[{"data":1,"prerenderedAt":2264},["ShallowReactive",2],{"lang-switch-post-\u002Fplaylists\u002Fmachine-learning-specialization\u002Floss-functions":3,"post-pt-machine-learning-specialization-loss-functions":4},"\u002Fen\u002Fplaylists\u002Fmachine-learning-specialization\u002Floss-functions",{"id":5,"title":6,"body":7,"cover":2247,"date":2248,"description":2249,"extension":2250,"meta":2251,"navigation":1990,"order":1994,"path":2252,"playlist":2253,"seo":2254,"status":2255,"stem":2256,"tags":2257,"__hash__":2263},"posts\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Floss-functions.md","Só pra complementar: Funções de Perda (MSE, MAE, Huber)",{"type":8,"value":9,"toc":2238},"minimark",[10,18,32,37,55,605,611,615,626,1126,1132,1136,1139,1144,1147,1151,1192,1778,1811,1815,1831,1843,1846,1850,1917,1920,1942,1946,1956,2038,2056,2228,2231,2234],[11,12,13],"p",{},[14,15],"img",{"alt":16,"src":17},"Meme \"olha o que eles precisam pra imitar uma fração do nosso poder\": uma GPU e um gráfico 3D de uma superfície de custo cheia de vales, ao lado de um cérebro gigante, com a legenda debaixo","\u002Fimages\u002Fposts\u002Fmachine-learning-specialization\u002Floss-functions\u002Fmeme-loss-function.jpeg",[11,19,20,21,26,27,31],{},"Esse post não vem de nenhum lab específico do curso, é um extra que a gente ganhou de tanto martelar em cima da função de custo nos ",[22,23,25],"a",{"href":24},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab03-cost-function","posts 2"," ",[22,28,30],{"href":29},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab04-gradient-descent","e 3",". Lá atrás a gente elevou o erro ao quadrado sem questionar muito o porquê, só que \"elevar ao quadrado\" é uma escolha, não a única opção. Bora abrir esse leque.",[33,34,36],"h2",{"id":35},"dando-nome-ao-que-você-já-construiu-mse","Dando nome ao que você já construiu: MSE",[11,38,39,40,43,44,49,50,54],{},"A função de custo que você já usa desde o ",[22,41,42],{"href":24},"post 2"," tem um nome oficial: ",[45,46,48],"glossary-term",{"definition":47},"Mean Squared Error, erro quadrático médio, a mesma função de custo que você já usa desde o post 2","MSE"," (",[51,52,53],"em",{},"Mean Squared Error",", erro quadrático médio).",[11,56,57],{},[58,59,62,189],"span",{"className":60},[61],"katex",[58,63,66],{"className":64},[65],"katex-mathml",[67,68,70],"math",{"xmlns":69},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[71,72,73,184],"semantics",{},[74,75,76,79,83,94,119],"mrow",{},[77,78,48],"mtext",{},[80,81,82],"mo",{},"=",[84,85,86,90],"mfrac",{},[87,88,89],"mn",{},"1",[91,92,93],"mi",{},"m",[95,96,97,100,110],"msubsup",{},[80,98,99],{},"∑",[74,101,102,105,107],{},[91,103,104],{},"i",[80,106,82],{},[87,108,109],{},"0",[74,111,112,114,117],{},[91,113,93],{},[80,115,116],{},"−",[87,118,89],{},[120,121,122,181],"msup",{},[74,123,124,128,145,148,162,164,166,179],{},[80,125,127],{"fence":126},"true","(",[129,130,131,134],"msub",{},[91,132,133],{},"f",[74,135,136,139,142],{},[91,137,138],{},"w",[80,140,141],{"separator":126},",",[91,143,144],{},"b",[80,146,127],{"stretchy":147},"false",[120,149,150,153],{},[91,151,152],{},"x",[74,154,155,157,159],{},[80,156,127],{"stretchy":147},[91,158,104],{},[80,160,161],{"stretchy":147},")",[80,163,161],{"stretchy":147},[80,165,116],{},[120,167,168,171],{},[91,169,170],{},"y",[74,172,173,175,177],{},[80,174,127],{"stretchy":147},[91,176,104],{},[80,178,161],{"stretchy":147},[80,180,161],{"fence":126},[87,182,183],{},"2",[185,186,188],"annotation",{"encoding":187},"application\u002Fx-tex","\\text{MSE} = \\frac{1}{m}\\sum_{i=0}^{m-1}\\left(f_{w,b}(x^{(i)}) - y^{(i)}\\right)^2",[58,190,193,222],{"className":191,"ariaHidden":126},[192],"katex-html",[58,194,197,202,210,215,219],{"className":195},[196],"base",[58,198],{"className":199,"style":201},[200],"strut","height:0.6833em;",[58,203,207],{"className":204},[205,206],"mord","text",[58,208,48],{"className":209},[205],[58,211],{"className":212,"style":214},[213],"mspace","margin-right:0.2778em;",[58,216,82],{"className":217},[218],"mrel",[58,220],{"className":221,"style":214},[213],[58,223,225,229,320,324,404,407],{"className":224},[196],[58,226],{"className":227,"style":228},[200],"height:1.442em;vertical-align:-0.35em;",[58,230,232,237,316],{"className":231},[205],[58,233],{"className":234},[235,236],"mopen","nulldelimiter",[58,238,240],{"className":239},[84],[58,241,245,307],{"className":242},[243,244],"vlist-t","vlist-t2",[58,246,249,302],{"className":247},[248],"vlist-r",[58,250,254,276,287],{"className":251,"style":253},[252],"vlist","height:0.8451em;",[58,255,257,262],{"style":256},"top:-2.655em;",[58,258],{"className":259,"style":261},[260],"pstrut","height:3em;",[58,263,269],{"className":264},[265,266,267,268],"sizing","reset-size6","size3","mtight",[58,270,272],{"className":271},[205,268],[58,273,93],{"className":274},[205,275,268],"mathnormal",[58,277,279,282],{"style":278},"top:-3.23em;",[58,280],{"className