[{"data":1,"prerenderedAt":3681},["ShallowReactive",2],{"lang-switch-post-\u002Fplaylists\u002Fmachine-learning-specialization\u002Ffeature-engineering-pitfalls":3,"post-pt-machine-learning-specialization-feature-engineering-pitfalls":4},"\u002Fen\u002Fplaylists\u002Fmachine-learning-specialization\u002Ffeature-engineering-pitfalls",{"id":5,"title":6,"body":7,"cover":3664,"date":3665,"description":3666,"extension":3667,"meta":3668,"navigation":3669,"order":3670,"path":3671,"playlist":3672,"seo":3673,"status":3674,"stem":3675,"tags":3676,"__hash__":3680},"posts\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Ffeature-engineering-pitfalls.md","Só pra complementar: Pegadinhas de Engenharia de Features",{"type":8,"value":9,"toc":3645},"minimark",[10,20,25,347,892,896,1117,1177,1180,1263,1274,1338,1346,1350,1360,1364,1489,1840,1918,1922,1963,2298,2512,2643,2765,2858,2889,2898,2930,2934,2937,2942,2963,2981,2985,2996,3493,3497,3556,3565,3569,3584,3593,3597,3600],[11,12,13,14,19],"p",{},"Esse post não vem de nenhuma seção obrigatória do lab, é o que sobrou depois que eu separei o essencial de engenharia de features e overfitting no post principal. Curiosamente, essa é a primeira vez que eu consigo mostrar de verdade a solução pro problema que o ",[15,16,18],"a",{"href":17},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw2-lab04-feature-engineering","post anterior"," só diagnosticou.",[21,22,24],"h2",{"id":23},"normalizo-depois-de-criar-a-feature-não-antes","Normalizo depois de criar a feature, não antes",[11,26,27,28,74,75,280,281,342,343,346],{},"A ordem importa. Se eu normalizasse ",[29,30,33,55],"span",{"className":31},[32],"katex",[29,34,37],{"className":35},[36],"katex-mathml",[38,39,41],"math",{"xmlns":40},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[42,43,44,51],"semantics",{},[45,46,47],"mrow",{},[48,49,50],"mi",{},"x",[52,53,50],"annotation",{"encoding":54},"application\u002Fx-tex",[29,56,60],{"className":57,"ariaHidden":59},[58],"katex-html","true",[29,61,64,69],{"className":62},[63],"base",[29,65],{"className":66,"style":68},[67],"strut","height:0.4306em;",[29,70,50],{"className":71},[72,73],"mord","mathnormal"," primeiro e só depois elevasse ao quadrado, chegaria em ",[29,76,78,122],{"className":77},[32],[29,79,81],{"className":80},[36],[38,82,83],{"xmlns":40},[42,84,85,119],{},[45,86,87],{},[88,89,90,115],"msup",{},[45,91,92,96,112],{},[93,94,95],"mo",{"fence":59},"(",[97,98,99,109],"mfrac",{},[45,100,101,103,106],{},[48,102,50],{},[93,104,105],{},"−",[48,107,108],{},"μ",[48,110,111],{},"σ",[93,113,114],{"fence":59},")",[116,117,118],"mn",{},"2",[52,120,121],{"encoding":54},"\\left(\\frac{x-\\mu}{\\sigma}\\right)^2",[29,123,125],{"className":124,"ariaHidden":59},[58],[29,126,128,132],{"className":127},[63],[29,129],{"className":130,"style":131},[67],"height:1.4085em;vertical-align:-0.35em;",[29,133,136,253],{"className":134},[135],"minner",[29,137,139,150,247],{"className":138},[135],[29,140,145],{"className":141,"style":144},[142,143],"mopen","delimcenter","top:0em;",[29,146,95],{"className":147},[148,149],"delimsizing","size1",[29,151,153,157,243],{"className":152},[72],[29,154],{"className":155},[142,156],"nulldelimiter",[29,158,160],{"className":159},[97],[29,161,165,234],{"className":162},[163,164],"vlist-t","vlist-t2",[29,166,169,229],{"className":167},[168],"vlist-r",[29,170,174,196,207],{"className":171,"style":173},[172],"vlist","height:0.8544em;",[29,175,177,182],{"style":176},"top:-2.655em;",[29,178],{"className":179,"style":181},[180],"pstrut","height:3em;",[29,183,189],{"className":184},[185,186,187,188],"sizing","reset-size6","size3","mtight",[29,190,192],{"className":191},[72,188],[29,193,111],{"className":194,"style":195},[72,73,188],"margin-right:0.0359em;",[29,197,199,202],{"style":198},"top:-3.23em;",[29,200],{"className":201,"style":181},[180],[29,203],{"className":204,"style":206},[205],"frac-line","border-bottom-width:0.04em;",[29,208,210,213],{"style":209},"top:-3.4461em;",[29,211],{"className":212,"style":181},[180],[29,214,216],{"className":215},[185,186,187,188],[29,217,219,222,226],{"className":218},[72,188],[29,220,50],{"className":221},[72,73,188],[29,223,105],{"className":224},[225,188],"mbin",[29,227,108],{"className":228},[72,73,188],[29,230,233],{"className":231},[232],"vlist-s","​",[29,235,237],{"className":236},[168],[29,238,241],{"className":239,"style":240},[172],"height:0.345em;",[29,242],{},[29,244],{"className":245},[246,156],"mclose",[29,248,250],{"className":249,"style":144},[246,143],[29,251,114],{"className":252},[148,149],[29,254,257],{"className":255},[256],"msupsub",[29,258,260],{"className":259},[163],[29,261,263],{"className":262},[168],[29,264,267],{"className":265,"style":266},[172],"height:1.0584em;",[29,268,270,274],{"style":269},"top:-3.3073em;margin-right:0.05em;",[29,271],{"className":272,"style":273},[180],"height:2.7em;",[29,275,277],{"className":276},[185,186,187,188],[29,278,118],{"className":279},[72,188],", que não é a mesma feature que normalizar ",[29,282,284,302],{"className":283},[32],[29,285,287],{"className":286},[36],[38,288,289],{"xmlns":40},[42,290,291,299],{},[45,292,293],{},[88,294,295,297],{},[48,296,50],{},[116,298,118],{},[52,300,301],{"encoding":54},"x^2",[29,303,305],{"className":304,"ariaHidden":59},[58],[29,306,308,312],{"className":307},[63],[29,309],{"className":310,"style":311},[67],"height:0.8141em;",[29,313,315,318],{"className":314},[72],[29,316,50],{"className":317},[72,73],[29,319,321],{"className":320},[256],[29,322,324],{"className":323},[163],[29,325,327],{"className":326},[168],[29,328,330],{"className":329,"style":311},[172],[29,331,333,336],{"style":332},"top:-3.063em;margin-right:0.05em;",[29,334],{"className":335,"style":273},[180],[29,337,339],{"className":338},[185,186,187,188],[29,340,118],{"className":341},[72,188]," direto. As duas funcionam, mas produzem colunas diferentes, e a segunda ordem (criar a feature, normalizar depois) é a que eu uso desde ",[15,344,345],{"href":17},"o post principal",".",[11,348,349,350,510,511,738,739,797,798,826,827,855,856,886,887,891],{},"Já adianto o final feliz: o RMSE das duas ordens acaba praticamente igual, então relaxa, não é um erro grave se você inverter. O motivo é que ",[29,351,353,386],{"className":352},[32],[29,354,356],{"className":355},[36],[38,357,358],{"xmlns":40},[42,359,360,384],{},[45,361,362],{},[88,363,364,382],{},[45,365,366,368,380],{},[93,367,95],{"fence":59},[97,369,370,378],{},[45,371,372,374,376],{},[48,373,50],{},[93,375,105],{},[48,377,108],{},[48,379,111],{},[93,381,114],{"fence":59},[116,383,118],{},[52,385,121],{"encoding":54},[29,387,389],{"className":388,"ariaHidden":59},[58],[29,390,392,395],{"className":391},[63],[29,393],{"className":394,"style":131},[67],[29,396,398,487],{"className":397},[135],[29,399,401,407,481],{"className":400},[135],[29,402,404],{"className":403,"style":144},[142,143],[29,405,95],{"className":406},[148,149],[29,408,410,413,478],{"className":409},[72],[29,411],{"className":412},[142,156],[29,414,416],{"className":415},[97],[29,417,419,470],{"className":418},[163,164],[29,420,422,467],{"className":421},[168],[29,423,425,439,447],{"className":424,"style":173},[172],[29,426,427,430],{"style":176},[29,428],{"className":429,"style":181},[180],[29,431,433],{"className":432},[185,186,187,188],[29,434,436],{"className":435},[72,188],[29,437,111],{"className":438,"style":195},[72,73,188],[29,440,441,444],{"style":198},[29,442],{"className":443,"style":181},[180],[29,445],{"className":446,"style":206},[205],[29,448,449,452],{"style":209},[29,450],{"className":451,"style":181},[180],[29,453,455],{"className":454},[185,186,187,188],[29,456,458,461,464],{"className":457},[72,188],[29,459,50],{"className":460},[72,73,188],[29,462,105],{"className":463},[225,188],[29,465,108],{"className":466},[72,73,188],[29,468,233],{"className":469},[232],[29,471,473],{"className":472},[168],[29,474,476],{"className":475,"style":240},[172],[29,477],{},[29,479],{"className":480},[246,156],[29,482,484],{"className":483,"style":144},[246,143],[29,485,114],{"className":486},[148,149],[29,488,490],{"className":489},[256],[29,491,493],{"className":492},[163],[29,494,496],{"className":495},[168],[29,497,499],{"className":498,"style":266},[172],[29,500,501,504],{"style":269},[29,502],{"className":503,"style":273},[180],[29,505,507],{"className":506},[185,186,187,188],[29,508,118],{"className":509},[72,188]," dá