[{"data":1,"prerenderedAt":3440},["ShallowReactive",2],{"lang-switch-post-\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab03-cost-function":3,"post-pt-machine-learning-specialization-lab03-cost-function":4},"\u002Fen\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab03-cost-function",{"id":5,"title":6,"body":7,"cover":3425,"date":3426,"description":3427,"extension":3428,"meta":3429,"navigation":1844,"order":1829,"path":3430,"playlist":3431,"seo":3432,"status":3433,"stem":3434,"tags":3435,"__hash__":3439},"posts\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab03-cost-function.md","Lab Opcional: a Função de Custo",{"type":8,"value":9,"toc":3415},"minimark",[10,153,231,777,780,785,793,797,1028,1625,1628,1773,1806,1810,1966,1981,1985,2124,2172,2183,2186,2427,2482,2486,2489,2550,2606,2670,2677,2791,2803,2807,2814,2989,2994,3001,3005,3294,3304,3308,3326,3390,3405,3408,3411],[11,12,13,18,19,97,98,152],"p",{},[14,15,17],"a",{"href":16},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab02-model-representation","No post passado"," você achou ",[20,21,24,55],"span",{"className":22},[23],"katex",[20,25,28],{"className":26},[27],"katex-mathml",[29,30,32],"math",{"xmlns":31},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[33,34,35,50],"semantics",{},[36,37,38,42,46],"mrow",{},[39,40,41],"mi",{},"w",[43,44,45],"mo",{},"=",[47,48,49],"mn",{},"200",[51,52,54],"annotation",{"encoding":53},"application\u002Fx-tex","w = 200",[20,56,60,87],{"className":57,"ariaHidden":59},[58],"katex-html","true",[20,61,64,69,75,80,84],{"className":62},[63],"base",[20,65],{"className":66,"style":68},[67],"strut","height:0.4306em;",[20,70,41],{"className":71,"style":74},[72,73],"mord","mathnormal","margin-right:0.0269em;",[20,76],{"className":77,"style":79},[78],"mspace","margin-right:0.2778em;",[20,81,45],{"className":82},[83],"mrel",[20,85],{"className":86,"style":79},[78],[20,88,90,94],{"className":89},[63],[20,91],{"className":92,"style":93},[67],"height:0.6444em;",[20,95,49],{"className":96},[72]," e ",[20,99,101,121],{"className":100},[23],[20,102,104],{"className":103},[27],[29,105,106],{"xmlns":31},[33,107,108,118],{},[36,109,110,113,115],{},[39,111,112],{},"b",[43,114,45],{},[47,116,117],{},"100",[51,119,120],{"encoding":53},"b = 100",[20,122,124,143],{"className":123,"ariaHidden":59},[58],[20,125,127,131,134,137,140],{"className":126},[63],[20,128],{"className":129,"style":130},[67],"height:0.6944em;",[20,132,112],{"className":133},[72,73],[20,135],{"className":136,"style":79},[78],[20,138,45],{"className":139},[83],[20,141],{"className":142,"style":79},[78],[20,144,146,149],{"className":145},[63],[20,147],{"className":148,"style":93},[67],[20,150,117],{"className":151},[72]," brincando com o slider até o erro zerar. Beleza, funcionou. Mas para. Como você sabia que tinha achado o \"melhor\" ajuste? Você olhou pro número de erro total caindo até zero e confiou nele.",[11,154,155,156,161,162,230],{},"Esse post é sobre dar nome, sobrenome e fórmula pra esse número. Ele se chama ",[157,158,160],"glossary-term",{"definition":159},"uma fórmula que resume, num único número, o quanto um modelo erra nos dados de treino","função de custo",", escrita 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= \\frac{1}{2m}\\sum_{i=0}^{m-1}\\left(f_{w,b}(x^{(i)}) - y^{(i)}\\right)^2",[20,359,361,397],{"className":360,"ariaHidden":59},[58],[20,362,364,367,370,373,376,379,382,385,388,391,394],{"className":363},[63],[20,365],{"className":366,"style":203},[67],[20,368,176],{"className":369,"style":207},[72,73],[20,371,180],{"className":372},[211],[20,374,41],{"className":375,"style":74},[72,73],[20,377,185],{"className":378},[218],[20,380],{"className":381,"style":222},[78],[20,383,112],{"className":384},[72,73],[20,386,190],{"className":387},[229],[20,389],{"className":390,"style":79},[78],[20,392,45],{"className":393},[83],[20,395],{"className":396,"style":79},[78],[20,398,400,404,495,498,578,581],{"className":399},[63],[20,401],{"className":402,"style":403},[67],"height:1.442em;vertical-align:-0.35em;",[20,405,407,411,492],{"className":406},[72],[20,408],{"className":409},[211,410],"nulldelimiter",[20,412,414],{"className":413},[260],[20,415,419,483],{"className":416},[417,418],"vlist-t","vlist-t2",[20,420,423,478],{"className":421},[422],"vlist-r",[20,424,428,452,463],{"className":425,"style":427},[426],"vlist","height:0.8451em;",[20,429,431,436],{"style":430},"top:-2.655em;",[20,432],{"className":433,"style":435},[434],"pstrut","height:3em;",[20,437,443],{"className":438},[439,440,441,442],"sizing","reset-size6","size3","mtight",[20,444,446,449],{"className":445},[72,442],[20,447,269],{"className":448},[72,442],[20,450,272],{"className":451},[72,73,442],[20,453,455,458],{"style":454},"top:-3.23em;",[20,456],{"className":457,"style":435},[434],[20,459],{"className":460,"style":462},[461],"frac-line","border-bottom-width:0.04em;",[20,464,466,469],{"style":465},"top:-3.394em;",[20,467],{"className":468,"style":435},[434],[20,470,472],{"className":471},[439,440,441,442],[20,473,475],{"className":474},[72,442],[20,476,264],{"className":477},[72,442],[20,479,482],{"className":480},[481],"vlist-s","​",[20,484,486],{"className":485},[422],[20,487,490],{"className":488,"style":489},[426],"height:0.345em;",[20,491],{},[20,493],{"className":494},[229,410],[20,496],{"className":497,"style":222},[78],[20,499,502,508],{"className":500},[501],"mop",[20,503,278],{"className":504,"style":507},[501,505,506],"op-symbol","small-op","position:relative;top:0em;",[20,509,512],{"className":510},[511],"msupsub",[20,513,515,569],{"className":514},[417,418],[20,516,518,566],{"className":517},[422],[20,519,522,544],{"className":520,"style":521},[426],"height:0.954em;",[20,523,525,529],{"style":524},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[20,526],{"className":527,"style":528},[434],"height:2.7em;",[20,530,532],{"className":531},[439,440,441,442],[20,533,535,538,541],{"className":534},[72,442],[20,536,283],{"className":537},[72,73,442],[20,539,45],{"className":540},[83,442],[20,542,288],{"className":543},[72,442],[20,545,547,550],{"style":546},"top:-3.2029em;margin-right:0.05em;",[20,548],{"className":549,"style":528},[434],[20,551,553],{"className":552},[439,440,441,442],[20,554,556,559,563],{"className":555},[72,442],[20,557,272],{"className":558},[72,73,442],[20,560,295],{"className":561},[562,442],"mbin",[20,564,264],{"className":565},[72,442],[20,567,482],{"className":568},[481],[20,570,572],{"className":571},[422],[20,573,576],{"className":574,"style":575},[426],"height:0.2997em;",[20,577],{},[20,579],{"className":580,"style":222},[78],[20,582,585,752],{"className":583},[584],"minner",[20,586,588,598,651,654,694,697,701,704,707,746],{"className":587},[584],[20,589,593],{"className":590,"style":592},[211,591],"delimcenter","top:0em;",[20,594,180],{"className":595},[596,597],"delimsizing","size1",[20,599,601,605],{"className":600},[72],[20,602,310],{"className":603,"style":604},[72,73],"margin-right:0.1076em;",[20,606,608],{"className":607},[511],[20,609,611,642],{"className":610},[417,418],[20,612,614,639],{"className":613},[422],[20,615,618],{"className":616,"style":617},[426],"height:0.3361em;",[20,619,621,624],{"style":620},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[20,622],{"className":623,"style":528},[434],[20,625,627],{"className":626},[439,440,441,442],[20,628,630,633,636],{"className":629},[72,442],[20,631,41],{"className":632,"style":74},[72,73,442],[20,634,185],{"className":635},[218,442],[20,637,112],{"className":638},[72,73,442],[20,640,482],{"className":641},[481],[20,643,645],{"className":644},[422],[20,646,649],{"className":647,"style":648},[426],"height:0.2861em;",[20,650],{},[20,652,180],{"className":653},[211],[20,655,657,660],{"className":656},[72],[20,658,325],{"className":659},[72,73],[20,661,663],{"className":662},[511],[20,664,666],{"className":665},[417],[20,667,669],{"className":668},[422],[20,670,673],{"className":671,"style":672},[426],"height:0.888em;",[20,674,676,679],{"style":675},"top:-3.063em;margin-right:0.05em;",[20,677],{"className":678,"style":528},[434],[20,680,682],{"className":681},[439,440,441,442],[20,683,685,688,691],{"className":684},[72,442],[20,686,180],{"className":687},[211,442],[20,689,283],{"className":690},[72,73,442],[20,692,190],{"className":693},[229,442],[20,695,190],{"className":696},[229],[20,698],{"className":699,"style":700},[78],"margin-right:0.2222em;",[20,702,295],{"className":703},[562],[20,705],{"className":706,"style":700},[78],[20,708,710,714],{"className":709},[72],[20,711,342],{"className":712,"style":713},[72,73],"margin-right:0.0359em;",[20,715,717],{"className":716},[511],[20,718,720],{"className":719},[417],[20,721,723],{"className":722},[422],[20,724,726],{"className":725,"style":672},[426],[20,727,728,731],{"style":675},[20,729],{"className":730,"style":528},[434],[20,732,734],{"className":733},[439,440,441,442],[20,735,737,740,743],{"className":736},[72,442],[20,738,180],{"className":739},[211,442],[20,741,283],{"className":742},[72,73,442],[20,744,190],{"className":745},[229,442],[20,747,749],{"className":748,"style":592},[229,591],[20,750,190],{"className":751},[596,597],[20,753,755],{"className":754},[511],[20,756,758],{"className":757},[417],[20,759,761],{"className":760},[422],[20,762,765],{"className":763,"style":764},[426],"height:1.092em;",[20,766,768,771],{"style":767},"top:-3.3409em;margin-right:0.05em;",[20,769],{"className":770,"style":528},[434],[20,772,774],{"className":773},[439,440,441,442],[20,775,269],{"className":776},[72,442],[11,778,779],{},"Eu sei, parece assustador. Vamos abrir essa fórmula peça por peça, tipo desmontando um Lego.",[781,782,784],"h2",{"id":783},"cuidado-com-a-palavra-custo","Cuidado com a palavra \"custo\"",[11,786,787,788,792],{},"Antes de mais nada: aqui ",[789,790,791],"em",{},"custo"," não tem nada a ver com preço de casa. É a medida de quão errado o modelo está. Pra preço da casa a gente continua usando a palavra preço mesmo. Essa confusão de vocabulário pega muita gente no começo, porque \"custo\" no dia a dia é sempre dinheiro.",[781,794,796],{"id":795},"desmontando-a-fórmula","Desmontando a fórmula",[11,798,799,800,875,876,1022,1023,1027],{},"Pensa numa prova de tiro ao alvo. Cada casa do seu conjunto de treino é uma tentativa de acertar o centro do alvo (o preço real, ",[20,801,803,827],{"className":802},[23],[20,804,806],{"className":805},[27],[29,807,808],{"xmlns":31},[33,809,810,824],{},[36,811,812],{},[299,813,814,816],{},[39,815,342],{},[36,817,818,820,822],{},[43,819,180],{"stretchy":179},[39,821,283],{},[43,823,190],{"stretchy":179},[51,825,826],{"encoding":53},"y^{(i)}",[20,828,830],{"className":829,"ariaHidden":59},[58],[20,831,833,837],{"className":832},[63],[20,834],{"className":835,"style":836},[67],"height:1.0824em;vertical-align:-0.1944em;",[20,838,840,843],{"className":839},[72],[20,841,342],{"className":842,"style":713},[72,73],[20,844,846],{"className":845},[511],[20,847,849],{"className":848},[417],[20,850,852],{"className":851},[422],[20,853,855],{"className":854,"style":672},[426],[20,856,857,860],{"style":675},[20,858],{"className":859,"style":528},[434],[20,861,863],{"className":862},[439,440,441,442],[20,864,866,869,872],{"className":865},[72,442],[20,867,180],{"className":868},[211,442],[20,870,283],{"className":871},[72,73,442],[20,873,190],{"className":874},[229,442],"). ",[20,877,879,919],{"className":878},[23],[20,880,882],{"className":881},[27],[29,883,884],{"xmlns":31},[33,885,886,916],{},[36,887,888,900,902,914],{},[306,889,890,892],{},[39,891,310],{},[36,893,894,896,898],{},[39,895,41],{},[43,897,185],{"separator":59},[39,899,112],{},[43,901,180],{"stretchy":179},[299,903,904,906],{},[39,905,325],{},[36,907,908,910,912],{},[43,909,180],{"stretchy":179},[39,911,283],{},[43,913,190],{"stretchy":179},[43,915,190],{"stretchy":179},[51,917,918],{"encoding":53},"f_{w,b}(x^{(i)})",[20,920,922],{"className":921,"ariaHidden":59},[58],[20,923,925,929,978,981,1019],{"className":924},[63],[20,926],{"className":927,"style":928},[67],"height:1.1741em;vertical-align:-0.2861em;",[20,930,932,935],{"className":931},[72],[20,933,310],{"className":934,"style":604},[72,73],[20,936,938],{"className":937},[511],[20,939,941,970],{"className":940},[417,418],[20,942,944,967],{"className":943},[422],[20,945,947],{"className":946,"style":617},[426],[20,948,949,952],{"style":620},[20,950],{"className":951,"style":528},[434],[20,953,955],{"className":954},[439,440,441,442],[20,956,958,961,964],{"className":957},[72,442],[20,959,41],{"className":960,"style":74},[72,73,442],[20,962,185],{"className":963},[218,442],[20,965,112],{"className":966},[72,73,442],[20,968,482],{"className":969},[481],[20,971,973],{"className":972},[422],[20,974,976],{"className":975,"style":648},[426],[20,977],{},[20,979,180],{"className":980},[211],[20,982,984,987],{"className":983},[72],[20,985,325],{"className":986},[72,73],[20,988,990],{"className":989},[511],[20,991,993],{"className":992},[417],[20,994,996],{"className":995},[422],[20,997,999],{"className":998,"style":672},[426],[20,1000,1001,1004],{"style":675},[20,1002],{"className":1003,"style":528},[434],[20,1005,1007],{"className":1006},[439,440,441,442],[20,1008,1010,1013,1016],{"className":1009},[72,442],[20,1011,180],{"className":1012},[211,442],[20,1014,283],{"className":1015},[72,73,442],[20,1017,190],{"className":1018},[229,442],[20,1020,190],{"className":1021},[229]," é onde a sua flecha caiu (a previsão do modelo). A distância entre onde a flecha caiu e o centro é o ",[157,1024,1026],{"definition":1025},"a diferença entre o que o modelo previu e o valor real daquele exemplo, também chamado de resíduo","erro"," daquele tiro específico.",[1029,1030,1031,1048],"table",{},[1032,1033,1034],"thead",{},[1035,1036,1037,1042,1045],"tr",{},[1038,1039,1041],"th",{"align":1040},"left","Pedaço da fórmula",[1038,1043,1044],{"align":1040},"Nome",[1038,1046,1047],{"align":1040},"O que