":281,"style":261},[260],[58,283],{"className":284,"style":286},[285],"frac-line","border-bottom-width:0.04em;",[58,288,290,293],{"style":289},"top:-3.394em;",[58,291],{"className":292,"style":261},[260],[58,294,296],{"className":295},[265,266,267,268],[58,297,299],{"className":298},[205,268],[58,300,89],{"className":301},[205,268],[58,303,306],{"className":304},[305],"vlist-s","​",[58,308,310],{"className":309},[248],[58,311,314],{"className":312,"style":313},[252],"height:0.345em;",[58,315],{},[58,317],{"className":318},[319,236],"mclose",[58,321],{"className":322,"style":323},[213],"margin-right:0.1667em;",[58,325,328,334],{"className":326},[327],"mop",[58,329,99],{"className":330,"style":333},[327,331,332],"op-symbol","small-op","position:relative;top:0em;",[58,335,338],{"className":336},[337],"msupsub",[58,339,341,395],{"className":340},[243,244],[58,342,344,392],{"className":343},[248],[58,345,348,370],{"className":346,"style":347},[252],"height:0.954em;",[58,349,351,355],{"style":350},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[58,352],{"className":353,"style":354},[260],"height:2.7em;",[58,356,358],{"className":357},[265,266,267,268],[58,359,361,364,367],{"className":360},[205,268],[58,362,104],{"className":363},[205,275,268],[58,365,82],{"className":366},[218,268],[58,368,109],{"className":369},[205,268],[58,371,373,376],{"style":372},"top:-3.2029em;margin-right:0.05em;",[58,374],{"className":375,"style":354},[260],[58,377,379],{"className":378},[265,266,267,268],[58,380,382,385,389],{"className":381},[205,268],[58,383,93],{"className":384},[205,275,268],[58,386,116],{"className":387},[388,268],"mbin",[58,390,89],{"className":391},[205,268],[58,393,306],{"className":394},[305],[58,396,398],{"className":397},[248],[58,399,402],{"className":400,"style":401},[252],"height:0.2997em;",[58,403],{},[58,405],{"className":406,"style":323},[213],[58,408,411,580],{"className":409},[410],"minner",[58,412,414,424,479,482,522,525,529,532,535,574],{"className":413},[410],[58,415,419],{"className":416,"style":418},[235,417],"delimcenter","top:0em;",[58,420,127],{"className":421},[422,423],"delimsizing","size1",[58,425,427,431],{"className":426},[205],[58,428,133],{"className":429,"style":430},[205,275],"margin-right:0.1076em;",[58,432,434],{"className":433},[337],[58,435,437,470],{"className":436},[243,244],[58,438,440,467],{"className":439},[248],[58,441,444],{"className":442,"style":443},[252],"height:0.3361em;",[58,445,447,450],{"style":446},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[58,448],{"className":449,"style":354},[260],[58,451,453],{"className":452},[265,266,267,268],[58,454,456,460,464],{"className":455},[205,268],[58,457,138],{"className":458,"style":459},[205,275,268],"margin-right:0.0269em;",[58,461,141],{"className":462},[463,268],"mpunct",[58,465,144],{"className":466},[205,275,268],[58,468,306],{"className":469},[305],[58,471,473],{"className":472},[248],[58,474,477],{"className":475,"style":476},[252],"height:0.2861em;",[58,478],{},[58,480,127],{"className":481},[235],[58,483,485,488],{"className":484},[205],[58,486,152],{"className":487},[205,275],[58,489,491],{"className":490},[337],[58,492,494],{"className":493},[243],[58,495,497],{"className":496},[248],[58,498,501],{"className":499,"style":500},[252],"height:0.888em;",[58,502,504,507],{"style":503},"top:-3.063em;margin-right:0.05em;",[58,505],{"className":506,"style":354},[260],[58,508,510],{"className":509},[265,266,267,268],[58,511,513,516,519],{"className":512},[205,268],[58,514,127],{"className":515},[235,268],[58,517,104],{"className":518},[205,275,268],[58,520,161],{"className":521},[319,268],[58,523,161],{"className":524},[319],[58,526],{"className":527,"style":528},[213],"margin-right:0.2222em;",[58,530,116],{"className":531},[388],[58,533],{"className":534,"style":528},[213],[58,536,538,542],{"className":537},[205],[58,539,170],{"className":540,"style":541},[205,275],"margin-right:0.0359em;",[58,543,545],{"className":544},[337],[58,546,548],{"className":547},[243],[58,549,551],{"className":550},[248],[58,552,554],{"className":553,"style":500},[252],[58,555,556,559],{"style":503},[58,557],{"className":558,"style":354},[260],[58,560,562],{"className":561},[265,266,267,268],[58,563,565,568,571],{"className":564},[205,268],[58,566,127],{"className":567},[235,268],[58,569,104],{"className":570},[205,275,268],[58,572,161],{"className":573},[319,268],[58,575,577],{"className":576,"style":418},[319,417],[58,578,161],{"className":579},[422,423],[58,581,583],{"className":582},[337],[58,584,586],{"className":585},[243],[58,587,589],{"className":588},[248],[58,590,593],{"className":591,"style":592},[252],"height:1.092em;",[58,594,596,599],{"style":595},"top:-3.3409em;margin-right:0.05em;",[58,597],{"className":598,"style":354},[260],[58,600,602],{"className":601},[265,266,267,268],[58,603,183],{"className":604},[205,268],[11,606,607,608,610],{},"Repara que é basicamente