,1381],{"className":1380,"style":283},[252],[48,1382],{},[48,1384],{"className":1385,"style":289},[208],[48,1387,152],{"className":1388},[293],[48,1390],{"className":1391,"style":289},[208],[48,1393,1395,1399],{"className":1394},[181],[48,1396],{"className":1397,"style":1398},[185],"height:0.6944em;",[48,1400,1173],{"className":1401},[190,191],", uma combinação ",[29,1404,1405],{},"linear"," das entradas, por isso a fronteira sai reta. Mas nada impede de alimentar a sigmoide com termos polinomiais, por exemplo ",[48,1408,1410,1448],{"className":1409},[102],[48,1411,1413],{"className":1412},[106],[108,1414,1415],{"xmlns":110},[112,1416,1417,1445],{},[115,1418,1419,1421,1423,1433,1435,1441,1443],{},[118,1420,1139],{},[122,1422,135],{},[1424,1425,1426,1428,1430],"msubsup",{},[118,1427,129],{},[147,1429,149],{},[147,1431,1432],{},"2",[122,1434,152],{},[142,1436,1437,1439],{},[118,1438,129],{},[147,1440,159],{},[122,1442,162],{},[147,1444,159],{},[169,1446,1447],{"encoding":171},"z = x_0^2+x_1-1",[48,1449,1451,1469,1540,1595],{"className":1450,"ariaHidden":177},[176],[48,1452,1454,1457,1460,1463,1466],{"className":1453},[181],[48,1455],{"className":1456,"style":1186},[185],[48,1458,1139],{"className":1459,"style":1190},[190,191],[48,1461],{"className":1462,"style":209},[208],[48,1464,135],{"className":1465},[213],[48,1467],{"className":1468,"style":209},[208],[48,1470,1472,1476,1531,1534,1537],{"className":1471},[181],[48,1473],{"className":1474,"style":1475},[185],"height:1.0622em;vertical-align:-0.2481em;",[48,1477,1479,1482],{"className":1478},[190],[48,1480,129],{"className":1481},[190,191],[48,1483,1485],{"className":1484},[239],[48,1486,1488,1522],{"className":1487},[243,244],[48,1489,1491,1519],{"className":1490},[248],[48,1492,1495,1507],{"className":1493,"style":1494},[252],"height:0.8141em;",[48,1496,1498,1501],{"style":1497},"top:-2.4519em;margin-left:0em;margin-right:0.05em;",[48,1499],{"className":1500,"style":261},[260],[48,1502,1504],{"className":1503},[265,266,267,268],[48,1505,149],{"className":1506},[190,268],[48,1508,1510,1513],{"style":1509},"top:-3.063em;margin-right:0.05em;",[48,1511],{"className":1512,"style":261},[260],[48,1514,1516],{"className":1515},[265,266,267,268],[48,1517,1432],{"className":1518},[190,268],[48,1520,276],{"className":1521},[275],[48,1523,1525],{"className":1524},[248],[48,1526,1529],{"className":1527,"style":1528},[252],"height:0.2481em;",[48,1530],{},[48,1532],{"className":1533,"style":289},[208],[48,1535,152],{"className":1536},[293],[48,1538],{"className":1539,"style":289},[208],[48,1541,1543,1546,1586,1589,1592],{"className":1542},[181],[48,1544],{"className":1545,"style":303},[185],[48,1547,1549,1552],{"className":1548},[190],[48,1550,129],{"className":1551},[190,191],[48,1553,1555],{"className":1554},[239],[48,1556,1558,1578],{"className":1557},[243,244],[48,1559,1561,1575],{"className":1560},[248],[48,1562,1564],{"className":1563,"style":253},[252],[48,1565,1566,1569],{"style":256},[48,1567],{"className":1568,"style":261},[260],[48,1570,1572],{"className":1571},[265,266,267