faz",[1049,1050,1051,1274,1356,1480],"tbody",{},[1035,1052,1053,1268,1271],{},[1054,1055,1056],"td",{"align":1040},[20,1057,1059,1113],{"className":1058},[23],[20,1060,1062],{"className":1061},[27],[29,1063,1064],{"xmlns":31},[33,1065,1066,1110],{},[36,1067,1068,1080,1082,1094,1096,1098],{},[306,1069,1070,1072],{},[39,1071,310],{},[36,1073,1074,1076,1078],{},[39,1075,41],{},[43,1077,185],{"separator":59},[39,1079,112],{},[43,1081,180],{"stretchy":179},[299,1083,1084,1086],{},[39,1085,325],{},[36,1087,1088,1090,1092],{},[43,1089,180],{"stretchy":179},[39,1091,283],{},[43,1093,190],{"stretchy":179},[43,1095,190],{"stretchy":179},[43,1097,295],{},[299,1099,1100,1102],{},[39,1101,342],{},[36,1103,1104,1106,1108],{},[43,1105,180],{"stretchy":179},[39,1107,283],{},[43,1109,190],{"stretchy":179},[51,1111,1112],{"encoding":53},"f_{w,b}(x^{(i)}) - y^{(i)}",[20,1114,1116,1224],{"className":1115,"ariaHidden":59},[58],[20,1117,1119,1122,1171,1174,1212,1215,1218,1221],{"className":1118},[63],[20,1120],{"className":1121,"style":928},[67],[20,1123,1125,1128],{"className":1124},[72],[20,1126,310],{"className":1127,"style":604},[72,73],[20,1129,1131],{"className":1130},[511],[20,1132,1134,1163],{"className":1133},[417,418],[20,1135,1137,1160],{"className":1136},[422],[20,1138,1140],{"className":1139,"style":617},[426],[20,1141,1142,1145],{"style":620},[20,1143],{"className":1144,"style":528},[434],[20,1146,1148],{"className":1147},[439,440,441,442],[20,1149,1151,1154,1157],{"className":1150},[72,442],[20,1152,41],{"className":1153,"style":74},[72,73,442],[20,1155,185],{"className":1156},[218,442],[20,1158,112],{"className":1159},[72,73,442],[20,1161,482],{"className":1162},[481],[20,1164,1166],{"className":1165},[422],[20,1167,1169],{"className":1168,"style":648},[426],[20,1170],{},[20,1172,180],{"className":1173},[211],[20,1175,1177,1180],{"className":1176},[72],[20,1178,325],{"className":1179},[72,73],[20,1181,1183],{"className":1182},[511],[20,1184,1186],{"className":1185},[417],[20,1187,1189],{"className":1188},[422],[20,1190,1192],{"className":1191,"style":672},[426],[20,1193,1194,1197],{"style":675},[20,1195],{"className":1196,"style":528},[434],[20,1198,1200],{"className":1199},[439,440,441,442],[20,1201,1203,1206,1209],{"className":1202},[72,442],[20,1204,180],{"className":1205},[211,442],[20,1207,283],{"className":1208},[72,73,442],[20,1210,190],{"className":1211},[229,442],[20,1213,190],{"className":1214},[229],[20,1216],{"className":1217,"style":700},[78],[20,1219,295],{"className":1220},[562],[20,1222],{"className":1223,"style":700},[78],[20,1225,1227,1230],{"className":1226},[63],[20,1228],{"className":1229,"style":836},[67],[20,1231,1233,1236],{"className":1232},[72],[20,1234,342],{"className":1235,"style":713},[72,73],[20,1237,1239],{"className":1238},[511],[20,1240,1242],{"className":1241},[417],[20,1243,1245],{"className":1244},[422],[20,1246,1248],{"className":1247,"style":672},[426],[20,1249,1250,1253],{"style":675},[20,1251],{"className":1252,"style":528},[434],[20,1254,1256],{"className":1255},[439,440,441,442],[20,1257,1259,1262,1265],{"className":1258},[72,442],[20,1260,180],{"className":1261},[211,442],[20,1263,283],{"className":1264},[72,73,442],[20,1266,190],{"className":1267},[229,442],[1054,1269,1270],{"align":1040},"erro (resíduo)",[1054,1272,1273],{"align":1040},"a distância entre a previsão e o real",[1035,1275,1276,1350,1353],{},[1054,1277,1278],{"align":1040},[20,1279,1281,1304],{"className":1280},[23],[20,1282,1284],{"className":1283},[27],[29,1285,1286],{"xmlns":31},[33,1287,1288,1301],{},[36,1289,1290,1292,1295],{},[43,1291,180],{"stretchy":179},[43,1293,1294],{},"…",[299,1296,1297,1299],{},[43,1298,190],{"stretchy":179},[47,1300,269],{},[51,1302,1303],{"encoding":53},"(\\ldots)^2",[20,1305,1307],{"className":1306,"ariaHidden":59},[58],[20,1308,1310,1314,1317,1320],{"className":1309},[63],[20,1311],{"className":1312,"style":1313},[67],"height:1.0641em;vertical-align:-0.25em;",[20,1315,180],{"className":1316},[211],[20,1318,1294],{"className":1319},[584],[20,1321,1323,1326],{"className":1322},[229],[20,1324,190],{"className":1325},[229],[20,1327,1329],{"className":1328},[511],[20,1330,1332],{"className":1331},[417],[20,1333,1335],{"className":1334},[422],[20,1336,1339],{"className":1337,"style":1338},[426],"height:0.8141em;",[20,1340,1341,1344],{"style":675},[20,1342],{"className":1343,"style":528},[434],[20,1345,1347],{"className":1346},[439,440,441,442],[20,1348,269],{"className":1349},[72,442],[1054,1351,1352],{"align":1040},"erro ao quadrado",[1054,1354,1355],{"align":1040},"tira o sinal (errar pra cima ou pra baixo pesa igual) e pune erro grande com força bem maior",[1035,1357,1358,1474,1477],{},[1054,1359,1360],{"align":1040},[20,1361,1363,1395],{"className":1362},[23],[20,1364,1366],{"className":1365},[27],[29,1367,1368],{"xmlns":31},[33,1369,1370,1392],{},[36,1371,1372],{},[274,1373,1374,1376,1384],{},[43,1375,278],{},[36,1377,1378,1380,1382],{},[39,1379,283],{},[43,1381,45],{},[47,1383,288],{},[36,1385,1386,1388,1390],{},[39,1387,272],{},[43,1389,295],{},[47,1391,264],{},[51,1393,1394],{"encoding":53},"\\sum_{i=0}^{m-1}",[20,1396,1398],{"className":1397,"ariaHidden":59},[58],[20,1399,1401,1405],{"className":1400},[63],[20,1402],{"className":1403,"style":1404},[67],"height:1.2537em;vertical-align:-0.2997em;",[20,1406,1408,1411],{"className":1407},[501],[20,1409,278],{"className":1410,"style":507},[501,505,506],[20,1412,1414],{"className":1413},[511],[20,1415,1417,1466],{"className":1416},[417,418],[20,1418,1420,1463],{"className":1419},[422],[20,1421,1423,1443],{"className":1422,"style":521},[426],[20,1424,1425,1428],{"style":524},[20,1426],{"className":1427,"style":528},[434],[20,1429,1431],{"className":1430},[439,440,441,442],[20,1432,1434,1437,1440],{"className":1433},[72,442],[20,1435,283],{"className":1436},[72,73,442],[20,1438,45],{"className":1439},[83,442],[20,1441,288],{"className":1442},[72,442],[20,1444,1445,1448],{"style":546},[20,1446],{"className":1447,"style":528},[434],[20,1449,1451],{"className":1450},[439,440,441,442],[20,1452,1454,1457,1460],{"className":1453},[72,442],[20,1455,272],{"className":1456},[72,73,442],[20,1458,295],{"className":1459},[562,442],[20,1461,264],{"className":1462},[72,442],[20,1464,482],{"className":1465},[481],[20,1467,1469],{"className":1468},[422],[20,1470,1472],{"className":1471,"style":575},[426],[20,1473],{},[1054,1475,1476],{"align":1040},"soma",[1054,1478,1479],{"align":1040},"junta o erro de todo