pra abrir em ",[29,512,514,559],{"className":513},[32],[29,515,517],{"className":516},[36],[38,518,519],{"xmlns":40},[42,520,521,556],{},[45,522,523],{},[97,524,525,550],{},[45,526,527,533,535,537,539,541,544],{},[88,528,529,531],{},[48,530,50],{},[116,532,118],{},[93,534,105],{},[116,536,118],{},[48,538,108],{},[48,540,50],{},[93,542,543],{},"+",[88,545,546,548],{},[48,547,108],{},[116,549,118],{},[88,551,552,554],{},[48,553,111],{},[116,555,118],{},[52,557,558],{"encoding":54},"\\frac{x^2 - 2\\mu x + \\mu^2}{\\sigma^2}",[29,560,562],{"className":561,"ariaHidden":59},[58],[29,563,565,569],{"className":564},[63],[29,566],{"className":567,"style":568},[67],"height:1.415em;vertical-align:-0.345em;",[29,570,572,575,735],{"className":571},[72],[29,573],{"className":574},[142,156],[29,576,578],{"className":577},[97],[29,579,581,727],{"className":580},[163,164],[29,582,584,724],{"className":583},[168],[29,585,588,632,640],{"className":586,"style":587},[172],"height:1.07em;",[29,589,590,593],{"style":176},[29,591],{"className":592,"style":181},[180],[29,594,596],{"className":595},[185,186,187,188],[29,597,599],{"className":598},[72,188],[29,600,602,605],{"className":601},[72,188],[29,603,111],{"className":604,"style":195},[72,73,188],[29,606,608],{"className":607},[256],[29,609,611],{"className":610},[163],[29,612,614],{"className":613},[168],[29,615,618],{"className":616,"style":617},[172],"height:0.7463em;",[29,619,621,625],{"style":620},"top:-2.786em;margin-right:0.0714em;",[29,622],{"className":623,"style":624},[180],"height:2.5em;",[29,626,629],{"className":627},[185,628,149,188],"reset-size3",[29,630,118],{"className":631},[72,188],[29,633,634,637],{"style":198},[29,635],{"className":636,"style":181},[180],[29,638],{"className":639,"style":206},[205],[29,641,642,645],{"style":209},[29,643],{"className":644,"style":181},[180],[29,646,648],{"className":647},[185,186,187,188],[29,649,651,682,685,688,692,695],{"className":650},[72,188],[29,652,654,657],{"className":653},[72,188],[29,655,50],{"className":656},[72,73,188],[29,658,660],{"className":659},[256],[29,661,663],{"className":662},[163],[29,664,666],{"className":665},[168],[29,667,670],{"className":668,"style":669},[172],"height:0.8913em;",[29,671,673,676],{"style":672},"top:-2.931em;margin-right:0.0714em;",[29,674],{"className":675,"style":624},[180],[29,677,679],{"className":678},[185,628,149,188],[29,680,118],{"className":681},[72,188],[29,683,105],{"className":684},[225,188],[29,686,118],{"className":687},[72,188],[29,689,691],{"className":690},[72,73,188],"μx",[29,693,543],{"className":694},[225,188],[29,696,698,701],{"className":697},[72,188],[29,699,108],{"className":700},[72,73,188],[29,702,704],{"className":703},[256],[29,705,707],{"className":706},[163],[29,708,710],{"className":709},[168],[29,711,713],{"className":712,"style":669},[172],[29,714,715,718],{"style":672},[29,716],{"className":717,"style":624},[180],[29,719,721],{"className":720},[185,628,149,188],[29,722,118],{"className":723},[72,188],[29,725,233],{"className":726},[232],[29,728,730],{"className":729},[168],[29,731,733],{"className":732,"style":240},[172],[29,734],{},[29,736],{"className":737},[246,156],", que é só uma combinação linear de ",[29,740,742,759],{"className":741},[32],[29,743,745],{"className":744},[36],[38,746,747],{"xmlns":40},[42,748,749,757],{},[45,750,751],{},[88,752,753,755],{},[48,754,50],{},[116,756,118],{},[52,758,301],{"encoding":54},[29,760,762],{"className":761,"ariaHidden":59},[58],[29,763,765,768],{"className":764},[63],[29,766],{"className":767,"style":311},[67],[29,769,771,774],{"className":770},[72],[29,772,50],{"className":773},[72,73],[29,775,777],{"className":776},[256],[29,778,780],{"className":779},[163],[29,781,783],{"className":782},[168],[29,784,786],{"className":785,"style":311},[172],[29,787,788,791],{"style":332},[29,789],{"className":790,"style":273},[180],[29,792,794],{"className":793},[185,186,187,188],[29,795,118],{"className":796},[72,188],", ",[29,799,801,814],{"className":800},[32],[29,802,804],{"className":803},[36],[38,805,806],{"xmlns":40},[42,807,808,812],{},[45,809,810],{},[48,811,50],{},[52,813,50],{"encoding":54},[29,815,817],{"className":816,"ariaHidden":59},[58],[29,818,820,823],{"className":819},[63],[29,821],{"className":822,"style":68},[67],[29,824,50],{"className":825},[72,73]," e uma constante, três coisas que o modelo já tem à disposição (o próprio ",[29,828,830,843],{"className":829},[32],[29,831,833],{"className":832},[36],[38,834,835],{"xmlns":40},[42,836,837,841],{},[45,838,839],{},[48,840,50],{},[52,842,50],{"encoding":54},[29,844,846],{"className":845,"ariaHidden":59},[58],[29,847,849,852],{"className":848},[63],[29,850],{"className":851,"style":68},[67],[29,853,50],{"className":854},[72,73]," e o viés ",[29,857,859,873],{"className":858},[32],[29,860,862],{"className":861},[36],[38,863,864],{"xmlns":40},[42,865,866,871],{},[45,867,868],{},[48,869,870],{},"b",[52,872,870],{"encoding":54},[29,874,876],{"className":875,"ariaHidden":59},[58],[29,877,879,883],{"className":878},[63],[29,880],{"className":881,"style":882},[67],"height:0.6944em;",[29,884,870],{"className":885},[72,73],"). Ou seja, normalizar antes ou depois não muda o que o modelo ",[888,889,890],"strong",{},"consegue"," representar, só reescreve a mesma função numa base de coordenadas diferente. O que muda de verdade é a escala dos pesos e a velocidade com que o gradiente descendente converge até eles, não o resultado final. (Detalho a conta inteira no Exercício 2, lá embaixo, se quiser ver isso na régua.)",[21,893,895],{"id":894},"features-polinomiais-são-extremamente-colineares","Features polinomiais são extremamente colineares",[11,897,898,797,926,984,985,1045,1046,1116],{},[29,899,901,914],{"className":900},[32],[29,902,904],{"className":903},[36],[38,905,906],{"xmlns":40},[42,907,908,912],{},[45,909,910],{},[48,911,50],{},[52,913,50],{"encoding":54},[29,915,917],{"className":916,"ariaHidden":59},[58],[29,918,920,923],{"className":919},[63],[29,921],{"className":922,"style":68},[67],[29,924,50],{"className":925},[72,73],[29,927,929,946],{"className":928},[32],[29,930,932],{"className":931},[36],[38,933,934],{"xmlns":40},[42,935,936,944],{},[45,937,938],{},[88,939,940,942],{},[48,941,50],{},[116,943,118],{},[52,945,301],{"encoding":54},[29,947,949],{"className":948,"ariaHidden":59},[58],[29,950,952,955],{"className":951},[63],[29,953],{"className":954,"style":311},[67],[29,956,958,961],{"className":957},[72],[29,959,50],{"className":960},[72,73],[29,962,964],{"className":963},[256],[29,965,967],{"className":966},[163],[29,968,970],{"className":969},[168],[29,971,973],{"className":972,"style":311},[172],[29,974,975,978],{"style":332},[29,976],{"className":977,"style":273},[180],[29,979,981],{"className":980},[185,186,187,188],[29,982,118],{"className":983},[72,188]," e ",[29,986,988,1007],{"className":987},[32],[29,989,991],{"className":990},[36],[38,992,993],{"xmlns":40},[42,994,995,1004],{},[45,996,997],{},[88,998,999,1001],{},[48,1000,50],{},[116,1002,1003],{},"3",[52,1005,1006],{"encoding":54},"x^3",[29,1008,1010],{"className":1009,"ariaHidden":59},[58],[29,1011,1013,1016],{"className":1012},[63],[29,1014],{"className":1015,"style":311},[67],[29,1017,1019,1022],{"className":1018},[72],[29,1020,50],{"className":1021},[72,73],[29,1023,1025],{"className":1024},[256],[29,1026,1028],{"className":1027},[163],[29,1029,1031],{"className":1030},[168],[29,1032,1034],{"className":1033,"style":311},[172],[29,1035,1036,1039],{"style":332},[29,1037],{"className":1038,"style":273},[180],[29,1040,1042],{"className":1041},[185,186,187,188],[29,1043,1003],{"className":1044},[72,188]," carregam quase a mesma informação num intervalo estreito. Isso deixa a matriz ",[29,1047,1049,1073],{"className":1048},[32],[29,1050,1052],{"className":1051},[36],[38,1053,1054],{"xmlns":40},[42,1055,1056,1070],{},[45,1057,1058,1068],{},[88,1059,1060,1064],{},[48,1061,1063],{"mathvariant":1062},"bold","X",[48,1065,1067],{"mathvariant":1066},"normal","⊤",[48,1069,1063],{"mathvariant":1062},[52,1071,1072],{"encoding":54},"\\mathbf{X}^\\top\\mathbf{X}",[29,1074,1076],{"className":1075,"ariaHidden":59},[58],[29,1077,1079,1083,1113],{"className":1078},[63],[29,1080],{"className":1081,"style":1082},[67],"height:0.8491em;",[29,1084,1086,1090],{"className":1085},[72],[29,1087,1063],{"className":1088},[72,1089],"mathbf",[29,1091,1093],{"className":1092},[256],[29,1094,1096],{"className":1095},[163],[29,1097,1099],{"className":1098},[168],[29,1100,1102],{"className":1101,"style":1082},[172],[29,1103,1104,1107],{"style":332},[29,1105],{"className":1106,"style":273},[180],[29,1108,1110],{"className":1109},[185,186,187,188],[29,1111,1067],{"className":1112},[72,188],[29,1114,1063],{"className":1115},[72,1089]," mal condicionada. Calculei a razão entre a amplitude cru da maior e da menor coluna por grau:",[1118,1119,1120,1135],"table",{},[1121,1122,1123],"thead",{},[1124,1125,1126,1131],"tr",{},[1127,1128,1130],"th",{"align":1129},"center","Grau",[1127,1132,1134],{"align":1133},"right","Amplitude máx\u002Fmín (cru)",[1136,1137,1138,1146,1153,1161,1169],"tbody",{},[1124,1139,1140,1144],{},[1141,1142,1143],"td",{"align":1129},"1",[1141,1145,1143],{"align":1133},[1124,1147,1148,1150],{},[1141,1149,1003],{"align":1129},[1141,1151,1152],{"align":1133},"361",[1124,1154,1155,1158],{},[1141,1156,1157],{"align":1129},"5",[1141,1159,1160],{"align":1133},"1.3 × 10⁵",[1124,1162,1163,1166],{},[1141,1164,1165],{"align":1129},"9",[1141,1167,1168],{"align":1133},"1.7 × 10¹⁰",[1124,1170,1171,1174],{},[1141,1172,1173],{"align":1129},"13",[1141,1175,1176],{"align":1133},"2.2 × 10¹⁵",[11,1178,1179],{},"No grau 13 essa razão já está perto do limite de precisão do ponto flutuante de 64 bits (~2.2×10⁻¹⁶ de precisão relativa). Não é exagero dizer que a matriz crua nesse grau está no limiar da singularidade numérica.",[11,1181,1182,1183,1262],{},"E \"mal condicionada\" não é só um adjetivo assustador, tem uma consequência bem concreta pro peso que sai do ajuste. Resolver a equação normal envolve, no fundo, inverter essa matriz, e quando ela está quase singular, essa inversão se parece muito com dividir por um número quase zero: um tremelique pequeno no numerador (um pouquinho de ruído nos dados, um arredondamento de ponto flutuante) vira uma resposta gigante e instável do outro lado. Na prática, isso significa que dois conjuntos de dados quase idênticos podem produzir pesos ",[29,1184,1186,1207],{"className":1185},[32],[29,1187,1189],{"className":1188},[36],[38,1190,1191],{"xmlns":40},[42,1192,1193,1204],{},[45,1194,1195],{},[1196,1197,1198,1201],"msub",{},[48,1199,1200],{},"w",[48,1202,1203],{},"j",[52,1205,1206],{"encoding":54},"w_j",[29,1208,1210],{"className":1209,"ariaHidden":59},[58],[29,1211,1213,1217],{"className":1212},[63],[29,1214],{"className":1215,"style":1216},[67],"height:0.7167em;vertical-align:-0.2861em;",[29,1218,1220,1224],{"className":1219},[72],[29,1221,1200],{"className":1222,"style":1223},[72,73],"margin-right:0.0269em;",[29,1225,1227],{"className":1226},[256],[29,1228,1230,1253],{"className":1229},[163,164],[29,1231,1233,1250],{"className":1232},[168],[29,1234,1237],{"className":1235,"style":1236},[172],"height:0.3117em;",[29,1238,1240,1243],{"style":1239},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[29,1241],{"className":1242,"style":273},[180],[29,1244,1246],{"className":1245},[185,186,187,188],[29,1247,1203],{"className":1248,"style":1249},[72,73,188],"margin-right:0.0572em;",[29,1251,233],{"className":1252},[232],[29,1254,1256],{"className":1255},[168],[29,1257,1260],{"className":1258,"style":1259},[172],"height:0.2861em;",[29,1261],{}," completamente diferentes, às vezes com sinais opostos se cancelando quase perfeitamente, mesmo que a curva final prevista pareça igualzinha. Os pesos individuais deixam de significar algo confiável, só a combinação deles ainda presta.",[11,1264,1265,1266,1269,1270,1273],{},"Normalizar (o que meu componente do ",[15,1267,1268],{"href":17},"post principal"," já faz por baixo dos panos) melhora isso em várias ordens de grandeza, mas não resolve a colinearidade ",[888,1271,1272],{},"intrínseca"," entre as potências, só a diferença de escala entre elas. Pra colinearidade de verdade, o remédio é regularização, que eu mostro mais embaixo.",[21,1275,1277,1278,984,1308,1337],{"id":1276},"guardo-μmuμ-e-σsigmaσ-sempre","Guardo ",[29,1279,1281,1295],{"className":1280},[32],[29,1282,1284],{"className":1283},[36],[38,1285,1286],{"xmlns":40},[42,1287,1288,1292],{},[45,1289,1290],{},[48,1291,108],{},[52,1293,1294],{"encoding":54},"\\mu",[29,1296,1298],{"className":1297,"ariaHidden":59},[58],[29,1299,1301,1305],{"className":1300},[63],[29,1302],{"className":1303,"style":1304},[67],"height:0.625em;vertical-align:-0.1944em;",[29,1306,108],{"className":1307},[72,73],[29,1309,1311,1325],{"className":1310},[32],[29,1312,1314],{"className":1313},[36],[38,1315,1316],{"xmlns":40},[42,1317,1318,1322],{},[45,1319,1320],{},[48,1321,111],{},[52,1323,1324],{"encoding":54},"\\sigma",[29,1326,1328],{"className":1327,"ariaHidden":59},[58],[29,1329,1331,1334],{"className":1330},[63],[29,1332],{"className":1333,"style":68},[67],[29,1335,111],{"className":1336,"style":195},[72,73],", sempre",[11,1339,1340,1341,1345],{},"Bati nessa tecla no ",[15,1342,1344],{"href":1343},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw2-lab03-feature-scaling","post de normalização"," e bato de novo aqui: sem guardar a média e o desvio-padrão do treino, não dá pra normalizar nenhum dado novo do mesmo jeito, e o modelo vira enfeite. Todo componente que eu construí pra esse post guarda isso