a mesma fórmula do ",[22,609,42],{"href":24},", só sem o \"2\" extra no denominador (aquele 2 só existia pra facilitar a derivada do gradiente descendente, lembra?). O nome muda, a essência não.",[33,612,614],{"id":613},"a-alternativa-mais-direta-mae","A alternativa mais direta: MAE",[11,616,617,618,49,622,625],{},"E se, em vez de elevar ao quadrado, a gente só pegasse o valor absoluto do erro? Essa é a ",[45,619,621],{"definition":620},"Mean Absolute Error, erro absoluto médio, usa o valor absoluto do erro em vez de elevar ao quadrado","MAE",[51,623,624],{},"Mean Absolute Error",", erro absoluto médio):",[11,627,628],{},[58,629,631,722],{"className":630},[61],[58,632,634],{"className":633},[65],[67,635,636],{"xmlns":69},[71,637,638,719],{},[74,639,640,642,644,650,670],{},[77,641,621],{},[80,643,82],{},[84,645,646,648],{},[87,647,89],{},[91,649,93],{},[95,651,652,654,662],{},[80,653,99],{},[74,655,656,658,660],{},[91,657,104],{},[80,659,82],{},[87,661,109],{},[74,663,664,666,668],{},[91,665,93],{},[80,667,116],{},[87,669,89],{},[74,671,672,675,687,689,701,703,705,717],{},[80,673,674],{"fence":126},"∣",[129,676,677,679],{},[91,678,133],{},[74,680,681,683,685],{},[91,682,138],{},[80,684,141],{"separator":126},[91,686,144],{},[80,688,127],{"stretchy":147},[120,690,691,693],{},[91,692,152],{},[74,694,695,697,699],{},[80,696,127],{"stretchy":147},[91,698,104],{},[80,700,161],{"stretchy":147},[80,702,161],{"stretchy":147},[80,704,116],{},[120,706,707,709],{},[91,708,170],{},[74,710,711,713,715],{},[80,712,127],{"stretchy":147},[91,714,104],{},[80,716,161],{"stretchy":147},[80,718,674],{"fence":126},[185,720,721],{"encoding":187},"\\text{MAE} = \\frac{1}{m}\\sum_{i=0}^{m-1}\\left|f_{w,b}(x^{(i)}) - y^{(i)}\\right|",[58,723,725,746],{"className":724,"ariaHidden":126},[192],[58,726,728,731,737,740,743],{"className":727},[196],[58,729],{"className":730,"style":201},[200],[58,732,734],{"className":733},[205,206],[58,735,621],{"className":736},[205],[58,738],{"className":739,"style":214},[213],[58,741,82],{"className":742},[218],[58,744],{"className":745,"style":214},[213],[58,747,749,753,821,824,893,896],{"className":748},[196],[58,750],{"className":751,"style":752},[200],"height:1.304em;vertical-align:-0.35em;",[58,754,756,759,818],{"className":755},[205],[58,757],{"className":758},[235,236],[58,760,762],{"className":761},[84],[58,763,765,810],{"className":764},[243,244],[58,766,768,807],{"className":767},[248],[58,769,771,785,793],{"className":770,"style":253},[252],[58,772,773,776],{"style":256},[58,774],{"className":775,"style":261},[260],[58,777,779],{"className":778},[265,266,267,268],[58,780,782],{"className":781},[205,268],[58,783,93],{"className":784},[205,275,268],[58,786,787,790],{"style":278},[58,788],{"className":789,"style":261},[260],[58,791],{"className":792,"style":286},[285],[58,794,795,798],{"style":289},[58,796],{"className":797,"style":261},[260],[58,799,801],{"className":800},[265,266,267,268],[58,802,804],{"className":803},[205,268],[58,805,89],{"className":806},[205,268],[58,808,306],{"className":809},[305],[58,811,813],{"className":812},[248],[58,814,816],{"className":815,"style":313},[252],[58,817],{},[58,819],{"className":820},[319,236],[58,822],{"className":823,"style":323},[213],[58,825,827,830],{"className":826},[327],[58,828,99],{"className":829,"style":333},[327,331,332],[58,831,833],{"className":832},[337],[58,834,836,885],{"className":835},[243,244],[58,837,839,882],{"className":838},[248],[58,840,842,862],{"className":841,"style":347},[252],[58,843,844,847],{"style":350},[58,845],{"className":846,"style":354},[260],[58,848,850],{"className":849},[265,266,267,268],[58,851,853,856,859],{"className":852},[205,268],[58,854,104],{"className":855},[205,275,268],[58,857,82],{"className":858},[218,268],[58,860,109],{"className":861},[205,268],[58,863,864,867],{"style":372},[58,865],{"className":866,"style":354},[260],[58,868,870],{"className":869},[265,266,267,268],[58,871,873,876,879],{"className":872},[205,268],[58,874,93],{"className":875},[205,275,268],[58,877,116],{"className":878},[388,268],[58,880,89],{"className":881},[205,268],[58,883,306],{"className":884},[305],[58,886,888],{"className":887},[248],[58,889,891],{"className":890,"style":401},[252],[58,892],{},[58,894],{"className":895,"style":323},[213],[58,897,899,949,998,1001,1039,1042,1045,1048,1051,1089],{"className":898},[410],[58,900,902],{"className":901},[235],[58,903,906],{"className":904},[422,905],"mult",[58,907,909,940],{"className":908},[243,244],[58,910,912,937],{"className":911},[248],[58,913,916],{"className":914,"style":915},[252],"height:0.85em;",[58,917,919,923],{"style":918},"top:-2.85em;",[58,920],{"className":921,"style":922},[260],"height:3.2em;",[58,924,926],{"style":925},"width:0.333em;height:1.2em;",[927,928,933],"svg",{"xmlns":929,"width":930,"height":931,"viewBox":932},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.333em","1.2em","0 0 333 