,268],[48,1573,159],{"className":1574},[190,268],[48,1576,276],{"className":1577},[275],[48,1579,1581],{"className":1580},[248],[48,1582,1584],{"className":1583,"style":283},[252],[48,1585],{},[48,1587],{"className":1588,"style":289},[208],[48,1590,162],{"className":1591},[293],[48,1593],{"className":1594,"style":289},[208],[48,1596,1598,1601],{"className":1597},[181],[48,1599],{"className":1600,"style":565},[185],[48,1602,159],{"className":1603},[190],". A fronteira vira uma curva (nesse caso, uma parábola), mas a lógica é idêntica: a fronteira é sempre o lugar onde ",[20,1606,1607],{},"z=0",", só que agora ",[20,1610,1139],{}," não é mais linear em ",[20,1613,129],{},". Esse é o mesmo truque de ",[14,1616,1618],{"href":1617},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw2-lab04-feature-engineering","engenharia de features"," que já vi na regressão, aplicado à classificação.",[34,1621,1623],{"id":1622},"fechando","Fechando",[1625,1626,1627,1641],"table",{},[1628,1629,1630],"thead",{},[1631,1632,1633,1638],"tr",{},[1634,1635,1637],"th",{"align":1636},"left","O que eu já sabia",[1634,1639,1640],{"align":1636},"O que essa aula assentou",[1642,1643,1644,1658,1672],"tbody",{},[1631,1645,1646,1653],{},[1647,1648,1649,388,1651],"td",{"align":1636},[20,1650,373],{},[20,1652,377],{},[1647,1654,1655,1656],{"align":1636},"Isso define uma fronteira geométrica exata: o lugar onde ",[20,1657,1607],{},[1631,1659,1660,1666],{},[1647,1661,1662,1665],{"align":1636},[20,1663,1664],{},"z = w·x+b"," é linear nas entradas",[1647,1667,1668,1669,1671],{"align":1636},"Por isso a fronteira sai reta (ou plana, com mais variáveis); com termos polinomiais em ",[20,1670,1139],{},", a fronteira vira curva",[1631,1673,1674,1677],{},[1647,1675,1676],{"align":1636},"Engenharia de features ajuda regressão a curvar",[1647,1678,1679],{"align":1636},"O mesmo truque também curva a fronteira de decisão em classificação",[34,1681,1683],{"id":1682},"aplicação-prática","Aplicação Prática",[11,1685,1686,1687,1689,1690,1693,1694,67,1697,1701],{},"Ajusto uma regressão logística de verdade (gradiente descendente) no dataset real de câncer de mama, agora com ",[29,1688,31],{}," variáveis: ",[20,1691,1692],{},"worst concave points"," e ",[20,1695,1696],{},"worst perimeter",[14,1698,1700],{"href":1699},"\u002Fplaylists\u002Fpattern-recognition\u002Fclassification-threshold","as duas mais correlacionadas com o diagnóstico",", ambas normalizadas por z-score:",[39,1703,1705],{"className":41,"code":1704,"language":43,"meta":44,"style":44},"w, b = fit_logistic(X_train_z, y_train)  # duas colunas\nprint(f\"w={w}, b={b:.4f}\")\n",[20,1706,1707,1712],{"__ignoreMap":44},[48,1708,1709],{"class":50,"line":51},[48,1710,1711],{},"w, b = fit_logistic(X_train_z, y_train)  # duas colunas\n",[48,1713,1714],{"class":50,"line":57},[48,1715,1716],{},"print(f\"w={w}, b={b:.4f}\")\n",[1718,1719,1720],"blockquote",{},[11,1721,1722,370,1725,67,1728,1731,1732,1735,1736,79],{},[29,1723,1724],{},"Saída:",[20,1726,1727],{},"w=[2.5494, 4.0739]",[20,1729,1730],{},"b=-1.0038",", acurácia