internamente antes de prever qualquer coisa.",[21,1347,1349],{"id":1348},"mais-features-nunca-piora-o-erro-de-treino","Mais features nunca piora o erro de treino",[11,1351,1352,1353,1356,1357,1359],{},"Isso não é coincidência, é praticamente um teorema: acrescentar uma coluna só amplia o espaço de modelos possíveis, então o mínimo do custo de treino só pode cair ou empatar, nunca subir. Por isso erro de treino sozinho ",[888,1354,1355],{},"não serve"," pra escolher a complexidade do modelo, sempre precisa de um conjunto separado (o que eu já mostrei no ",[15,1358,1268],{"href":17},").",[21,1361,1363],{"id":1362},"engenharia-de-feature-não-é-só-potência","Engenharia de feature não é só potência",[11,1365,1366,1367,1488],{},"Potência é o exemplo didático mais fácil de mostrar. No mundo real, as features mais úteis costumam vir de conhecimento de domínio: raiz quadrada, log, razões, produtos entre colunas. Testei isso com um alvo 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parâmetros",[1127,1503,1504],{"align":1133},"RMSE",[1136,1506,1507,1544,1629,1754],{},[1124,1508,1509,1539,1541],{},[1141,1510,1511],{"align":1497},[29,1512,1514,1527],{"className":1513},[32],[29,1515,1517],{"className":1516},[36],[38,1518,1519],{"xmlns":40},[42,1520,1521,1525],{},[45,1522,1523],{},[48,1524,50],{},[52,1526,50],{"encoding":54},[29,1528,1530],{"className":1529,"ariaHidden":59},[58],[29,1531,1533,1536],{"className":1532},[63],[29,1534],{"className":1535,"style":68},[67],[29,1537,50],{"className":1538},[72,73],[1141,1540,118],{"align":1133},[1141,1542,1543],{"align":1133},"0.300",[1124,1545,1546,1624,1626],{},[1141,1547,1548],{"align":1497},[29,1549,1551,1574],{"className":1550},[32],[29,1552,1554],{"className":1553},[36],[38,1555,1556],{"xmlns":40},[42,1557,1558,1571],{},[45,1559,1560,1562,1565],{},[48,1561,50],{},[93,1563,1564],{"separator":59},",",[88,1566,1567,1569],{},[48,1568,50],{},[116,1570,118],{},[52,1572,1573],{"encoding":54},"x, 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x^2, x^3",[29,1667,1669],{"className":1668,"ariaHidden":59},[58],[29,1670,1672,1675,1678,1681,1684,1713,1716,1719],{"className":1671},[63],[29,1673],{"className":1674,"style":1583},[67],[29,1676,50],{"className":1677},[72,73],[29,1679,1564],{"className":1680},[1590],[29,1682],{"className":1683,"style":1594},[1408],[29,1685,1687,1690],{"className":1686},[72],[29,1688,50],{"className":1689},[72,73],[29,1691,1693],{"className":1692},[256],[29,1694,1696],{"className":1695},[163],[29,1697,1699],{"className":1698},[168],[29,1700,1702],{"className":1701,"style":311},[172],[29,1703,1704,1707],{"style":332},[29,1705],{"className":1706,"style":273},[180],[29,1708,1710],{"className":1709},[185,186,187,188],[29,1711,118],{"className":1712},[72,188],[29,1714,1564],{"className":1715},[1590],[29,1717],{"className":1718,"style":1594},[1408],[29,1720,1722,1725],{"className":1721},[72],[29,1723,50],{"className":1724},[72,73],[29,1726,1728],{"className":1727},[256],[29,1729,1731],{"className":1730},[163],[29,1732,1734],{"className":1733},[168],[29,1735,1737],{"className":1736,"style":311},[172],[29,1738,1739,1742],{"style":332},[29,1740],{"className":1741,"style":273},[180],[29,1743,1745],{"className":1744},[185,186,187,188],[29,1746,1003],{"className":1747},[72,188],[1141,1749,1750],{"align":1133},"4",[1141,1752,1753],{"align":1133},"0.104",[1124,1755,1756,1833,1835],{},[1141,1757,1758],{"align":1497},[29,1759,1761,1777],{"className":1760},[32],[29,1762,1764],{"className":1763},[36],[38,1765,1766],{"xmlns":40},[42,1767,1768,1774],{},[45,1769,1770],{},[1386,1771,1772],{},[48,1773,50],{},[52,1775,1776],{"encoding":54},"\\sqrt{x}",[29,1778,1780],{"className":1779,"ariaHidden":59},[58],[29,1781,1783,1786],{"className":1782},[63],[29,1784],{"className":1785,"style":1423},[67],[29,1787,1789],{"className":1788},[72,1427],[29,1790,1792,1825],{"className":1791},[163,164],[29,1793,1795,1822],{"className":1794},[168],[29,1796,1798,1810],{"className":1797,"style":1437},[172],[29,1799,1801,1804],{"className":1800,"style":1442},[1441],[29,1802],{"className":1803,"style":181},[180],[29,1805,1807],{"className":1806,"style":1449},[72],[29,1808,50],{"className":1809},[72,73],[29,1811,1812,1815],{"style":1455},[29,1813],{"className":1814,"style":181},[180],[29,1816,1818],{"className":1817,"style":1463},[1462],[1465,1819,1820],{"xmlns":1467,"width":1468,"height":1469,"viewBox":1470,"preserveAspectRatio":1471},[1473,1821],{"d":1475},[29,1823,233],{"className":1824},[232],[29,1826,1828],{"className":1827},[168],[29,1829,1831],{"className":1830,"style":1485},[172],[29,1832],{},[1141,1834,118],{"align":1133},[1141,1836,1837],{"align":1133},[888,1838,1839],{},"0.000",[11,1841,1842,1843,1917],{},"Uma única feature ",[29,1844,1846,1861],{"className":1845},[32],[29,1847,1849],{"className":1848},[36],[38,1850,1851],{"xmlns":40},[42,1852,1853,1859],{},[45,1854,1855],{},[1386,1856,1857],{},[48,1858,50],{},[52,1860,1776],{"encoding":54},[29,1862,1864],{"className":1863,"ariaHidden":59},[58],[29,1865,1867,1870],{"className":1866},[63],[29,1868],{"className":1869,"style":1423},[67],[29,1871,1873],{"className":1872},[72,1427],[29,1874,1876,1909],{"className":1875},[163,164],[29,1877,1879,1906],{"className":1878},[168],[29,1880,1882,1894],{"className":1881,"style":1437},[172],[29,1883,1885,1888],{"className":1884,"style":1442},[1441],[29,1886],{"className":1887,"style":181},[180],[29,1889,1891],{"className":1890,"style":1449},[72],[29,1892,50],{"className":1893},[72,73],[29,1895,1896,1899],{"style":1455},[29,1897],{"className":1898,"style":181},[180],[29,1900,1902],{"className":1901,"style":1463},[1462],[1465,1903,1904],{"xmlns":1467,"width":1468,"height":1469,"viewBox":1470,"preserveAspectRatio":1471},[1473,1905],{"d":1475},[29,1907,233],{"className":1908},[232],[29,1910,1912],{"className":1911},[168],[29,1913,1915],{"className":1914,"style":1485},[172],[29,1916],{}," zera o erro com 2 parâmetros, enquanto três potências gastam 4 parâmetros e ainda erram. Conhecimento de domínio vale mais que força bruta.",[21,1919,1921],{"id":1920},"domando-o-overfitting-regularização","Domando o overfitting: regularização",[11,1923,1924,1927,1928,1931,1932,1962],{},[15,1925,1926],{"href":17},"O post principal"," terminou com uma pergunta em aberto: dá pra manter toda a flexibilidade de um grau alto sem pagar o preço do overfitting? A resposta é regularização L2, ou ",[888,1929,1930],{},"Ridge",". Em vez de escolher um grau discreto, eu adiciono uma penalidade contínua ",[29,1933,1935,1950],{"className":1934},[32],[29,1936,1938],{"className":1937},[36],[38,1939,1940],{"xmlns":40},[42,1941,1942,1947],{},[45,1943,1944],{},[48,1945,1946],{},"λ",[52,1948,1949],{"encoding":54},"\\lambda",[29,1951,1953],{"className":1952,"ariaHidden":59},[58],[29,1954,1956,1959],{"className":1955},[63],[29,1957],{"className":1958,"style":882},[67],[29,1960,1946],{"className":1961},[72,73]," que castiga pesos