mundo",[1035,1481,1482,1590,1593],{},[1054,1483,1484],{"align":1040},[20,1485,1487,1509],{"className":1486},[23],[20,1488,1490],{"className":1489},[27],[29,1491,1492],{"xmlns":31},[33,1493,1494,1506],{},[36,1495,1496],{},[260,1497,1498,1500],{},[47,1499,264],{},[36,1501,1502,1504],{},[47,1503,269],{},[39,1505,272],{},[51,1507,1508],{"encoding":53},"\\frac{1}{2m}",[20,1510,1512],{"className":1511,"ariaHidden":59},[58],[20,1513,1515,1519],{"className":1514},[63],[20,1516],{"className":1517,"style":1518},[67],"height:1.1901em;vertical-align:-0.345em;",[20,1520,1522,1525,1587],{"className":1521},[72],[20,1523],{"className":1524},[211,410],[20,1526,1528],{"className":1527},[260],[20,1529,1531,1579],{"className":1530},[417,418],[20,1532,1534,1576],{"className":1533},[422],[20,1535,1537,1554,1562],{"className":1536,"style":427},[426],[20,1538,1539,1542],{"style":430},[20,1540],{"className":1541,"style":435},[434],[20,1543,1545],{"className":1544},[439,440,441,442],[20,1546,1548,1551],{"className":1547},[72,442],[20,1549,269],{"className":1550},[72,442],[20,1552,272],{"className":1553},[72,73,442],[20,1555,1556,1559],{"style":454},[20,1557],{"className":1558,"style":435},[434],[20,1560],{"className":1561,"style":462},[461],[20,1563,1564,1567],{"style":465},[20,1565],{"className":1566,"style":435},[434],[20,1568,1570],{"className":1569},[439,440,441,442],[20,1571,1573],{"className":1572},[72,442],[20,1574,264],{"className":1575},[72,442],[20,1577,482],{"className":1578},[481],[20,1580,1582],{"className":1581},[422],[20,1583,1585],{"className":1584,"style":489},[426],[20,1586],{},[20,1588],{"className":1589},[229,410],[1054,1591,1592],{"align":1040},"média (com o 2 extra)",[1054,1594,1595,1596,1624],{"align":1040},"dividir por ",[20,1597,1599,1612],{"className":1598},[23],[20,1600,1602],{"className":1601},[27],[29,1603,1604],{"xmlns":31},[33,1605,1606,1610],{},[36,1607,1608],{},[39,1609,272],{},[51,1611,272],{"encoding":53},[20,1613,1615],{"className":1614,"ariaHidden":59},[58],[20,1616,1618,1621],{"className":1617},[63],[20,1619],{"className":1620,"style":68},[67],[20,1622,272],{"className":1623},[72,73]," vira média (senão o custo só cresceria por ter mais dados, mesmo que o ajuste seja igualmente bom), e o 2 é só um ajuste de conta pro próximo post ficar mais limpo, explico melhor lá",[11,1626,1627],{},"Duas coisas saem direto dessa fórmula, e eu nem precisei decorar nada:",[1629,1630,1631,1691],"ol",{},[1632,1633,1634,1690],"li",{},[20,1635,1637,1660],{"className":1636},[23],[20,1638,1640],{"className":1639},[27],[29,1641,1642],{"xmlns":31},[33,1643,1644,1658],{},[36,1645,1646,1648,1650,1652,1654,1656],{},[39,1647,176],{},[43,1649,180],{"stretchy":179},[39,1651,41],{},[43,1653,185],{"separator":59},[39,1655,112],{},[43,1657,190],{"stretchy":179},[51,1659,193],{"encoding":53},[20,1661,1663],{"className":1662,"ariaHidden":59},[58],[20,1664,1666,1669,1672,1675,1678,1681,1684,1687],{"className":1665},[63],[20,1667],{"className":1668,"style":203},[67],[20,1670,176],{"className":1671,"style":207},[72,73],[20,1673,180],{"className":1674},[211],[20,1676,41],{"className":1677,"style":74},[72,73],[20,1679,185],{"className":1680},[218],[20,1682],{"className":1683,"style":222},[78],[20,1685,112],{"className":1686},[72,73],[20,1688,190],{"className":1689},[229]," nunca é negativo. É soma de coisas ao quadrado, então o menor valor possível é zero.",[1632,1692,1693,1772],{},[20,1694,1696,1724],{"className":1695},[23],[20,1697,1699],{"className":1698},[27],[29,1700,1701],{"xmlns":31},[33,1702,1703,1721],{},[36,1704,1705,1707,1709,1711,1713,1715,1717,1719],{},[39,1706,176],{},[43,1708,180],{"stretchy":179},[39,1710,41],{},[43,1712,185],{"separator":59},[39,1714,112],{},[43,1716,190],{"stretchy":179},[43,1718,45],{},[47,1720,288],{},[51,1722,1723],{"encoding":53},"J(w,b) = 0",[20,1725,1727,1763],{"className":1726,"ariaHidden":59},[58],[20,1728,1730,1733,1736,1739,1742,1745,1748,1751,1754,1757,1760],{"className":1729},[63],[20,1731],{"className":1732,"style":203},[67],[20,1734,176],{"className":1735,"style":207},[72,73],[20,1737,180],{"className":1738},[211],[20,1740,41],{"className":1741,"style":74},[72,73],[20,1743,185],{"className":1744},[218],[20,1746],{"className":1747,"style":222},[78],[20,1749,112],{"className":1750},[72,73],[20,1752,190],{"className":1753},[229],[20,1755],{"className":1756,"style":79},[78],[20,1758,45],{"className":1759},[83],[20,1761],{"className":1762,"style":79},[78],[20,1764,1766,1769],{"className":1765},[63],[20,1767],{"className":1768,"style":93},[67],[20,1770,288],{"className":1771},[72]," significa ajuste perfeito. A reta passa exatamente em cima de todos os pontos.",[11,1774,1775,1776,1805],{},"E por que elevar ao quadrado em vez de, sei lá, pegar o módulo do erro? Porque o quadrado castiga desproporcionalmente os erros grandes. Errar o dobro custa quatro vezes mais caro em ",[20,1777,1779,1792],{"className":1778},[23],[20,1780,1782],{"className":1781},[27],[29,1783,1784],{"xmlns":31},[33,1785,1786,1790],{},[36,1787,1788],{},[39,1789,176],{},[51,1791,176],{"encoding":53},[20,1793,1795],{"className":1794,"ariaHidden":59},[58],[20,1796,1798,1802],{"className":1797},[63],[20,1799],{"className":1800,"style":1801},[67],"height:0.6833em;",[20,1803,176],{"className":1804,"style":207},[72,73],", não o dobro. Isso faz o modelo detestar previsões muito ruins de um jeito que o módulo não faria, e é justamente esse comportamento que dá pro custo o formato de U que a gente vai ver daqui a pouco. Voltando pro tiro ao alvo: é como se o juiz da competição desse nota exponencialmente pior quanto mais longe do centro a flecha cair. Errar por pouco dói pouco, errar feio dói muito mais que o dobro.",[781,1807,1809],{"id":1808},"colocando-isso-em-código","Colocando isso em código",[1811,1812,1817],"pre",{"className":1813,"code":1814,"language":1815,"meta":1816,"style":1816},"language-python shiki shiki-themes github-light github-dark","def compute_cost(x, y, w, b):\n    \"\"\"\n    Calcula a função de custo da regressão linear.\n\n    Args:\n      x (ndarray (m,)) : dados de entrada, m exemplos\n      y (ndarray (m,)) : valores-alvo\n      w, b (scalar)    : parâmetros do modelo\n\n    Returns:\n      total_cost (float): o custo de usar w e b como parâmetros para ajustar\n                          os pontos (x, y)\n    \"\"\"\n    m = x.shape[0]\n\n    cost_sum = 0\n\n    for i in range(m):\n        f_wb = w * x[i] + b           # previsão do modelo pro exemplo i\n        cost = (f_wb - y[i]) ** 2     # erro do exemplo i, ao quadrado\n        cost_sum = cost_sum + cost    # acumula no total\n\n    total_cost = (1 \u002F (2 * m)) * cost_sum\n\n    return total_cost\n","python","",[1818,1819,1820,1827,1833,1839,1846,1852,1858,1864,1870,1875,1881,1887,1893,1898,1904,1909,1915,1920,1926,1932,1938,1944,1949,1955,1960],"code",{"__ignoreMap":1816},[20,1821,1824],{"class":1822,"line":1823},"line",1,[20,1825,1826],{},"def compute_cost(x, y, w, b):\n",[20,1828,1830],{"class":1822,"line":1829},2,[20,1831,1832],{},"    \"\"\"\n",[20,1834,1836],{"class":1822,"line":1835},3,[20,1837,1838],{},"    Calcula a função de custo da regressão linear.