1200",[934,935],"path",{"d":936},"M145 15 v585 v0 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v0 v585 h43z",[58,938,306],{"className":939},[305],[58,941,943],{"className":942},[248],[58,944,947],{"className":945,"style":946},[252],"height:0.35em;",[58,948],{},[58,950,952,955],{"className":951},[205],[58,953,133],{"className":954,"style":430},[205,275],[58,956,958],{"className":957},[337],[58,959,961,990],{"className":960},[243,244],[58,962,964,987],{"className":963},[248],[58,965,967],{"className":966,"style":443},[252],[58,968,969,972],{"style":446},[58,970],{"className":971,"style":354},[260],[58,973,975],{"className":974},[265,266,267,268],[58,976,978,981,984],{"className":977},[205,268],[58,979,138],{"className":980,"style":459},[205,275,268],[58,982,141],{"className":983},[463,268],[58,985,144],{"className":986},[205,275,268],[58,988,306],{"className":989},[305],[58,991,993],{"className":992},[248],[58,994,996],{"className":995,"style":476},[252],[58,997],{},[58,999,127],{"className":1000},[235],[58,1002,1004,1007],{"className":1003},[205],[58,1005,152],{"className":1006},[205,275],[58,1008,1010],{"className":1009},[337],[58,1011,1013],{"className":1012},[243],[58,1014,1016],{"className":1015},[248],[58,1017,1019],{"className":1018,"style":500},[252],[58,1020,1021,1024],{"style":503},[58,1022],{"className":1023,"style":354},[260],[58,1025,1027],{"className":1026},[265,266,267,268],[58,1028,1030,1033,1036],{"className":1029},[205,268],[58,1031,127],{"className":1032},[235,268],[58,1034,104],{"className":1035},[205,275,268],[58,1037,161],{"className":1038},[319,268],[58,1040,161],{"className":1041},[319],[58,1043],{"className":1044,"style":528},[213],[58,1046,116],{"className":1047},[388],[58,1049],{"className":1050,"style":528},[213],[58,1052,1054,1057],{"className":1053},[205],[58,1055,170],{"className":1056,"style":541},[205,275],[58,1058,1060],{"className":1059},[337],[58,1061,1063],{"className":1062},[243],[58,1064,1066],{"className":1065},[248],[58,1067,1069],{"className":1068,"style":500},[252],[58,1070,1071,1074],{"style":503},[58,1072],{"className":1073,"style":354},[260],[58,1075,1077],{"className":1076},[265,266,267,268],[58,1078,1080,1083,1086],{"className":1079},[205,268],[58,1081,127],{"className":1082},[235,268],[58,1084,104],{"className":1085},[205,275,268],[58,1087,161],{"className":1088},[319,268],[58,1090,1092],{"className":1091},[319],[58,1093,1095],{"className":1094},[422,905],[58,1096,1098,1118],{"className":1097},[243,244],[58,1099,1101,1115],{"className":1100},[248],[58,1102,1104],{"className":1103,"style":915},[252],[58,1105,1106,1109],{"style":918},[58,1107],{"className":1108,"style":922},[260],[58,1110,1111],{"style":925},[927,1112,1113],{"xmlns":929,"width":930,"height":931,"viewBox":932},[934,1114],{"d":936},[58,1116,306],{"className":1117},[305],[58,1119,1121],{"className":1120},[248],[58,1122,1124],{"className":1123,"style":946},[252],[58,1125],{},[11,1127,1128,1129,1131],{},"A diferença parece pequena no papel, mas muda tudo no comportamento. No MSE, errar o dobro custa quatro vezes mais (lembra do ",[22,1130,42],{"href":24},"?). No MAE, errar o dobro custa exatamente o dobro, nem mais, nem menos. É a diferença entre um juiz que enlouquece quando você erra feio e um juiz que só conta pontos de forma proporcional, sem drama extra.",[33,1133,1135],{"id":1134},"as-duas-formas-lado-a-lado","As duas formas lado a lado",[11,1137,1138],{},"Nada de imaginar a forma, olha ela:",[1140,1141],"loss-shape-chart",{":error-max":1142,":initial-delta":1143},"10","4",[11,1145,1146],{},"Repara: MSE é uma parábola (cresce cada vez mais rápido), MAE é um V (cresce sempre na mesma taxa). Segura essa imagem na cabeça, ela explica tudo que vem a seguir.",[33,1148,1150],{"id":1149},"o-melhor-dos-dois-mundos-huber","O melhor dos dois mundos: Huber",[11,1152,1153,1154,1158,1159,1191],{},"MSE é sensível demais a erro grande. MAE é durão demais, até com erro pequeno (repara no V: mesmo erros minúsculos custam proporcionalmente ao tamanho deles, sem o \"desconto\" que o quadrado dá perto de zero). A ",[45,1155,1157],{"definition":1156},"uma função de perda híbrida, parábola pra erro pequeno e reta pra erro grande, com um limiar delta que decide onde a transição acontece","perda de Huber"," tenta pegar o melhor dos dois: parábola suave pertinho de zero, reta a partir de um limiar ",[58,1160,1162,1177],{"className":1161},[61],[58,1163,1165],{"className":1164},[65],[67,1166,1167],{"xmlns":69},[71,1168,1169,1174],{},[74,1170,1171],{},[91,1172,1173],{},"δ",[185,1175,1176],{"encoding":187},"\\delta",[58,1178,1180],{"className":1179,"ariaHidden":126},[192],[58,1181,1183,1187],{"className":1182},[196],[58,1184],{"className":1185,"style":1186},[200],"height:0.6944em;",[58,1188,1173],{"className":1189,"style":1190},[205,275],"margin-right:0.0379em;"," (delta).",[11,1193,1194],{},[58,1195,1197,1331],{"className":1196},[61],[58,1198,1200],{"className":1199},[65],[67,1201,1202],{"xmlns":69},[71,1203,1204,1328],{},[74,1205,1206,1213,1215,1218,1220,1222],{},[129,1207,1208,1211],{},[91,1209,1210],{},"L",[91,1212,1173],{},[80,1214,127],{"stretchy":147},[91,1216,1217],{},"e",[80,1219,161],{"stretchy":147},[80,1221,82],{},[74,1223,1224,1227],{},[80,1225,1226],{"fence":126},"{",[1228,1229,1233,1277],"mtable",{"rowspacing":1230,"columnalign":1231,"columnspacing":1232},"0.36em","left