grandes:",[11,1964,1965],{},[29,1966,1968,2047],{"className":1967},[32],[29,1969,1971],{"className":1970},[36],[38,1972,1973],{"xmlns":40},[42,1974,1975,2044],{},[45,1976,1977,1999,2002,2004,2006,2008,2010,2012,2014,2016,2018,2020,2022,2024,2026,2028,2035],{},[1196,1978,1979,1982],{},[48,1980,1981],{},"J",[45,1983,1984,1987,1990,1993,1996],{},[48,1985,1986],{},"r",[48,1988,1989],{},"i",[48,1991,1992],{},"d",[48,1994,1995],{},"g",[48,1997,1998],{},"e",[93,2000,95],{"stretchy":2001},"false",[48,2003,1200],{"mathvariant":1062},[93,2005,1564],{"separator":59},[48,2007,870],{},[93,2009,114],{"stretchy":2001},[93,2011,1384],{},[48,2013,1981],{},[93,2015,95],{"stretchy":2001},[48,2017,1200],{"mathvariant":1062},[93,2019,1564],{"separator":59},[48,2021,870],{},[93,2023,114],{"stretchy":2001},[93,2025,543],{},[48,2027,1946],{},[1196,2029,2030,2033],{},[93,2031,2032],{},"∑",[48,2034,1203],{},[2036,2037,2038,2040,2042],"msubsup",{},[48,2039,1200],{},[48,2041,1203],{},[116,2043,118],{},[52,2045,2046],{"encoding":54},"J_{ridge}(\\mathbf{w}, b) = J(\\mathbf{w}, b) + \\lambda \\sum_j w_j^2",[29,2048,2050,2144,2182],{"className":2049,"ariaHidden":59},[58],[29,2051,2053,2057,2116,2119,2123,2126,2129,2132,2135,2138,2141],{"className":2052},[63],[29,2054],{"className":2055,"style":2056},[67],"height:1.0361em;vertical-align:-0.2861em;",[29,2058,2060,2064],{"className":2059},[72],[29,2061,1981],{"className":2062,"style":2063},[72,73],"margin-right:0.0962em;",[29,2065,2067],{"className":2066},[256],[29,2068,2070,2108],{"className":2069},[163,164],[29,2071,2073,2105],{"className":2072},[168],[29,2074,2077],{"className":2075,"style":2076},[172],"height:0.3361em;",[29,2078,2080,2083],{"style":2079},"top:-2.55em;margin-left:-0.0962em;margin-right:0.05em;",[29,2081],{"className":2082,"style":273},[180],[29,2084,2086],{"className":2085},[185,186,187,188],[29,2087,2089,2093,2096,2099,2102],{"className":2088},[72,188],[29,2090,1986],{"className":2091,"style":2092},[72,73,188],"margin-right:0.0278em;",[29,2094,1989],{"className":2095},[72,73,188],[29,2097,1992],{"className":2098},[72,73,188],[29,2100,1995],{"className":2101,"style":195},[72,73,188],[29,2103,1998],{"className":2104},[72,73,188],[29,2106,233],{"className":2107},[232],[29,2109,2111],{"className":2110},[168],[29,2112,2114],{"className":2113,"style":1259},[172],[29,2115],{},[29,2117,95],{"className":2118},[142],[29,2120,1200],{"className":2121,"style":2122},[72,1089],"margin-right:0.016em;",[29,2124,1564],{"className":2125},[1590],[29,2127],{"className":2128,"style":1594},[1408],[29,2130,870],{"className":2131},[72,73],[29,2133,114],{"className":2134},[246],[29,2136],{"className":2137,"style":1409},[1408],[29,2139,1384],{"className":2140},[1413],[29,2142],{"className":2143,"style":1409},[1408],[29,2145,2147,2151,2154,2157,2160,2163,2166,2169,2172,2176,2179],{"className":2146},[63],[29,2148],{"className":2149,"style":2150},[67],"height:1em;vertical-align:-0.25em;",[29,2152,1981],{"className":2153,"style":2063},[72,73],[29,2155,95],{"className":2156},[142],[29,2158,1200],{"className":2159,"style":2122},[72,1089],[29,2161,1564],{"className":2162},[1590],[29,2164],{"className":2165,"style":1594},[1408],[29,2167,870],{"className":2168},[72,73],[29,2170,114],{"className":2171},[246],[29,2173],{"className":2174,"style":2175},[1408],"margin-right:0.2222em;",[29,2177,543],{"className":2178},[225],[29,2180],{"className":2181,"style":2175},[1408],[29,2183,2185,2189,2192,2195,2242,2245],{"className":2184},[63],[29,2186],{"className":2187,"style":2188},[67],"height:1.2499em;vertical-align:-0.4358em;",[29,2190,1946],{"className":2191},[72,73],[29,2193],{"className":2194,"style":1594},[1408],[29,2196,2199,2205],{"className":2197},[2198],"mop",[29,2200,2032],{"className":2201,"style":2204},[2198,2202,2203],"op-symbol","small-op","position:relative;top:0em;",[29,2206,2208],{"className":2207},[256],[29,2209,2211,2233],{"className":2210},[163,164],[29,2212,2214,2230],{"className":2213},[168],[29,2215,2218],{"className":2216,"style":2217},[172],"height:0.162em;",[29,2219,2221,2224],{"style":2220},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[29,2222],{"className":2223,"style":273},[180],[29,2225,2227],{"className":2226},[185,186,187,188],[29,2228,1203],{"className":2229,"style":1249},[72,73,188],[29,2231,233],{"className":2232},[232],[29,2234,2236],{"className":2235},[168],[29,2237,2240],{"className":2238,"style":2239},[172],"height:0.4358em;",[29,2241],{},[29,2243],{"className":2244,"style":1594},[1408],[29,2246,2248,2251],{"className":2247},[72],[29,2249,1200],{"className":2250,"style":1223},[72,73],[29,2252,2254],{"className":2253},[256],[29,2255,2257,2289],{"className":2256},[163,164],[29,2258,2260,2286],{"className":2259},[168],[29,2261,2263,2275],{"className":2262,"style":311},[172],[29,2264,2266,2269],{"style":2265},"top:-2.4413em;margin-left:-0.0269em;margin-right:0.05em;",[29,2267],{"className":2268,"style":273},[180],[29,2270,2272],{"className":2271},[185,186,187,188],[29,2273,1203],{"className":2274,"style":1249},[72,73,188],[29,2276,2277,2280],{"style":332},[29,2278],{"className":2279,"style":273},[180],[29,2281,2283],{"className":2282},[185,186,187,188],[29,2284,118],{"className":2285},[72,188],[29,2287,233],{"className":2288},[232],[29,2290,2292],{"className":2291},[168],[29,2293,2296],{"className":2294,"style":2295},[172],"height:0.3948em;",[29,2297],{},[11,2299,2300,2301,2370,2371,2511],{},"Por que isso funciona, na prática? Um polinômio de grau alto decorando 10 pontos de treino precisa, em algum lugar da curva, subir muito rápido e descer muito rápido pra passar exatamente em cima de cada ponto ruidoso, e isso só é possível se alguns pesos ",[29,2302,2304,2321],{"className":2303},[32],[29,2305,2307],{"className":2306},[36],[38,2308,2309],{"xmlns":40},[42,2310,2311,2319],{},[45,2312,2313],{},[1196,2314,2315,2317],{},[48,2316,1200],{},[48,2318,1203],{},[52,2320,1206],{"encoding":54},[29,2322,2324],{"className":2323,"ariaHidden":59},[58],[29,2325,2327,2330],{"className":2326},[63],[29,2328],{"className":2329,"style":1216},[67],[29,2331,2333,2336],{"className":2332},[72],[29,2334,1200],{"className":2335,"style":1223},[72,73],[29,2337,2339],{"className":2338},[256],[29,2340,2342,2362],{"className":2341},[163,164],[29,2343,2345,2359],{"className":2344},[168],[29,2346,2348],{"className":2347,"style":1236},[172],[29,2349,2350,2353],{"style":1239},[29,2351],{"className":2352,"style":273},[180],[29,2354,2356],{"className":2355},[185,186,187,188],[29,2357,1203],{"className":2358,"style":1249},[72,73,188],[29,2360,233],{"className":2361},[232],[29,2363,2365],{"className":2364},[168],[29,2366,2368],{"className":2367,"style":1259},[172],[29,2369],{}," ficarem enormes (frequentemente com sinais opostos se cancelando na maior parte do domínio, e \"descancelando\" bem na hora de fazer aquela curva colar num ponto específico). Se eu simplesmente proíbo os pesos de ficarem grandes demais, cobrando um preço (",[29,2372,2374,2402],{"className":2373},[32],[29,2375,2377],{"className":2376},[36],[38,2378,2379],{"xmlns":40},[42,2380,2381,2399],{},[45,2382,2383,2385,2391],{},[48,2384,1946],{},[1196,2386,2387,2389],{},[93,2388,2032],{},[48,2390,1203],{},[2036,2392,2393,2395,2397],{},[48,2394,1200],{},[48,2396,1203],{},[116,2398,118],{},[52,2400,2401],{"encoding":54},"\\lambda \\sum_j