\n",[20,1840,1842],{"class":1822,"line":1841},4,[20,1843,1845],{"emptyLinePlaceholder":1844},true,"\n",[20,1847,1849],{"class":1822,"line":1848},5,[20,1850,1851],{},"    Args:\n",[20,1853,1855],{"class":1822,"line":1854},6,[20,1856,1857],{},"      x (ndarray (m,)) : dados de entrada, m exemplos\n",[20,1859,1861],{"class":1822,"line":1860},7,[20,1862,1863],{},"      y (ndarray (m,)) : valores-alvo\n",[20,1865,1867],{"class":1822,"line":1866},8,[20,1868,1869],{},"      w, b (scalar)    : parâmetros do modelo\n",[20,1871,1873],{"class":1822,"line":1872},9,[20,1874,1845],{"emptyLinePlaceholder":1844},[20,1876,1878],{"class":1822,"line":1877},10,[20,1879,1880],{},"    Returns:\n",[20,1882,1884],{"class":1822,"line":1883},11,[20,1885,1886],{},"      total_cost (float): o custo de usar w e b como parâmetros para ajustar\n",[20,1888,1890],{"class":1822,"line":1889},12,[20,1891,1892],{},"                          os pontos (x, y)\n",[20,1894,1896],{"class":1822,"line":1895},13,[20,1897,1832],{},[20,1899,1901],{"class":1822,"line":1900},14,[20,1902,1903],{},"    m = x.shape[0]\n",[20,1905,1907],{"class":1822,"line":1906},15,[20,1908,1845],{"emptyLinePlaceholder":1844},[20,1910,1912],{"class":1822,"line":1911},16,[20,1913,1914],{},"    cost_sum = 0\n",[20,1916,1918],{"class":1822,"line":1917},17,[20,1919,1845],{"emptyLinePlaceholder":1844},[20,1921,1923],{"class":1822,"line":1922},18,[20,1924,1925],{},"    for i in range(m):\n",[20,1927,1929],{"class":1822,"line":1928},19,[20,1930,1931],{},"        f_wb = w * x[i] + b           # previsão do modelo pro exemplo i\n",[20,1933,1935],{"class":1822,"line":1934},20,[20,1936,1937],{},"        cost = (f_wb - y[i]) ** 2     # erro do exemplo i, ao quadrado\n",[20,1939,1941],{"class":1822,"line":1940},21,[20,1942,1943],{},"        cost_sum = cost_sum + cost    # acumula no total\n",[20,1945,1947],{"class":1822,"line":1946},22,[20,1948,1845],{"emptyLinePlaceholder":1844},[20,1950,1952],{"class":1822,"line":1951},23,[20,1953,1954],{},"    total_cost = (1 \u002F (2 * m)) * cost_sum\n",[20,1956,1958],{"class":1822,"line":1957},24,[20,1959,1845],{"emptyLinePlaceholder":1844},[20,1961,1963],{"class":1822,"line":1962},25,[20,1964,1965],{},"    return total_cost\n",[11,1967,1968,1969,1972,1973,1976,1977,1980],{},"Repara que é o mesmo laço ",[1818,1970,1971],{},"for"," do ",[14,1974,1975],{"href":16},"post passado"," (o ",[1818,1978,1979],{},"compute_model_output","), só que em vez de guardar as previsões, a gente acumula o erro ao quadrado de cada uma. Estrutura idêntica, propósito diferente.",[781,1982,1984],{"id":1983},"congelando-um-parâmetro-pra-enxergar-o-outro","Congelando um parâmetro pra enxergar o outro",[11,1986,1987,1988,97,2016,2044,2045,2095,2096,230],{},"Com dois parâmetros pra mexer (",[20,1989,1991,2004],{"className":1990},[23],[20,1992,1994],{"className":1993},[27],[29,1995,1996],{"xmlns":31},[33,1997,1998,2002],{},[36,1999,2000],{},[39,2001,41],{},[51,2003,41],{"encoding":53},[20,2005,2007],{"className":2006,"ariaHidden":59},[58],[20,2008,2010,2013],{"className":2009},[63],[20,2011],{"className":2012,"style":68},[67],[20,2014,41],{"className":2015,"style":74},[72,73],[20,2017,2019,2032],{"className":2018},[23],[20,2020,2022],{"className":2021},[27],[29,2023,2024],{"xmlns":31},[33,2025,2026,2030],{},[36,2027,2028],{},[39,2029,112],{},[51,2031,112],{"encoding":53},[20,2033,2035],{"className":2034,"ariaHidden":59},[58],[20,2036,2038,2041],{"className":2037},[63],[20,2039],{"className":2040,"style":130},[67],[20,2042,112],{"className":2043},[72,73],"), eu tive dificuldade de visualizar o custo direto. Truque clássico: trava um deles e olha só pro outro. Fixa ",[20,2046,2048,2065],{"className":2047},[23],[20,2049,2051],{"className":2050},[27],[29,2052,2053],{"xmlns":31},[33,2054,2055,2063],{},[36,2056,2057,2059,2061],{},[39,2058,112],{},[43,2060,45],{},[47,2062,117],{},[51,2064,120],{"encoding":53},[20,2066,2068,2086],{"className":2067,"ariaHidden":59},[58],[20,2069,2071,2074,2077,2080,2083],{"className":2070},[63],[20,2072],{"className":2073,"style":130},[67],[20,2075,112],{"className":2076},[72,73],[20,2078],{"className":2079,"style":79},[78],[20,2081,45],{"className":2082},[83],[20,2084],{"className":2085,"style":79},[78],[20,2087,2089,2092],{"className":2088},[63],[20,2090],{"className":2091,"style":93},[67],[20,2093,117],{"className":2094},[72]," e mexe só em ",[20,2097,2099,2112],{"className":2098},[23],[20,2100,2102],{"className":2101},[27],[29,2103,2104],{"xmlns":31},[33,2105,2106,2110],{},[36,2107,2108],{},[39,2109,41],{},[51,2111,41],{"encoding":53},[20,2113,2115],{"className":2114,"ariaHidden":59},[58],[20,2116,2118,2121],{"className":2117},[63],[20,2119],{"className":2120,"style":68},[67],[20,2122,41],{"className":2123,"style":74},[72,73],[11,2125,2126,2127,2171],{},"Arrasta o slider abaixo e olha duas coisas ao mesmo tempo: como a reta (painel esquerdo) se aproxima ou se afasta dos pontos, e onde o ponto vermelho fica na curva ",[20,2128,2130,2150],{"className":2129},[23],[20,2131,2133],{"className":2132},[27],[29,2134,2135],{"xmlns":31},[33,2136,2137,2147],{},[36,2138,2139,2141,2143,2145],{},[39,2140,176],{},[43,2142,180],{"stretchy":179},[39,2144,41],{},[43,2146,190],{"stretchy":179},[51,2148,2149],{"encoding":53},"J(w)",[20,2151,2153],{"className":2152,"ariaHidden":59},[58],[20,2154,2156,2159,2162,2165,2168],{"className":2155},[63],[20,2157],{"className":2158,"style":203},[67],[20,2160,176],{"className":2161,"style":207},[72,73],[20,2163,180],{"className":2164},[211],[20,2166,41],{"className":2167,"style":74},[72,73],[20,2169,190],{"className":2170},[229]," (painel direito). Conforme a reta melhora, o ponto desce na curva.",[2173,2174],"cost-intuition-explorer",{":b-fixed":117,":initial-w":2175,":w-max":2176,":w-min":288,":x-train":2177,":y-train":2178,"dataLabel":2179,"prediction-label":2180,"w-label":41,"x-label":2181,"y-label":2182},"150","400","[1, 2]","[300, 500]","Valores reais","Nossa previsão","Tamanho (1000 pés²)","Preço (1000 dólares)",[11,2184,2185],{},"Repara três coisas:",[2187,2188,2189,2300,2335],"ul",{},[1632,2190,2191,2245,2246,2248,2249,2299],{},[2192,2193,2194,2195],"strong",{},"O custo é mínimo exatamente em ",[20,2196,2198,2215],{"className":2197},[23],[20,2199,2201],{"className":2200},[27],[29,2202,2203],{"xmlns":31},[33,2204,2205,2213],{},[36,2206,2207,2209,2211],{},[39,2208,41],{},[43,2210,45],{},[47,2212,49],{},[51,2214,54],{"encoding":53},[20,2216,2218,2236],{"className":2217,"ariaHidden":59},[58],[20,2219,2221,2224,2227,2230,2233],{"className":2220},[63],[20,2222],{"className":2223,"style":68},[67],[20,2225,41],{"className":2226,"style":74},[72,73],[20,2228],{"className":2229,"style":79},[78],[20,2231,45],{"className":2232},[83],[20,2234],{"className":2235,"style":79},[78],[20,2237,2239,2242],{"className":2238},[63],[20,2240],{"className":2241,"style":93},[67],[20,2243,49],{"className":2244},[72],", o mesmo valor que você achou no olho no ",[14,2247,1975],{"href":16},". Com ",[20,2250,2252,2269],{"className":2251},[23],[20,2253,2255],{"className":2254},[27],[29,2256,2257],{"xmlns":31},[33,2258,2259,2267],{},[36,2260,2261,2263,2265],{},[39,2262,112],{},[43,2264,45],{},[47,2266,117],{},[51,2268,120],{"encoding":53},[20,2270,2272,2290],{"className":2271,"ariaHidden":59},[58],[20,2273,2275,2278,2281,2284,2287],{"className":2274},[63],[20,2276],{"className":2277,"style":130},[67],[20,2279,112],{"className":2280},[72,73],[20,2282],{"className":2283,"style":79},[78],[20,2285,45],{"className":2286},[83],[20,2288],{"className":2289,"style":79},[78],[20,2291,2293,2296],{"className":2292},[63],[20,2294],{"className":2295,"style":93},[67],[20,2297,117],{"className":2298},[72],", o