left","1em",[1234,1235,1236,1256],"mtr",{},[1237,1238,1239],"mtd",{},[1240,1241,1242],"mstyle",{"scriptlevel":109,"displaystyle":147},[74,1243,1244,1250],{},[84,1245,1246,1248],{},[87,1247,89],{},[87,1249,183],{},[120,1251,1252,1254],{},[91,1253,1217],{},[87,1255,183],{},[1237,1257,1258],{},[1240,1259,1260],{"scriptlevel":109,"displaystyle":147},[74,1261,1262,1265,1268,1270,1272,1275],{},[77,1263,1264],{},"se ",[91,1266,674],{"mathvariant":1267},"normal",[91,1269,1217],{},[91,1271,674],{"mathvariant":1267},[80,1273,1274],{},"≤",[91,1276,1173],{},[1234,1278,1279,1309],{},[1237,1280,1281],{},[1240,1282,1283],{"scriptlevel":109,"displaystyle":147},[74,1284,1285,1287],{},[91,1286,1173],{},[74,1288,1289,1291,1293,1295,1297,1299,1305,1307],{},[80,1290,127],{"fence":126},[91,1292,674],{"mathvariant":1267},[91,1294,1217],{},[91,1296,674],{"mathvariant":1267},[80,1298,116],{},[84,1300,1301,1303],{},[87,1302,89],{},[87,1304,183],{},[91,1306,1173],{},[80,1308,161],{"fence":126},[1237,1310,1311],{},[1240,1312,1313],{"scriptlevel":109,"displaystyle":147},[74,1314,1315,1317,1319,1321,1323,1326],{},[77,1316,1264],{},[91,1318,674],{"mathvariant":1267},[91,1320,1217],{},[91,1322,674],{"mathvariant":1267},[80,1324,1325],{},">",[91,1327,1173],{},[185,1329,1330],{"encoding":187},"L_\\delta(e) = \\begin{cases} \\frac{1}{2}e^2 & \\text{se } |e| \\le \\delta \\\\ \\delta\\left(|e| - \\frac{1}{2}\\delta\\right) & \\text{se } |e| > \\delta \\end{cases}",[58,1332,1334,1401],{"className":1333,"ariaHidden":126},[192],[58,1335,1337,1341,1383,1386,1389,1392,1395,1398],{"className":1336},[196],[58,1338],{"className":1339,"style":1340},[200],"height:1em;vertical-align:-0.25em;",[58,1342,1344,1347],{"className":1343},[205],[58,1345,1210],{"className":1346},[205,275],[58,1348,1350],{"className":1349},[337],[58,1351,1353,1374],{"className":1352},[243,244],[58,1354,1356,1371],{"className":1355},[248],[58,1357,1359],{"className":1358,"style":443},[252],[58,1360,1362,1365],{"style":1361},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[58,1363],{"className":1364,"style":354},[260],[58,1366,1368],{"className":1367},[265,266,267,268],[58,1369,1173],{"className":1370,"style":1190},[205,275,268],[58,1372,306],{"className":1373},[305],[58,1375,1377],{"className":1376},[248],[58,1378,1381],{"className":1379,"style":1380},[252],"height:0.15em;",[58,1382],{},[58,1384,127],{"className":1385},[235],[58,1387,1217],{"className":1388},[205,275],[58,1390,161],{"className":1391},[319],[58,1393],{"className":1394,"style":214},[213],[58,1396,82],{"className":1397},[218],[58,1399],{"className":1400,"style":214},[213],[58,1402,1404,1408],{"className":1403},[196],[58,1405],{"className":1406,"style":1407},[200],"height:3em;vertical-align:-1.25em;",[58,1409,1411,1418,1775],{"className":1410},[410],[58,1412,1414],{"className":1413,"style":418},[235,417],[58,1415,1226],{"className":1416},[422,1417],"size4",[58,1419,1421],{"className":1420},[205],[58,1422,1424,1677,1682],{"className":1423},[1228],[58,1425,1428],{"className":1426},[1427],"col-align-l",[58,1429,1431,1668],{"className":1430},[243,244],[58,1432,1434,1665],{"className":1433},[248],[58,1435,1438,1546],{"className":1436,"style":1437},[252],"height:1.69em;",[58,1439,1441,1445],{"style":1440},"top:-3.69em;",[58,1442],{"className":1443,"style":1444},[260],"height:3.008em;",[58,1446,1448,1516],{"className":1447},[205],[58,1449,1451,1454,1513],{"className":1450},[205],[58,1452],{"className":1453},[235,236],[58,1455,1457],{"className":1456},[84],[58,1458,1460,1505],{"className":1459},[243,244],[58,1461,1463,1502],{"className":1462},[248],[58,1464,1466,1480,1488],{"className":1465,"style":253},[252],[58,1467,1468,1471],{"style":256},[58,1469],{"className":1470,"style":261},[260],[58,1472,1474],{"className":1473},[265,266,267,268],[58,1475,1477],{"className":1476},[205,268],[58,1478,183],{"className":1479},[205,268],[58,1481,1482,1485],{"style":278},[58,1483],{"className":1484,"style":261},[260],[58,1486],{"className":1487,"style":286},[285],[58,1489,1490,1493],{"style":289},[58,1491],{"className":1492,"style":261},[260],[58,1494,1496],{"className":1495},[265,266,267,268],[58,1497,1499],{"className":1498},[205,268],[58,1500,89],{"className":1501},[205,268],[58,1503,306],{"className":1504},[305],[58,1506,1508],{"className":1507},[248],[58,1509,1511],{"className":1510,"style":313},[252],[58,1512],{},[58,1514],{"className":1515},[319,236],[58,1517,1519,1522],{"className":1518},[205],[58,1520,1217],{"className":1521},[205,275],[58,1523,1525],{"className":1524},[337