w_j^2",[29,2403,2405],{"className":2404,"ariaHidden":59},[58],[29,2406,2408,2411,2414,2417,2457,2460],{"className":2407},[63],[29,2409],{"className":2410,"style":2188},[67],[29,2412,1946],{"className":2413},[72,73],[29,2415],{"className":2416,"style":1594},[1408],[29,2418,2420,2423],{"className":2419},[2198],[29,2421,2032],{"className":2422,"style":2204},[2198,2202,2203],[29,2424,2426],{"className":2425},[256],[29,2427,2429,2449],{"className":2428},[163,164],[29,2430,2432,2446],{"className":2431},[168],[29,2433,2435],{"className":2434,"style":2217},[172],[29,2436,2437,2440],{"style":2220},[29,2438],{"className":2439,"style":273},[180],[29,2441,2443],{"className":2442},[185,186,187,188],[29,2444,1203],{"className":2445,"style":1249},[72,73,188],[29,2447,233],{"className":2448},[232],[29,2450,2452],{"className":2451},[168],[29,2453,2455],{"className":2454,"style":2239},[172],[29,2456],{},[29,2458],{"className":2459,"style":1594},[1408],[29,2461,2463,2466],{"className":2462},[72],[29,2464,1200],{"className":2465,"style":1223},[72,73],[29,2467,2469],{"className":2468},[256],[29,2470,2472,2503],{"className":2471},[163,164],[29,2473,2475,2500],{"className":2474},[168],[29,2476,2478,2489],{"className":2477,"style":311},[172],[29,2479,2480,2483],{"style":2265},[29,2481],{"className":2482,"style":273},[180],[29,2484,2486],{"className":2485},[185,186,187,188],[29,2487,1203],{"className":2488,"style":1249},[72,73,188],[29,2490,2491,2494],{"style":332},[29,2492],{"className":2493,"style":273},[180],[29,2495,2497],{"className":2496},[185,186,187,188],[29,2498,118],{"className":2499},[72,188],[29,2501,233],{"className":2502},[232],[29,2504,2506],{"className":2505},[168],[29,2507,2509],{"className":2508,"style":2295},[172],[29,2510],{},") proporcional ao tamanho deles ao quadrado, a curva perde a capacidade física de fazer essas curvas fechadas em volta de cada ponto individual. Ela é forçada a \"escolher\" uma tendência mais suave que passa perto da maioria dos pontos, em vez de exatamente em cima de cada um, o que é outra forma de dizer: ela para de decorar o ruído e passa a acompanhar o sinal.",[11,2513,2514,2515,2543,2544,2607,2608,2611,2612,2614,2615,1488],{},"Implementei isso na minha própria solução exata (somando ",[29,2516,2518,2531],{"className":2517},[32],[29,2519,2521],{"className":2520},[36],[38,2522,2523],{"xmlns":40},[42,2524,2525,2529],{},[45,2526,2527],{},[48,2528,1946],{},[52,2530,1949],{"encoding":54},[29,2532,2534],{"className":2533,"ariaHidden":59},[58],[29,2535,2537,2540],{"className":2536},[63],[29,2538],{"className":2539,"style":882},[67],[29,2541,1946],{"className":2542},[72,73]," à diagonal de ",[29,2545,2547,2566],{"className":2546},[32],[29,2548,2550],{"className":2549},[36],[38,2551,2552],{"xmlns":40},[42,2553,2554,2564],{},[45,2555,2556,2562],{},[88,2557,2558,2560],{},[48,2559,1063],{"mathvariant":1062},[48,2561,1067],{"mathvariant":1066},[48,2563,1063],{"mathvariant":1062},[52,2565,1072],{"encoding":54},[29,2567,2569],{"className":2568,"ariaHidden":59},[58],[29,2570,2572,2575,2604],{"className":2571},[63],[29,2573],{"className":2574,"style":1082},[67],[29,2576,2578,2581],{"className":2577},[72],[29,2579,1063],{"className":2580},[72,1089],[29,2582,2584],{"className":2583},[256],[29,2585,2587],{"className":2586},[163],[29,2588,2590],{"className":2589},[168],[29,2591,2593],{"className":2592,"style":1082},[172],[29,2594,2595,2598],{"style":332},[29,2596],{"className":2597,"style":273},[180],[29,2599,2601],{"className":2600},[185,186,187,188],[29,2602,1067],{"className":2603},[72,188],[29,2605,1063],{"className":2606},[72,1089],", excluindo o viés, que é exatamente a forma fechada que o ",[2609,2610,1930],"code",{}," do scikit-learn resolve por baixo dos panos). Não tenho scikit-learn instalado nesse ambiente, mas aqui está o equivalente calculado de verdade, não só o princípio: mesmo caso ruidoso de 10 pontos, grau 9, do ",[15,2613,1268],{"href":17},", variando ",[29,2616,2618,2631],{"className":2617},[32],[29,2619,2621],{"className":2620},[36],[38,2622,2623],{"xmlns":40},[42,2624,2625,2629],{},[45,2626,2627],{},[48,2628,1946],{},[52,2630,1949],{"encoding":54},[29,2632,2634],{"className":2633,"ariaHidden":59},[58],[29,2635,2637,2640],{"className":2636},[63],[29,2638],{"className":2639,"style":882},[67],[29,2641,1946],{"className":2642},[72,73],[1118,2644,2645,2685],{},[1121,2646,2647],{},[1124,2648,2649,2679,2682],{},[1127,2650,2651],{"align":1129},[29,2652,2654,2667],{"className":2653},[32],[29,2655,2657],{"className":2656},[36],[38,2658,2659],{"xmlns":40},[42,2660,2661,2665],{},[45,2662,2663],{},[48,2664,1946],{},[52,2666,1949],{"encoding":54},[29,2668,2670],{"className":2669,"ariaHidden":59},[58],[29,2671,2673,2676],{"className":2672},[63],[29,2674],{"className":2675,"style":882},[67],[29,2677,1946],{"className":2678},[72,73],[1127,2680,2681],{"align":1133},"RMSE treino",[1127,2683,2684],{"align":1133},"RMSE teste",[1136,2686,2687,2697,2710,2721,2732,2743,2754],{},[1124,2688,2689,2692,2694],{},[1141,2690,2691],{"align":1129},"0 (sem regularização)",[1141,2693,1839],{"align":1133},[1141,2695,2696],{"align":1133},"1.717",[1124,2698,2699,2702,2705],{},[1141,2700,2701],{"align":1129},"0.01",[1141,2703,2704],{"align":1133},"0.281",[1141,2706,2707],{"align":1133},[888,2708,2709],{},"0.296",[1124,2711,2712,2715,2718],{},[1141,2713,2714],{"align":1129},"0.1",[1141,2716,2717],{"align":1133},"0.478",[1141,2719,2720],{"align":1133},"0.646",[1124,2722,2723,2726,2729],{},[1141,2724,2725],{"align":1129},"0.5",[1141,2727,2728],{"align":1133},"0.587",[1141,2730,2731],{"align":1133},"0.652",[1124,2733,2734,2737,2740],{},[1141,2735,2736],{"align":1129},"1.0",[1141,2738,2739],{"align":1133},"0.631",[1141,2741,2742],{"align":1133},"0.650",[1124,2744,2745,2748,2751],{},[1141,2746,2747],{"align":1129},"2.0",[1141,2749,2750],{"align":1133},"0.666",[1141,2752,2753],{"align":1133},"0.658",[1124,2755,2756,2759,2762],{},[1141,2757,2758],{"align":1129},"5.0",[1141,2760,2761],{"align":1133},"0.696",[1141,2763,2764],{"align":1133},"0.674",[11,2766,2767,2768,2796,2797,2800,2801,2854,2855,2857],{},"Repara no padrão: sem regularização o treino vai a zero (10 parâmetros pra 10 pontos, ajuste exato) e o teste é o pior de todos. Conforme ",[29,2769,2771,2784],{"className":2770},[32],[29,2772,2774],{"className":2773},[36],[38,2775,2776],{"xmlns":40},[42,2777,2778,2782],{},[45,2779,2780],{},[48,2781,1946],{},[52,2783,1949],{"encoding":54},[29,2785,2787],{"className":2786,"ariaHidden":59},[58],[29,2788,2790,2793],{"className":2789},[63],[29,2791],{"className":2792,"style":882},[67],[29,2794,1946],{"className":2795},[72,73]," cresce, o treino piora e o teste ",[888,2798,2799],{},"melhora",", até um ponto (",[29,2802,2804,2823],{"className":2803},[32],[29,2805,2807],{"className":2806},[36],[38,2808,2809],{"xmlns":40},[42,2810,2811,2820],{},[45,2812,2813,2815,2818],{},[48,2814,1946],{},[93,2816,2817],{},"≈",[116,2819,2701],{},[52,2821,2822],{"encoding":54},"\\lambda \\approx 0.01",[29,2824,2826,2844],{"className":2825,"ariaHidden":59},[58],[29,2827,2829,2832,2835,2838,2841],{"className":2828},[63],[29,2830],{"className":2831,"style":882},[67],[29,2833,1946],{"className":2834},[72,73],[29,2836],{"className":2837,"style":1409},[1408],[29,2839,2817],{"className":2840},[1413],[29,2842],{"className":2843,"style":1409},[1408],[29,2845,2847,2851],{"className":2846},[63],[29,2848],{"className":2849,"style":2850},[67],"height:0.6444em;",[29,2852,2701],{"className":2853},[72]," aqui) onde o teste passa a piorar de novo porque o modelo já ficou rígido demais. É o mesmo trade-off viés-variância do ",[15,2856,1268],{"href":17},", só que controlado por um botão contínuo em vez da escolha discreta de grau.",[11,2859,2860,2861,1488],{},"Testa você mesmo, arrastando ",[29,2862,2864,2877],{"className":2863},[32],[29,2865,2867],{"className":2866},[36],[38,2868,2869],{"xmlns":40},[42,2870,2871,2875],{},[45,2872,2873],{},[48,2874,1946],{},[52,2876,1949],{"encoding":54},[29,2878,2880],{"className":2879,"ariaHidden":59},[58],[29,2881,2883,2886],{"className":2882},[63],[29,2884],{"className":2885,"style":882},[67],[29,2887,1946],{"className":2888},[72,73],[2890,2891],"ridge-fit-explorer",{":degree":1165,":initial-lambda":2892,":lambda-max":1003,":x-test":2893,":x-train":2894,":y-test":2895,":y-train":2896,"x-label":50,"y-label":2897},"0","[1, 3, 5, 7, 9, 11, 13, 15, 17, 19]","[0, 2, 4, 6, 8, 10, 12, 14, 16, 18]","[1.094999, -0.043944, -0.796443, -1.151981, -0.19079, 0.571574, 0.966876, 0.427335, -0.243645, -1.018878]","[1.193228, 0.550253, -0.579973, -1.143308, -0.623747, 0.365632, 0.960921, 0.528028, -0.097393, -0.880685]","y (com ruído)",[11,2899,2900,2901,2929],{},"Repara como a curva para de decorar cada ponto de treino e vira parecida com o formato verdadeiro assim que ",[29,2902,2904,2917],{"className":2903},[32],[29,2905,2907],{"className":2906},[36],[38,2908,2909],{"xmlns":40},[42,2910,2911,2915],{},[45,2912,2913],{},[48,2914,1946],{},[52,2916,1949],{"encoding":54},[29,2918,2920],{"className":2919,"ariaHidden":59},[58],[29,2921,2923,2926],{"className":2922},[63],[29,2924],{"className":2925,"style":882},[67],[29,2927,1946],{"className":2928},[72,73]," sai de zero, sem eu precisar mexer no grau.",[21,2931,2933],{"id":2932},"exercícios","Exercícios",[11,2935,2936],{},"Tenta antes de abrir a resposta.",[2938,2939,2941],"h3",{"id":2940},"exercício-1-descubra-a-transformação","Exercício 1: descubra a transformação",[11,2943,2944,2945,2948,2949,2951,2952,2954,2955,2958,2959,2962],{},"Gere ",[2609,2946,2947],{},"y = 3 * log(x + 1) + 2"," pra ",[2609,2950,50],{}," de 0 a 19. Ajusta (a) só com ",[2609,2953,50],{},", (b) com ",[2609,2956,2957],{},"x, x², x³"," e (c) com ",[2609,2960,2961],{},"log(x+1)",". Compara os RMSE.",[2964,2965,2966,2972],"details",{},[2967,2968,2969],"summary",{},[870,2970,2971],{},"Resposta",[11,2973,2974,2975,2977,2978,2980],{},"A feature ",[2609,2976,2961],{}," acerta praticamente na mosca com um único peso, porque o alvo é linear nela por construção. O polinômio de grau 3 chega perto (todo polinômio aproxima o log num intervalo limitado), mas gasta 3 parâmetros e erra fora da faixa. Só ",[2609,2979,50],{}," fica ruim. A moral: quando você conhece a forma da relação, a feature certa vale mais que qualquer quantidade de potências.",[2938,2982,2984],{"id":2983},"exercício-2-a-ordem-da-normalização-importa","Exercício 2: a ordem da normalização importa?",[11,2986,2987,2988,2991,2992,2995],{},"Compara ajustar ",[2609,2989,2990],{},"zscore(x)²"," contra ",[2609,2993,2994],{},"zscore(x²)",". Os RMSE finais são iguais? E os pesos?",[2964,2997,2998,3002],{},[2967,2999,3000],{},[870,3001,2971],{},[11,3003,3004,3005,3376,3377,797,3435,3463,3464,3492],{},"O RMSE final é praticamente igual, mas os pesos e a velocidade de convergência não são. O motivo: ",[29,3006,3008,3076],{"className":3007},[32],[29,3009,3011],{"className":3010},[36],[38,3012,3013],{"xmlns":40},[42,3014,3015,3073],{},[45,3016,3017,3039,3041],{},[88,3018,3019,3037],{},[45,3020,3021,3023,3035],{},[93,3022,95],{"fence":59},[97,3024,3025,3033],{},[45,3026,3027,3029,3031],{},[48,3028,50],{},[93,3030,105],{},[48,3032,108],{},[48,3034,111],{},[93,3036,114],{"fence":59},[116,3038,118],{},[93,3040,1384],{},[97,3042,3043,3067],{},[45,3044,3045,3051,3053,3055,3057,3059,3061],{},[88,3046,3047,3049],{},[48,3048,50],{},[116,3050,118],{},[93,3052,105],{},[116,3054,118],{},[48,3056,108],{},[48,3058,50],{},[93,3060,543],{},[88,3062,3063,3065],{},[48,3064,108],{},[116,3066,118],{},[88,3068,3069,3071],{},[48,3070,111],{},[116,3072,118],{},[52,3074,3075],{"encoding":54},"\\left(\\frac{x-\\mu}{\\sigma}\\right)^2 = \\frac{x^2 - 2\\mu x + \\mu^2}{\\sigma^2}",[29,3077,3079,3209],{"className":3078,"ariaHidden":59},[58],[29,3080,3082,3085,3200,3203,3206],{"className":3081},[63],[29,3083],{"className":3084,"style":131},[67],[29,3086,3088,3177],{"className":3087},[135],[29,3089,3091,3097,3171],{"className":3090},[135],[29,3092,3094],{"className":3093,"style":144},[142,143],[29,3095,95],{"className":3096},[148,149],[29,3098,3100,3103,3168],{"className":3099},[72],[29,3101],{"className":3102},[142,156],[29,3104,3106],{"className":3105},[97],[29,3107,3109,3160],{"className":3108},[163,164],[29,3110,3112,3157],{"className":3111},[168],[29,3113,3115,3129,3137],{"className":3114,"style":173},[172],[29,3116,3117,3120],{"style":176},[29,3118],{"className":3119,"style":181},[180],[29,3121,3123],{"className":3122},[185,186,187,188],[29,3124,3126],{"className":3125},[72,188],[29,3127,111],{"className":3128,"style":195},[72,73,188],[29,3130,3131,3134],{"style":198},[29,3132],{"className":3133,"style":181},[180],[29,3135],{"className":3136,"style":206},[205],[29,3138,3139,3142],{"style":209},[29,3140],{"className":3141,"style":181},[180],[29,3143,3145],{"className":3144},[185,186,187,188],[29,3146,3148,3151,3154],{"className":3147},[72,188],[29,3149,50],{"className":3150},[72,73,188],[29,3152,105],{"className":3153},[225,188],[29,3155,108],{"className":3156},[72,73,188],[29,3158,233],{"className":3159},[232],[29,3161,3163],{"className":3162},[168],[29,3164,3166],{"className":3165,"style":240},[172],[29,3167],{},[29,3169],{"className":3170},[246,156],[29,3172,3174],{"className":3173,"style":144},[246,143],[29,3175,114],{"className":3176},[148,149],[29,3178,3180],{"className":3179},[256],[29,3181,3183],{"className":3182},[163],[29,3184,3186],{"className":3185},[168],[29,3187,3189],{"className":3188,"style":266},[172],[29,3190,3191,3194],{"style":269},[29,3192],{"className":3193,"style":273},[180],[29,3195,3197],{"className":3196},[185,186,187,188],[29,3198,118],{"className":3199},[72,188],[29,3201],{"className":3202,"style":1409},[1408],[29,3204,1384],{"className":3205},[1413],[29,3207],{"className":3208,"style":1409},[1408],[29,3210,3212,3215],{"className":3211},[63],[29,3213],{"className":3214,"style":568},[67],[29,3216,3218,3221,3373],{"className":3217},[72],[29,3219],{"className":3220},[142,156],[29,3222,3224],{"className":3223},[97],[29,3225,3227,3365],{"className":3226},[163,164],[29,3228,3230,3362],{"className":3229},[168],[29,3231,3233,3273,3281],{"className":3232,"style":587},[172],[29,3234,3235,3238],{"style":176},[29,3236],{"className":3237,"style":181},[180],[29,3239,3241],{"className":3240},[185,186,187,188],[29,3242,3244],{"className":3243},[72,188],[29,3245,3247,3250],{"className":3246},[72,188],[29,3248,111],{"className":3249,"style":195},[72,73,188],[29,3251,3253],{"className":3252},[256],[29,3254,3256],{"className":3255},[163],[29,3257,3259],{"className":3258},[168],[29,3260,3262],{"className":3261,"style":617},[172],[29,3263,3264,3267],{"style":620},[29,3265],{"className":3266,"style":624},[180],[29,3268,3270],{"className":3269},[185,628,149,188],[29,3271,118],{"className":3272},[72,188],[29,3274,3275,3278],{"style":198},[29,3276],{"className":3277,"style":181},[180],[29,3279],{"className":3280,"style":206},[205],[29,3282,3283,3286],{"style":209},[29,3284],{"className":3285,"style":181},[180],[29,3287,3289],{"className":3288},[185,186,187,188],[29,3290,3292,3321,3324,3327,3330,3333],{"className":3291},[72,188],[29,3293,3295,3298],{"className":3294},[72,188],[29,3296,50],{"className":3297},[72,73,188],[29,3299,3301],{"className