de treino ",[29,1733,1734],{},"0.9319",", acurácia de teste ",[29,1737,1738],{},"0.9737",[11,1740,1741],{},"Fronteira de decisão sobre 60 pacientes reais do treino (coordenadas já normalizadas):",[1102,1743],{":boundaries":1744,":classes":1745,":points":1746,":x-max":165,":x-min":1747,":y-max":1108,":y-min":1748,"negative-label":1749,"positive-label":1750,"x-label":1751,"y-label":1752},"[{\"w\":[2.5494,4.0739],\"bias\":-1.0038,\"label\":\"fronteira treinada\"}]","[1,-1,1,-1,-1,1,1,-1,1,1,-1,1,1,-1,-1,-1,-1,1,-1,1,1,1,-1,-1,1,1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,-1,-1,1,1,-1,1]","[[-0.32,-0.452],[-0.488,-0.489],[1.029,0.792],[-1.323,-0.679],[-1.107,-0.354],[0.028,0.285],[1.357,0.6],[-0.482,-0.821],[0.645,1.668],[2.438,2.097],[-0.216,-0.078],[0.423,0.588],[0.592,0.924],[-1.75,-0.661],[-0.581,-0.569],[-0.006,-0.627],[-0.409,-0.708],[2.699,2.082],[0.097,-0.469],[2.365,1.92],[0.635,0.105],[1.917,0.54],[-1.357,-1.215],[-0.144,-0.207],[1.455,1.89],[0.537,0.18],[-1.09,-0.835],[-0.456,-0.646],[-0.343,0.66],[-0.464,-0.522],[-0.231,-1.021],[-1.29,-0.86],[-1.608,-0.568],[-0.191,-0.096],[0.42,-0.569],[-0.617,-0.605],[-0.135,-0.274],[-0.45,-0.075],[-1.015,-0.69],[-0.397,-0.398],[-0.473,-1.081],[1.894,1.305],[0.495,-0.918],[-0.289,-0.543],[2.369,3.41],[-1.004,-1.172],[2.196,-0.247],[-0.095,-0.449],[0.816,1.149],[0.888,1.446],[0.406,-0.171],[-0.785,-0.839],[-0.251,-0.416],[0.497,0.981],[-1.385,-1.149],[-0.185,-0.162],[0.955,1.623],[1.487,1.791],[-0.842,-0.481],[0.986,1.629]]","-2","-1.5","benigno","maligno","worst concave points (normalizado)","worst perimeter (normalizado)",[11,1754,1755,1756,79],{},"A maioria dos pacientes malignos (azuis) cai acima e à direita da fronteira, a maioria dos benignos (laranjas) cai abaixo e à esquerda, exatamente o padrão de separação que a acurácia de 97% no teste já sugeria. Os poucos pontos do lado \"errado\" da linha são justamente os erros do modelo, casos onde as duas variáveis sozinhas não bastam pra decidir com segurança, o mesmo tipo de ambiguidade que ",[14,1757,1758],{"href":1699},"já vi quando usei só uma variável",[1760,1761,1762],"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":44,"searchDepth":57,"depth":57,"links":1764},[1765,1766,1767,1768,1769],{"id":36,"depth":57,"text":37},{"id":82,"depth":57,"text":83},{"id":1120,"depth":57,"text":1121},{"id":1622,"depth":57,"text":1623},{"id":1682,"depth":57,"text":1683},null,"2026-09-04","Semana 3, Lab 3: com duas variáveis de entrada, dá pra desenhar exatamente onde o modelo troca de decisão. Essa linha (ou curva) tem nome: fronteira de decisão, e ela mora inteirinha dentro da parte linear do modelo, antes da sigmoide entrar em cena.","md",{},true,14,"\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab03-decision-boundary","machine-learning-specialization",{"title":6,"description":1772},"published","pt\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw3-lab03-decision-boundary",[1783,1784,1785],"classificacao","regressao-logistica","fronteira-de-decisao","oTULmxN0kSbYeifJ-E7XS6-b9jCQS0mqhrgkEhPCTG4",1788965098034]