],[58,1526,1528],{"className":1527},[243],[58,1529,1531],{"className":1530},[248],[58,1532,1535],{"className":1533,"style":1534},[252],"height:0.8141em;",[58,1536,1537,1540],{"style":503},[58,1538],{"className":1539,"style":354},[260],[58,1541,1543],{"className":1542},[265,266,267,268],[58,1544,183],{"className":1545},[205,268],[58,1547,1549,1552],{"style":1548},"top:-2.25em;",[58,1550],{"className":1551,"style":1444},[260],[58,1553,1555,1558,1561],{"className":1554},[205],[58,1556,1173],{"className":1557,"style":1190},[205,275],[58,1559],{"className":1560,"style":323},[213],[58,1562,1564,1570,1573,1576,1579,1582,1585,1588,1656,1659],{"className":1563},[410],[58,1565,1567],{"className":1566,"style":418},[235,417],[58,1568,127],{"className":1569},[422,423],[58,1571,674],{"className":1572},[205],[58,1574,1217],{"className":1575},[205,275],[58,1577,674],{"className":1578},[205],[58,1580],{"className":1581,"style":528},[213],[58,1583,116],{"className":1584},[388],[58,1586],{"className":1587,"style":528},[213],[58,1589,1591,1594,1653],{"className":1590},[205],[58,1592],{"className":1593},[235,236],[58,1595,1597],{"className":1596},[84],[58,1598,1600,1645],{"className":1599},[243,244],[58,1601,1603,1642],{"className":1602},[248],[58,1604,1606,1620,1628],{"className":1605,"style":253},[252],[58,1607,1608,1611],{"style":256},[58,1609],{"className":1610,"style":261},[260],[58,1612,1614],{"className":1613},[265,266,267,268],[58,1615,1617],{"className":1616},[205,268],[58,1618,183],{"className":1619},[205,268],[58,1621,1622,1625],{"style":278},[58,1623],{"className":1624,"style":261},[260],[58,1626],{"className":1627,"style":286},[285],[58,1629,1630,1633],{"style":289},[58,1631],{"className":1632,"style":261},[260],[58,1634,1636],{"className":1635},[265,266,267,268],[58,1637,1639],{"className":1638},[205,268],[58,1640,89],{"className":1641},[205,268],[58,1643,306],{"className":1644},[305],[58,1646,1648],{"className":1647},[248],[58,1649,1651],{"className":1650,"style":313},[252],[58,1652],{},[58,1654],{"className":1655},[319,236],[58,1657,1173],{"className":1658,"style":1190},[205,275],[58,1660,1662],{"className":1661,"style":418},[319,417],[58,1663,161],{"className":1664},[422,423],[58,1666,306],{"className":1667},[305],[58,1669,1671],{"className":1670},[248],[58,1672,1675],{"className":1673,"style":1674},[252],"height:1.19em;",[58,1676],{},[58,1678],{"className":1679,"style":1681},[1680],"arraycolsep","width:1em;",[58,1683,1685],{"className":1684},[1427],[58,1686,1688,1767],{"className":1687},[243,244],[58,1689,1691,1764],{"className":1690},[248],[58,1692,1694,1729],{"className":1693,"style":1437},[252],[58,1695,1696,1699],{"style":1440},[58,1697],{"className":1698,"style":1444},[260],[58,1700,1702,1708,1711,1714,1717,1720,1723,1726],{"className":1701},[205],[58,1703,1705],{"className":1704},[205,206],[58,1706,1264],{"className":1707},[205],[58,1709,674],{"className":1710},[205],[58,1712,1217],{"className":1713},[205,275],[58,1715,674],{"className":1716},[205],[58,1718],{"className":1719,"style":214},[213],[58,1721,1274],{"className":1722},[218],[58,1724],{"className":1725,"style":214},[213],[58,1727,1173],{"className":1728,"style":1190},[205,275],[58,1730,1731,1734],{"style":1548},[58,1732],{"className":1733,"style":1444},[260],[58,1735,1737,1743,1746,1749,1752,1755,1758,1761],{"className":1736},[205],[58,1738,1740],{"className":1739},[205,206],[58,1741,1264],{"className":1742},[205],[58,1744,674],{"className":1745},[205],[58,1747,1217],{"className":1748},[205,275],[58,1750,674],{"className":1751},[205],[58,1753],{"className":1754,"style":214},[213],[58,1756,1325],{"className":1757},[218],[58,1759],{"className":1760,"style":214},[213],[58,1762,1173],{"className":1763,"style":1190},[205,275],[58,1765,306],{"className":1766},[305],[58,1768,1770],{"className":1769},[248],[58,1771,1773],{"className":1772,"style":1674},[252],[58,1774],{},[58,1776],{"className":1777},[319,236],[11,1779,1780,1781,1810],{},"Onde ",[58,1782,1784,1797],{"className":1783},[61],[58,1785,1787],{"className":1786},[65],[67,1788,1789],{"xmlns":69},[71,1790,1791,1795],{},[74,1792,1793],{},[91,1794,1217],{},[185,1796,1217],{"encoding":187},[58,1798,1800],{"className":1799,"ariaHidden":126},[192],[58,1801,1803,1807],{"className":1802},[196],[58,1804],{"className":1805,"style":1806},[200],"height:0.4306em;",[58,1808,1217],{"className":1809},[205,275]," é o erro de um exemplo. Arrasta o slider do delta lá em cima de novo e observa a curva laranja: com delta pequeno, Huber vira quase um MAE, e com delta grande, vira quase um MSE. Delta é literalmente o controle de \"a partir de que tamanho de erro eu paro de dar desconto\".",[33,1812,1814],{"id":1813},"o-impacto-de-um-outlier","O impacto de um outlier",[11,1816,1817,1818,1820,1821,1825,1826,1830],{},"Aqui é onde a escolha da função de perda deixa de ser teoria e vira decisão de verdade. Pega o dataset de 6 casas do ",[22,1819,42],{"href":24}," e adiciona ",[1822,1823,1824],"strong",{},"uma"," casa a mais, numa posição fixa. Você controla o preço dela com o slider, arrastando de um valor razoável até um valor bem fora da curva (um ",[45,1827,1829],{"definition":1828},"um ponto de dado bem fora do padrão dos outros, seja por erro de digitação, medição estranha, ou caso raro de verdade","outlier","), e observa três retas ajustadas ao vivo, uma pra cada função de perda:",[1832,1833],"outlier-impact-explorer",{":base-x":1834,":base-y":1835,":huber-delta":1836,":initial-outlier-y":1837,":outlier-x":1838,":outlier-y-max":1839,":outlier-y-min":1840,"x-label":1841,"y-label":1842},"[1.0, 1.7, 2.0, 2.5, 3.0, 3.2]","[250, 300, 480, 430, 630, 730]","100","730","2.2","1800","200","Tamanho (1000 pés²)","Preço (1000 dólares)",[11,1844,1845],{},"Arrasta até o valor máximo e observa: a reta azul (MSE) sai correndo atrás do ponto vermelho, se contorcendo pra tentar \"agradar\" o outlier. A reta verde (MAE) mal se mexe. A laranja (Huber) fica no meio do caminho. Isso não é coincidência nem só desse exemplo, é a consequência direta do gráfico das duas formas que você viu ali em cima: quadrado pune erro grande sem limite, valor absoluto não.",[33,1847,1849],{"id":1848},"fechando","Fechando",[1851,1852,1853,1873],"table",{},[1854,1855,1856],"thead",{},[1857,1858,1859,1864,1867,1870],"tr",{},[1860,1861,1863],"th",{"align":1862},"left","Função de perda",[1860,1865,1866],{"align":1862},"Fórmula",[1860,1868,1869],{"align":1862},"Reação a outlier",[1860,1871,1872],{"align":1862},"Quando usar",[1874,1875,1876,1890,1903],"tbody",{},[1857,1877,1878,1881,1884,1887],{},[1879,1880,48],"td",{"align":1862},[1879,1882,1883],{"align":1862},"erro ao quadrado",[1879,1885,1886],{"align":1862},"sensível, se deixa puxar",[1879,1888,1889],{"align":1862},"dado limpo, sem outlier relevante",[1857,1891,1892,1894,1897,1900],{},[1879,1893,621],{"align":1862},[1879,1895,1896],{"align":1862},"valor absoluto do erro",[1879,1898,1899],{"align":1862},"robusta, quase imune",[1879,1901,1902],{"align":1862},"dado com outlier que você quer ignorar",[1857,1904,1905,1908,1911,1914],{},[1879,1906,1907],{"align":1862},"Huber",[1879,1909,1910],{"align":1862},"híbrida (quadrado perto de zero, reta longe)",[1879,1912,1913],{"align":1862},"meio-termo ajustável",[1879,1915,1916],{"align":1862},"quando você quer um pouco de cada, controlando via delta",[11,1918,1919],{},"Três ideias pra levar:",[1921,1922,1923,1930,1936],"ol",{},[1924,1925,1926,1929],"li",{},[1822,1927,1928],{},"A função de perda não é um detalhe técnico escondido, é uma escolha de design"," que muda o comportamento do modelo inteiro, principalmente na presença de dado real e sujo.",[1924,1931,1932,1935],{},[1822,1933,1934],{},"Elevar ao quadrado pune erro grande desproporcionalmente",", é ótimo quando você confia no seu dataset, perigoso quando não confia.",[1924,1937,1938,1941],{},[1822,1939,1940],{},"Huber existe justamente pra você não ter que escolher no escuro",": o delta é um botão que desliza entre os dois extremos.",[33,1943,1945],{"id":1944},"aplicação-prática","Aplicação prática",[11,1947,1948,1949,1955],{},"Mesmo dataset real de imóveis dos posts anteriores (",[22,1950,1954],{"href":1951,"rel":1952},"https:\u002F\u002Fwww.kaggle.com\u002Fdatasets\u002Fdenkuznetz\u002Fhousing-prices-regression",[1953],"nofollow","Housing Prices Regression, Kaggle","). Dessa vez, um cenário bem realista: um erro de digitação. Uma casa de 60 pés² (bem pequena) foi cadastrada por engano custando quase 2 milhões de dólares.",[1957,1958,1963],"pre",{"className":1959,"code":1960,"language":1961,"meta":1962,"style":1962},"language-python shiki shiki-themes github-light github-dark","# 50 casas reais + 1 erro de digitação: 60 pés², $1.9 milhão\nx_com_erro = [*x_sqft, 0.6]\ny_com_erro = [*y_price, 1900]\n\nols  = fit_mse(x_com_erro, y_com_erro)             # ajuste comum (mínimos quadrados)\nmae  = fit_irls(x_com_erro, y_com_erro, \"mae\")     # robusto a outlier\nhuber = fit_irls(x_com_erro, y_com_erro, \"huber\", delta=50)\n\ncasa_nova = 1.5   # 150 pés², na mesma escala dos posts anteriores\n\nfor nome, (w, b) in [(\"MSE\", ols), (\"MAE\", mae), (\"Huber\", huber)]:\n    print(f\"{nome}: ${(w * casa_nova + b) * 1000:,.0f}\")\n","python","",[1964,1965,1966,1973,1979,1985,1992,1998,2004,2010,2015,2021,2026,2032],"code",{"__ignoreMap":1962},[58,1967,1970],{"class":1968,"line":1969},"line",1,[58,1971,1972],{},"# 50 casas reais + 1 erro de digitação: 60 pés², $1.9 milhão\n",[58,1974,1976],{"class":1968,"line":1975},2,[58,1977,1978],{},"x_com_erro = [*x_sqft, 0.6]\n",[58,1980,1982],{"class":1968,"line":1981},3,[58,1983,1984],{},"y_com_erro = [*y_price, 1900]\n",[58,1986,1988],{"class":1968,"line":1987},4,[58,1989,1991],{"emptyLinePlaceholder":1990},true,"\n",[58,1993,1995],{"class":1968,"line":1994},5,[58,1996,1997],{},"ols  = fit_mse(x_com_erro, y_com_erro)             # ajuste comum (mínimos