":3300},[256],[29,3302,3304],{"className":3303},[163],[29,3305,3307],{"className":3306},[168],[29,3308,3310],{"className":3309,"style":669},[172],[29,3311,3312,3315],{"style":672},[29,3313],{"className":3314,"style":624},[180],[29,3316,3318],{"className":3317},[185,628,149,188],[29,3319,118],{"className":3320},[72,188],[29,3322,105],{"className":3323},[225,188],[29,3325,118],{"className":3326},[72,188],[29,3328,691],{"className":3329},[72,73,188],[29,3331,543],{"className":3332},[225,188],[29,3334,3336,3339],{"className":3335},[72,188],[29,3337,108],{"className":3338},[72,73,188],[29,3340,3342],{"className":3341},[256],[29,3343,3345],{"className":3344},[163],[29,3346,3348],{"className":3347},[168],[29,3349,3351],{"className":3350,"style":669},[172],[29,3352,3353,3356],{"style":672},[29,3354],{"className":3355,"style":624},[180],[29,3357,3359],{"className":3358},[185,628,149,188],[29,3360,118],{"className":3361},[72,188],[29,3363,233],{"className":3364},[232],[29,3366,3368],{"className":3367},[168],[29,3369,3371],{"className":3370,"style":240},[172],[29,3372],{},[29,3374],{"className":3375},[246,156],", ou seja, é uma combinação linear de ",[29,3378,3380,3397],{"className":3379},[32],[29,3381,3383],{"className":3382},[36],[38,3384,3385],{"xmlns":40},[42,3386,3387,3395],{},[45,3388,3389],{},[88,3390,3391,3393],{},[48,3392,50],{},[116,3394,118],{},[52,3396,301],{"encoding":54},[29,3398,3400],{"className":3399,"ariaHidden":59},[58],[29,3401,3403,3406],{"className":3402},[63],[29,3404],{"className":3405,"style":311},[67],[29,3407,3409,3412],{"className":3408},[72],[29,3410,50],{"className":3411},[72,73],[29,3413,3415],{"className":3414},[256],[29,3416,3418],{"className":3417},[163],[29,3419,3421],{"className":3420},[168],[29,3422,3424],{"className":3423,"style":311},[172],[29,3425,3426,3429],{"style":332},[29,3427],{"className":3428,"style":273},[180],[29,3430,3432],{"className":3431},[185,186,187,188],[29,3433,118],{"className":3434},[72,188],[29,3436,3438,3451],{"className":3437},[32],[29,3439,3441],{"className":3440},[36],[38,3442,3443],{"xmlns":40},[42,3444,3445,3449],{},[45,3446,3447],{},[48,3448,50],{},[52,3450,50],{"encoding":54},[29,3452,3454],{"className":3453,"ariaHidden":59},[58],[29,3455,3457,3460],{"className":3456},[63],[29,3458],{"className":3459,"style":68},[67],[29,3461,50],{"className":3462},[72,73]," e uma constante. Como o modelo já tem ",[29,3465,3467,3480],{"className":3466},[32],[29,3468,3470],{"className":3469},[36],[38,3471,3472],{"xmlns":40},[42,3473,3474,3478],{},[45,3475,3476],{},[48,3477,50],{},[52,3479,50],{"encoding":54},[29,3481,3483],{"className":3482,"ariaHidden":59},[58],[29,3484,3486,3489],{"className":3485},[63],[29,3487],{"className":3488,"style":68},[67],[29,3490,50],{"className":3491},[72,73]," e o viés disponíveis, o espaço de funções alcançáveis é o mesmo, muda só a base em que ele está escrito.",[2938,3494,3496],{"id":3495},"exercício-3-quantos-pontos-são-necessários","Exercício 3: quantos pontos são necessários?",[11,3498,3499,3500,3555],{},"Mantendo o grau 13, repete a análise treino\u002Fteste com 40, 100 e 500 pontos em ",[29,3501,3503,3528],{"className":3502},[32],[29,3504,3506],{"className":3505},[36],[38,3507,3508],{"xmlns":40},[42,3509,3510,3525],{},[45,3511,3512,3515,3517,3519,3522],{},[93,3513,3514],{"stretchy":2001},"[",[116,3516,2892],{},[93,3518,1564],{"separator":59},[116,3520,3521],{},"19",[93,3523,3524],{"stretchy":2001},"]",[52,3526,3527],{"encoding":54},"[0, 19]",[29,3529,3531],{"className":3530,"ariaHidden":59},[58],[29,3532,3534,3537,3540,3543,3546,3549,3552],{"className":3533},[63],[29,3535],{"className":3536,"style":2150},[67],[29,3538,3514],{"className":3539},[142],[29,3541,2892],{"className":3542},[72],[29,3544,1564],{"className":3545},[1590],[29,3547],{"className":3548,"style":1594},[1408],[29,3550,3521],{"className":3551},[72],[29,3553,3524],{"className":3554},[246],". O overfitting some?",[2964,3557,3558,3562],{},[2967,3559,3560],{},[870,3561,2971],{},[11,3563,3564],{},"Some em grande medida. Overfitting é uma relação entre capacidade do modelo e quantidade de dados, não uma propriedade do modelo sozinho. Com 500 pontos, 14 parâmetros deixam de ser demais. Isso dá as três saídas clássicas pra overfitting: mais dados, menos features, ou regularização.",[2938,3566,3568],{"id":3567},"exercício-4-interações-entre-variáveis","Exercício 4: interações entre variáveis",[11,3570,3571,3572,3575,3576,3579,3580,3583],{},"Com duas variáveis de entrada, features polinomiais de grau 2 geram ",[2609,3573,3574],{},"x1, x2, x1², x1x2, x2²",". O termo ",[2609,3577,3578],{},"x1x2"," é uma interação. Constrói um alvo em que a interação seja essencial (",[2609,3581,3582],{},"y = x1 * x2",") e mostra que um modelo sem ela falha.",[2964,3585,3586,3590],{},[2967,3587,3588],{},[870,3589,2971],{},[11,3591,3592],{},"Sem o termo cruzado, o modelo é aditivo e não consegue representar \"o efeito de x1 depende de x2\". Interações são a forma mais comum e mais útil de engenharia de features em dados tabulares reais, mais até que potências puras.",[2938,3594,3596],{"id":3595},"exercício-5-critério-de-parada-honesto","Exercício 5: critério de parada honesto",[11,3598,3599],{},"Se eu tivesse usado gradiente descendente em vez de solução exata, como eu pararia de forma confiável?",[2964,3601,3602,3606],{},[2967,3603,3604],{},[870,3605,2971],{},[11,3607,3608,3609,3612,3613,3644],{},"Pela norma do gradiente (",[2609,3610,3611],{},"max(|dj_dw|, |dj_db|) \u003C tol","), não pela melhora do custo. Com ",[29,3614,3616,3631],{"className":3615},[32],[29,3617,3619],{"className":3618},[36],[38,3620,3621],{"xmlns":40},[42,3622,3623,3628],{},[45,3624,3625],{},[48,3626,3627],{},"α",[52,3629,3630],{"encoding":54},"\\alpha",[29,3632,3634],{"className":3633,"ariaHidden":59},[58],[29,3635,3637,3640],{"className":3636},[63],[29,3638],{"className":3639,"style":68},[67],[29,3641,3627],{"className":3642,"style":3643},[72,73],"margin-right:0.0037em;"," pequeno demais, o custo também melhora pouco por iteração, e um critério baseado nele faria eu parar achando que convergi sem ter convergido de verdade.",{"title":3646,"searchDepth":3647,"depth":3647,"links":3648},"",2,[3649,3650,3651,3653,3654,3655,3656],{"id":23,"depth":3647,"text":24},{"id":894,"depth":3647,"text":895},{"id":1276,"depth":3647,"text":3652},"Guardo μ\\muμ e σ\\sigmaσ, sempre",{"id":1348,"depth":3647,"text":1349},{"id":1362,"depth":3647,"text":1363},{"id":1920,"depth":3647,"text":1921},{"id":2932,"depth":3647,"text":2933,"children":3657},[3658,3660,3661,3662,3663],{"id":2940,"depth":3659,"text":2941},3,{"id":2983,"depth":3659,"text":2984},{"id":3495,"depth":3659,"text":3496},{"id":3567,"depth":3659,"text":3568},{"id":3595,"depth":3659,"text":3596},null,"2026-08-19","Ordem de normalização, colinearidade entre potências, o teorema de que mais features nunca piora o treino, e como domei o overfitting do post anterior com regularização, calculada de verdade, sem scikit-learn.","md",{},true,9,"\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Ffeature-engineering-pitfalls","machine-learning-specialization",{"title":6,"description":3666},"draft","pt\u002Fplaylists\u002Fmachine-learning-specialization\u002Ffeature-engineering-pitfalls",[3677,3678,3679],"engenharia-de-features","ridge","regularizacao","UGPync49HoFviigm6ibQnQ86lYuLkcLlcCJTjInmrrM",1787338985139]