custo nesse ponto vai a zero, porque a reta passa nos dois pontos.",[1632,2301,2302,2305,2306,2334],{},[2192,2303,2304],{},"O custo explode rápido"," quando ",[20,2307,2309,2322],{"className":2308},[23],[20,2310,2312],{"className":2311},[27],[29,2313,2314],{"xmlns":31},[33,2315,2316,2320],{},[36,2317,2318],{},[39,2319,41],{},[51,2321,41],{"encoding":53},[20,2323,2325],{"className":2324,"ariaHidden":59},[58],[20,2326,2328,2331],{"className":2327},[63],[20,2329],{"className":2330,"style":68},[67],[20,2332,41],{"className":2333,"style":74},[72,73]," fica muito grande ou muito pequeno. É o quadrado da fórmula fazendo esse trabalho.",[1632,2336,2337,2340,2341,97,2369,2397,2398,2426],{},[2192,2338,2339],{},"Aí eu saquei: minimizar o custo é o mesmo que achar o melhor ajuste."," Não é coincidência, é a definição. Escolher ",[20,2342,2344,2357],{"className":2343},[23],[20,2345,2347],{"className":2346},[27],[29,2348,2349],{"xmlns":31},[33,2350,2351,2355],{},[36,2352,2353],{},[39,2354,41],{},[51,2356,41],{"encoding":53},[20,2358,2360],{"className":2359,"ariaHidden":59},[58],[20,2361,2363,2366],{"className":2362},[63],[20,2364],{"className":2365,"style":68},[67],[20,2367,41],{"className":2368,"style":74},[72,73],[20,2370,2372,2385],{"className":2371},[23],[20,2373,2375],{"className":2374},[27],[29,2376,2377],{"xmlns":31},[33,2378,2379,2383],{},[36,2380,2381],{},[39,2382,112],{},[51,2384,112],{"encoding":53},[20,2386,2388],{"className":2387,"ariaHidden":59},[58],[20,2389,2391,2394],{"className":2390},[63],[20,2392],{"className":2393,"style":130},[67],[20,2395,112],{"className":2396},[72,73]," que minimizam ",[20,2399,2401,2414],{"className":2400},[23],[20,2402,2404],{"className":2403},[27],[29,2405,2406],{"xmlns":31},[33,2407,2408,2412],{},[36,2409,2410],{},[39,2411,176],{},[51,2413,176],{"encoding":53},[20,2415,2417],{"className":2416,"ariaHidden":59},[58],[20,2418,2420,2423],{"className":2419},[63],[20,2421],{"className":2422,"style":1801},[67],[20,2424,176],{"className":2425,"style":207},[72,73]," é literalmente o que a gente chama de treinar um modelo.",[11,2428,2429,2430,2481],{},"Experimenta levar o slider até ",[20,2431,2433,2451],{"className":2432},[23],[20,2434,2436],{"className":2435},[27],[29,2437,2438],{"xmlns":31},[33,2439,2440,2448],{},[36,2441,2442,2444,2446],{},[39,2443,41],{},[43,2445,45],{},[47,2447,288],{},[51,2449,2450],{"encoding":53},"w = 0",[20,2452,2454,2472],{"className":2453,"ariaHidden":59},[58],[20,2455,2457,2460,2463,2466,2469],{"className":2456},[63],[20,2458],{"className":2459,"style":68},[67],[20,2461,41],{"className":2462,"style":74},[72,73],[20,2464],{"className":2465,"style":79},[78],[20,2467,45],{"className":2468},[83],[20,2470],{"className":2471,"style":79},[78],[20,2473,2475,2478],{"className":2474},[63],[20,2476],{"className":2477,"style":93},[67],[20,2479,288],{"className":2480},[72],": a reta fica horizontal (prevê o mesmo preço pra qualquer tamanho de casa) e o custo dispara.",[781,2483,2485],{"id":2484},"o-mundo-real-não-tem-só-2-pontos-perfeitos","O mundo real não tem só 2 pontos perfeitos",[11,2487,2488],{},"Até aqui, com 2 pontos e 2 parâmetros, eu conseguia zerar o custo. Isso é raro. Bora trocar o conjunto de treino por um mais realista, com 6 casas, onde os preços não caem exatamente sobre reta nenhuma (ruído de verdade, tipo casas parecidas vendendo por preços um pouco diferentes):",[1029,2490,2491,2500],{},[1032,2492,2493],{},[1035,2494,2495,2498],{},[1038,2496,2181],{"align":2497},"center",[1038,2499,2182],{"align":2497},[1049,2501,2502,2510,2518,2526,2534,2542],{},[1035,2503,2504,2507],{},[1054,2505,2506],{"align":2497},"1.0",[1054,2508,2509],{"align":2497},"250",[1035,2511,2512,2515],{},[1054,2513,2514],{"align":2497},"1.7",[1054,2516,2517],{"align":2497},"300",[1035,2519,2520,2523],{},[1054,2521,2522],{"align":2497},"2.0",[1054,2524,2525],{"align":2497},"480",[1035,2527,2528,2531],{},[1054,2529,2530],{"align":2497},"2.5",[1054,2532,2533],{"align":2497},"430",[1035,2535,2536,2539],{},[1054,2537,2538],{"align":2497},"3.0",[1054,2540,2541],{"align":2497},"630",[1035,2543,2544,2547],{},[1054,2545,2546],{"align":2497},"3.2",[1054,2548,2549],{"align":2497},"730",[11,2551,2552,2553,2605],{},"Pergunta que fica no ar: será que ainda existe algum ",[20,2554,2556,2578],{"className":2555},[23],[20,2557,2559],{"className":2558},[27],[29,2560,2561],{"xmlns":31},[33,2562,2563,2575],{},[36,2564,2565,2567,2569,2571,2573],{},[43,2566,180],{"stretchy":179},[39,2568,41],{},[43,2570,185],{"separator":59},[39,2572,112],{},[43,2574,190],{"stretchy":179},[51,2576,2577],{"encoding":53},"(w, b)",[20,2579,2581],{"className":2580,"ariaHidden":59},[58],[20,2582,2584,2587,2590,2593,2596,2599,2602],{"className":2583},[63],[20,2585],{"className":2586,"style":203},[67],[20,2588,180],{"className":2589},[211],[20,2591,41],{"className":2592,"style":74},[72,73],[20,2594,185],{"className":2595},[218],[20,2597],{"className":2598,"style":222},[78],[20,2600,112],{"className":2601},[72,73],[20,2603,190],{"className":2604},[229]," que zere o custo aqui?",[11,2607,2608,2609,2637,2638,2637,2641,2669],{},"Mexe nos dois sliders abaixo (agora ",[20,2610,2612,2625],{"className":2611},[23],[20,2613,2615],{"className":2614},[27],[29,2616,2617],{"xmlns":31},[33,2618,2619,2623],{},[36,2620,2621],{},[39,2622,41],{},[51,2624,41],{"encoding":53},[20,2626,2628],{"className":2627,"ariaHidden":59},[58],[20,2629,2631,2634],{"className":2630},[63],[20,2632],{"className":2633,"style":68},[67],[20,2635,41],{"className":2636,"style":74},[72,73]," ",[2192,2639,2640],{},"e",[20,2642,2644,2657],{"className":2643},[23],[20,2645,2647],{"className":2646},[27],[29,2648,2649],{"xmlns":31},[33,2650,2651,2655],{},[36,2652,2653],{},[39,2654,112],{},[51,2656,112],{"encoding":53},[20,2658,2660],{"className":2659,"ariaHidden":59},[58],[20,2661,2663,2666],{"className":2662},[63],[20,2664],{"className":2665,"style":130},[67],[20,2667,112],{"className":2668},[72,73]," ao mesmo tempo) e tenta chegar no centro do mapa de calor, onde o custo é mais baixo. Alterna pra visão 3D e gira a superfície com o dedo ou o mouse pra sentir o formato do \"vale\".",[2671,2672],"cost-explorer",{":b-max":49,":b-min":2673,":initial-b":288,":initial-w":2175,":w-max":2176,":w-min":288,":x-train":2674,":y-train":2675,"b-label":112,"dataLabel":2179,"prediction-label":2676,"w-label":41,"x-label":2181,"y-label":2182},"-200","[1.0, 1.7, 2.0, 2.5, 3.0, 3.2]","[250, 300, 480, 430, 630, 730]","Sua previsão",[11,2678,2679,2680,2683,2684,97,2738,2790],{},"Você deve ter percebido: dessa vez o custo ",[2192,2681,2682],{},"não zera",". O melhor que dá pra conseguir fica perto de ",[20,2685,2687,2707],{"className":2686},[23],[20,2688,2690],{"className":2689},[27],[29,2691,2692],{"xmlns":31},[33,2693,2694,2704],{},[36,2695,2696,2698,2701],{},[39,2697,41],{},[43,2699,2700],{},"≈",[47,2702,2703],{},"209",[51,2705,2706],{"encoding":53},"w \\approx 209",[20,2708,2710,2729],{"className":2709,"ariaHidden":59},[58],[20,2711,2713,2717,2720,2723,2726],{"className":2712},[63],[20,2714],{"className":2715,"style":2716},[67],"height:0.4831em;",[20,2718,41],{"className":2719,"style":74},[72,73],[20,2721],{"className":2722,"style":79},[78],[20,2724,2700],{"className":2725},[83],[20,2727],{"className":2728,"style":79},[78],[20,2730,2732,2735],{"className":2731},[63],[20,2733],{"className":2734,"style":93},[67],[20,2736,2703],{"className":2737},[72],[20,2739,2741,2760],{"className":2740},[23],[20,2742,2744],{"className":2743},[27],[29,2745,2746],{"xmlns":31},[33,2747,2748,2757],{},[36,2749,2750,2752,2754],{},[39,2751,112],{},[43,2753,2700],{},[47,2755,2756],{},"2.4",[51,2758,2759],{"encoding":53},"b \\approx 2.4",[20,2761,2763,2781],{"className":2762,"ariaHidden":59},[58],[20,2764,2766,2769,2772,2775,2778],{"className":2765},[63],[20,2767],{"className":2768,"style":130},[67],[20,2770,112],{"className":2771},[72,73],[20,2773],{"className":2774,"style":79},[78],[20,2776,2700],{"className":2777},[83],[20,2779],{"className":2780,"style":79},[78],[20,2782,2784,2787],{"className":2783},[63],[20,2785],{"className":2786,"style":93},[67],[20,2788,2756],{"className":2789},[72],", com custo em torno de 1736. Por quê? Porque essas 6 casas não estão alinhadas. Nenhuma reta única passa exatamente por todas. O melhor ajuste é aquele que deixa o menor erro quadrático total possível, e é isso que a função de custo define como \"o melhor\".",[11,2792,2793,2794,2797,2798,2802],{},"Guarda essa ideia: ",[2192,2795,2796],{},"custo mínimo diferente de zero é o normal",", não um bug. Custo zero costuma acontecer quando você tem poucos dados demais (como no nosso caso de 2 pontos) ou quando o modelo decorou os dados em vez de aprender o padrão deles (isso tem nome, ",[157,2799,2801],{"definition":2800},"quando o modelo memoriza os dados de treino em vez de aprender o padrão geral, e por isso vai mal em dados novos","overfitting",", mas isso é assunto pra mais pra frente no curso).",[781,2804,2806],{"id":2805},"por-que-a-superfície-é-sempre-uma-tigela","Por que a superfície é sempre uma tigela",[11,2808,2809,2810,230],{},"Girando a superfície 3D acima você deve ter notado: ela sempre tem essa cara de tigela de sopa, um único vale, sem picos falsos no meio do caminho. Isso não é coincidência do nosso exemplo específico, é consequência direta de elevar o erro ao quadrado na fórmula. Toda vez que a gente eleva algo ao quadrado, o resultado é uma superfície ",[157,2811,2813],{"definition":2812},"uma superfície com formato de tigela, um único vale, sem mínimos falsos onde um algoritmo de busca possa ficar preso","convexa",[11,2815,2816,2817,2845,2846,2874,2875,2988],{},"Pra ver isso de um jeito mais limpo, sem a distorção de escala que os dados reais trazem (repara que ",[20,2818,2820,2833],{"className":2819},[23],[20,2821,2823],{"className":2822},[27],[29,2824,2825],{"xmlns":31},[33,2826,2827,2831],{},[36,2828,2829],{},[39,2830,41],{},[51,2832,41],{"encoding":53},[20,2834,2836],{"className":2835,"ariaHidden":59},[58],[20,2837,2839,2842],{"className":2838},[63],[20,2840],{"className":2841,"style":68},[67],[20,2843,41],{"className":2844,"style":74},[72,73]," vai de 0 a 400 e ",[20,2847,2849,2862],{"className":2848},[23],[20,2850,2852],{"className":2851},[27],[29,2853,2854],{"xmlns":31},[33,2855,2856,2860],{},[36,2857,2858],{},[39,2859,112],{},[51,2861,112],{"encoding":53},[20,2863,2865],{"className":2864,"ariaHidden":59},[58],[20,2866,2868,2871],{"className":2867},[63],[20,2869],{"className":2870,"style":130},[67],[20,2872,112],{"className":2873},[72,73]," de -200 a 200 no gráfico acima, o que estica o vale), aqui vai a versão idealizada da mesma forma, só ",[20,2876,2878,2905],{"className":2877},[23],[20,2879,2881],{"className":2880},[27],[29,2882,2883],{"xmlns":31},[33,2884,2885,2902],{},[36,2886,2887,2893,2896],{},[299,2888,2889,2891],{},[39,2890,41],{},[47,2892,269],{},[43,2894,2895],{},"+",[299,2897,2898,2900],{},[39,2899,112],{},[47,2901,269],{},[51,2903,2904],{"encoding":53},"w^2 + b^2",[20,2906,2908,2953],{"className":2907,"ariaHidden":59},[58],[20,2909,2911,2915,2944,2947,2950],{"className":2910},[63],[20,2912],{"className":2913,"style":2914},[67],"height:0.8974em;vertical-align:-0.0833em;",[20,2916,2918,2921],{"className":2917},[72],[20,2919,41],{"className":2920,"style":74},[72,73],[20,2922,2924],{"className":2923},[511],[20,2925,2927],{"className":2926},[417],[20,2928,2930],{"className":2929},[422],[20,2931,2933],{"className":2932,"style":1338},[426],[20,2934,2935,2938],{"style":675},[20,2936],{"className":2937,"style":528},[434],[20,2939,2941],{"className":2940},[439,440,441,442],[20,2942,269],{"className":2943},[72,442],[20,2945],{"className":2946,"style":700},[78],[20,2948,2895],{"className":2949},[562],[20,2951],{"className":2952,"style":700},[78],[20,2954,2956,2959],{"className":2955},[63],[20,2957],{"className":2958,"style":1338},[67],[20,2960,2962,2965],{"className":2961},[72],[20,2963,112],{"className":2964},[72,73],[20,2966,2968],{"className":2967},[511],[20,2969,2971],{"className":2970},[417],[20,2972,2974],{"className":2973},[422],[20,2975,2977],{"className":2976,"style":1338},[426],[20,2978,2979,2982],{"style":675},[20,2980],{"className":2981,"style":528},[434],[20,2983,2985],{"className":2984},[439,440,441,442],[20,2986,269],{"className":2987},[72,442],", com os dois eixos na mesma escala:",[2990,2991],"cost-surface3d",{":b-max":2992,":b-min":2993,":w-max":2992,":w-min":2993},"20","-20",[11,2995,2996,2997,3000],{},"Por que essa forma importa tanto? Porque uma superfície convexa garante que só existe ",[2192,2998,2999],{},"um"," mínimo, o mínimo global. Não tem vale escondido em outro canto pra um algoritmo de busca cair e ficar preso, achando que já chegou no fundo sem ter chegado. Essa garantia é o que torna confiável o próximo passo do curso: um jeito automático de descer até o fundo dessa tigela, sem você precisar arrastar slider a vida inteira.",[781,3002,3004],{"id":3003},"fechando","Fechando",[1029,3006,3007,3017],{},[1032,3008,3009],{},[1035,3010,3011,3014],{},[1038,3012,3013],{"align":1040},"Conceito",[1038,3015,3016],{"align":1040},"O que ficou estabelecido",[1049,3018,3019,3083,3091,3161,3169,3286],{},[1035,3020,3021,3024],{},[1054,3022,3023],{"align":1040},"Função de