quadrados)\n",[58,1999,2001],{"class":1968,"line":2000},6,[58,2002,2003],{},"mae  = fit_irls(x_com_erro, y_com_erro, \"mae\")     # robusto a outlier\n",[58,2005,2007],{"class":1968,"line":2006},7,[58,2008,2009],{},"huber = fit_irls(x_com_erro, y_com_erro, \"huber\", delta=50)\n",[58,2011,2013],{"class":1968,"line":2012},8,[58,2014,1991],{"emptyLinePlaceholder":1990},[58,2016,2018],{"class":1968,"line":2017},9,[58,2019,2020],{},"casa_nova = 1.5   # 150 pés², na mesma escala dos posts anteriores\n",[58,2022,2024],{"class":1968,"line":2023},10,[58,2025,1991],{"emptyLinePlaceholder":1990},[58,2027,2029],{"class":1968,"line":2028},11,[58,2030,2031],{},"for nome, (w, b) in [(\"MSE\", ols), (\"MAE\", mae), (\"Huber\", huber)]:\n",[58,2033,2035],{"class":1968,"line":2034},12,[58,2036,2037],{},"    print(f\"{nome}: ${(w * casa_nova + b) * 1000:,.0f}\")\n",[2039,2040,2041],"blockquote",{},[11,2042,2043,26,2046,2049,2050,2049,2053],{},[1822,2044,2045],{},"Saída:",[1964,2047,2048],{},"MSE: $608,900"," \u002F ",[1964,2051,2052],{},"MAE: $570,700",[1964,2054,2055],{},"Huber: $569,800",[11,2057,2058,2059,2095,2096,2224,2225,2227],{},"Sem o erro de digitação, os três dão praticamente o mesmo palpite pra essa casa (por volta de ",[58,2060,2062,2079],{"className":2061},[61],[58,2063,2065],{"className":2064},[65],[67,2066,2067],{"xmlns":69},[71,2068,2069,2076],{},[74,2070,2071,2074],{},[87,2072,2073],{},"567",[91,2075,22],{},[185,2077,2078],{"encoding":187},"567 a ",[58,2080,2082],{"className":2081,"ariaHidden":126},[192],[58,2083,2085,2089,2092],{"className":2084},[196],[58,2086],{"className":2087,"style":2088},[200],"height:0.6444em;",[58,2090,2073],{"className":2091},[205],[58,2093,22],{"className":2094},[205,275],"573 mil). Com o erro de digitação, o MSE pula pra quase ",[58,2097,2099,2158],{"className":2098},[61],[58,2100,2102],{"className":2101},[65],[67,2103,2104],{"xmlns":69},[71,2105,2106,2155],{},[74,2107,2108,2111,2113,2115,2118,2120,2123,2125,2128,2130,2132,2135,2138,2141,2143,2145,2147,2149,2151,2153],{},[87,2109,2110],{},"609",[91,2112,93],{},[91,2114,104],{},[91,2116,2117],{},"l",[80,2119,141],{"separator":126},[91,2121,2122],{},"u",[91,2124,93],{},[91,2126,2127],{},"s",[91,2129,2122],{},[91,2131,2127],{},[91,2133,2134],{},"t",[91,2136,2137],{},"o",[91,2139,2140],{},"d",[91,2142,1217],{},[91,2144,93],{},[91,2146,22],{},[91,2148,104],{},[91,2150,2127],{},[91,2152,2140],{},[91,2154,1217],{},[185,2156,2157],{"encoding":187},"609 mil, um susto de mais de ",[58,2159,2161],{"className":2160,"ariaHidden":126},[192],[58,2162,2164,2168,2171,2174,2178,2181,2184,2187,2190,2193,2196,2199,2202,2205,2208,2211,2215,2218,2221],{"className":2163},[196],[58,2165],{"className":2166,"style":2167},[200],"height:0.8889em;vertical-align:-0.1944em;",[58,2169,2110],{"className":2170},[205],[58,2172,91],{"className":2173},[205,275],[58,2175,2117],{"className":2176,"style":2177},[205,275],"margin-right:0.0197em;",[58,2179,141],{"className":2180},[463],[58,2182],{"className":2183,"style":323},[213],[58,2185,2122],{"className":2186},[205,275],[58,2188,93],{"className":2189},[205,275],[58,2191,2127],{"className":2192},[205,275],[58,2194,2122],{"className":2195},[205,275],[58,2197,2127],{"className":2198},[205,275],[58,2200,2134],{"className":2201},[205,275],[58,2203,2137],{"className":2204},[205,275],[58,2206,2140],{"className":2207},[205,275],[58,2209,1217],{"className":2210},[205,275],[58,2212,2214],{"className":2213},[205,275],"mai",[58,2216,2127],{"className":2217},[205,275],[58,2219,2140],{"className":2220},[205,275],[58,2222,1217],{"className":2223},[205,275],"35 mil só por causa de ",[1822,2226,1824],{}," linha errada na planilha, enquanto MAE e Huber mal se mexem (menos de $3 mil de diferença). Testa você mesmo, arrastando o outlier:",[2229,2230],"housing-outlier-explorer",{},[11,2232,2233],{},"Numa base de dados de verdade, com milhares de linhas, erro de digitação acontece. A escolha da função de perda decide se um erro desses vira um problema seu ou não.",[2235,2236,2237],"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":1962,"searchDepth":1975,"depth":1975,"links":2239},[2240,2241,2242,2243,2244,2245,2246],{"id":35,"depth":1975,"text":36},{"id":613,"depth":1975,"text":614},{"id":1134,"depth":1975,"text":1135},{"id":1149,"depth":1975,"text":1150},{"id":1813,"depth":1975,"text":1814},{"id":1848,"depth":1975,"text":1849},{"id":1944,"depth":1975,"text":1945},null,"2026-08-18","Por que a gente elevou o erro ao quadrado lá no post 2, e o que acontece se a gente escolher diferente: MAE, Huber, e o impacto real que um único outlier tem em cada escolha.","md",{},"\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Floss-functions","machine-learning-specialization",{"title":6,"description":2249},"published","pt\u002Fplaylists\u002Fmachine-learning-specialization\u002Floss-functions",[2258,2259,2260,2261,2262],"funcao-de-perda","mse","mae","huber","robustez","_XtljLuJAzOT8lwsLGBPxhyg9A43hb_BiclnG4LCVzs",1787338983753]