custo",[1054,3025,3026,3082],{"align":1040},[20,3027,3029,3052],{"className":3028},[23],[20,3030,3032],{"className":3031},[27],[29,3033,3034],{"xmlns":31},[33,3035,3036,3050],{},[36,3037,3038,3040,3042,3044,3046,3048],{},[39,3039,176],{},[43,3041,180],{"stretchy":179},[39,3043,41],{},[43,3045,185],{"separator":59},[39,3047,112],{},[43,3049,190],{"stretchy":179},[51,3051,193],{"encoding":53},[20,3053,3055],{"className":3054,"ariaHidden":59},[58],[20,3056,3058,3061,3064,3067,3070,3073,3076,3079],{"className":3057},[63],[20,3059],{"className":3060,"style":203},[67],[20,3062,176],{"className":3063,"style":207},[72,73],[20,3065,180],{"className":3066},[211],[20,3068,41],{"className":3069,"style":74},[72,73],[20,3071,185],{"className":3072},[218],[20,3074],{"className":3075,"style":222},[78],[20,3077,112],{"className":3078},[72,73],[20,3080,190],{"className":3081},[229],", um número que mede o quanto as previsões erram os dados de treino",[1035,3084,3085,3088],{},[1054,3086,3087],{"align":1040},"Por que ao quadrado",[1054,3089,3090],{"align":1040},"remove o sinal do erro e pune fortemente erros grandes, além de garantir uma superfície convexa",[1035,3092,3093,3130],{},[1054,3094,3095,3096],{"align":1040},"Por que ",[20,3097,3099,3115],{"className":3098},[23],[20,3100,3102],{"className":3101},[27],[29,3103,3104],{"xmlns":31},[33,3105,3106,3112],{},[36,3107,3108,3110],{},[47,3109,269],{},[39,3111,272],{},[51,3113,3114],{"encoding":53},"2m",[20,3116,3118],{"className":3117,"ariaHidden":59},[58],[20,3119,3121,3124,3127],{"className":3120},[63],[20,3122],{"className":3123,"style":93},[67],[20,3125,269],{"className":3126},[72],[20,3128,272],{"className":3129},[72,73],[1054,3131,3132,3160],{"align":1040},[20,3133,3135,3148],{"className":3134},[23],[20,3136,3138],{"className":3137},[27],[29,3139,3140],{"xmlns":31},[33,3141,3142,3146],{},[36,3143,3144],{},[39,3145,272],{},[51,3147,272],{"encoding":53},[20,3149,3151],{"className":3150,"ariaHidden":59},[58],[20,3152,3154,3157],{"className":3153},[63],[20,3155],{"className":3156,"style":68},[67],[20,3158,272],{"className":3159},[72,73]," transforma soma em média, e o 2 simplifica a conta que vem no próximo post",[1035,3162,3163,3166],{},[1054,3164,3165],{"align":1040},"Formato",[1054,3167,3168],{"align":1040},"curva em U (um parâmetro) e tigela de sopa (dois parâmetros)",[1035,3170,3171,3174],{},[1054,3172,3173],{"align":1040},"Treinar o modelo",[1054,3175,3176,3177,3229,3230],{"align":1040},"é achar o par ",[20,3178,3180,3202],{"className":3179},[23],[20,3181,3183],{"className":3182},[27],[29,3184,3185],{"xmlns":31},[33,3186,3187,3199],{},[36,3188,3189,3191,3193,3195,3197],{},[43,3190,180],{"stretchy":179},[39,3192,41],{},[43,3194,185],{"separator":59},[39,3196,112],{},[43,3198,190],{"stretchy":179},[51,3200,3201],{"encoding":53},"(w,b)",[20,3203,3205],{"className":3204,"ariaHidden":59},[58],[20,3206,3208,3211,3214,3217,3220,3223,3226],{"className":3207},[63],[20,3209],{"className":3210,"style":203},[67],[20,3212,180],{"className":3213},[211],[20,3215,41],{"className":3216,"style":74},[72,73],[20,3218,185],{"className":3219},[218],[20,3221],{"className":3222,"style":222},[78],[20,3224,112],{"className":3225},[72,73],[20,3227,190],{"className":3228},[229]," que minimiza ",[20,3231,3233,3256],{"className":3232},[23],[20,3234,3236],{"className":3235},[27],[29,3237,3238],{"xmlns":31},[33,3239,3240,3254],{},[36,3241,3242,3244,3246,3248,3250,3252],{},[39,3243,176],{},[43,3245,180],{"stretchy":179},[39,3247,41],{},[43,3249,185],{"separator":59},[39,3251,112],{},[43,3253,190],{"stretchy":179},[51,3255,193],{"encoding":53},[20,3257,3259],{"className":3258,"ariaHidden":59},[58],[20,3260,3262,3265,3268,3271,3274,3277,3280,3283],{"className":3261},[63],[20,3263],{"className":3264,"style":203},[67],[20,3266,176],{"className":3267,"style":207},[72,73],[20,3269,180],{"className":3270},[211],[20,3272,41],{"className":3273,"style":74},[72,73],[20,3275,185],{"className":3276},[218],[20,3278],{"className":3279,"style":222},[78],[20,3281,112],{"className":3282},[72,73],[20,3284,190],{"className":3285},[229],[1035,3287,3288,3291],{},[1054,3289,3290],{"align":1040},"Custo mínimo diferente de zero",[1054,3292,3293],{"align":1040},"normal quando os dados têm ruído, não é sinal de erro",[11,3295,3296,3303],{},[2192,3297,3298,3302],{},[14,3299,3301],{"href":3300},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab04-gradient-descent","No próximo post",":"," você já sentiu na mão como é procurar o fundo da tigela arrastando slider. Não escala. O próximo post apresenta o gradiente descendente, um algoritmo que usa a inclinação da superfície de custo pra descer até o fundo sozinho, sem você precisar chutar valor nenhum.",[781,3305,3307],{"id":3306},"aplicação-prática","Aplicação prática",[11,3309,3310,3311,3314,3315,3321,3322,3325],{},"Mesmo dataset real de imóveis do ",[14,3312,3313],{"href":16},"post anterior"," (500 casas, ",[14,3316,3320],{"href":3317,"rel":3318},"https:\u002F\u002Fwww.kaggle.com\u002Fdatasets\u002Fdenkuznetz\u002Fhousing-prices-regression",[3319],"nofollow","Housing Prices Regression, Kaggle","). Agora com ",[1818,3323,3324],{},"compute_cost"," de verdade.",[1811,3327,3329],{"className":1813,"code":3328,"language":1815,"meta":1816,"style":1816},"def compute_cost(x, y, w, b):\n    m = x.shape[0]\n    cost_sum = 0\n    for i in range(m):\n        f_wb = w * x[i] + b\n        cost_sum += (f_wb - y[i]) ** 2\n    return (1 \u002F (2 * m)) * cost_sum\n\n# x_sqft já em \"centenas de pés²\", y_price já em \"milhares de dólares\"\n# (mesma amostra de 50 casas do post anterior)\n\nprint(\"custo com um chute ruim, w=50, b=100:\", compute_cost(x_sqft, y_price, 50, 100))\nprint(\"custo perto do ajuste ótimo, w=116, b=399:\", compute_cost(x_sqft, y_price, 116, 399))\n",[1818,3330,3331,3335,3339,3343,3347,3352,3357,3362,3366,3371,3376,3380,3385],{"__ignoreMap":1816},[20,3332,3333],{"class":1822,"line":1823},[20,3334,1826],{},[20,3336,3337],{"class":1822,"line":1829},[20,3338,1903],{},[20,3340,3341],{"class":1822,"line":1835},[20,3342,1914],{},[20,3344,3345],{"class":1822,"line":1841},[20,3346,1925],{},[20,3348,3349],{"class":1822,"line":1848},[20,3350,3351],{},"        f_wb = w * x[i] + b\n",[20,3353,3354],{"class":1822,"line":1854},[20,3355,3356],{},"        cost_sum += (f_wb - y[i]) ** 2\n",[20,3358,3359],{"class":1822,"line":1860},[20,3360,3361],{},"    return (1 \u002F (2 * m)) * cost_sum\n",[20,3363,3364],{"class":1822,"line":1866},[20,3365,1845],{"emptyLinePlaceholder":1844},[20,3367,3368],{"class":1822,"line":1872},[20,3369,3370],{},"# x_sqft já em \"centenas de pés²\", y_price já em \"milhares de dólares\"\n",[20,3372,3373],{"class":1822,"line":1877},[20,3374,3375],{},"# (mesma amostra de 50 casas do post anterior)\n",[20,3377,3378],{"class":1822,"line":1883},[20,3379,1845],{"emptyLinePlaceholder":1844},[20,3381,3382],{"class":1822,"line":1889},[20,3383,3384],{},"print(\"custo com um chute ruim, w=50, b=100:\", compute_cost(x_sqft, y_price, 50, 100))\n",[20,3386,3387],{"class":1822,"line":1895},[20,3388,3389],{},"print(\"custo perto do ajuste ótimo, w=116, b=399:\", compute_cost(x_sqft, y_price, 116, 399))\n",[3391,3392,3393],"blockquote",{},[11,3394,3395,2637,3398,3401,3402],{},[2192,3396,3397],{},"Saída:",[1818,3399,3400],{},"custo com um chute ruim, w=50, b=100: 90317.6"," \u002F ",[1818,3403,3404],{},"custo perto do ajuste ótimo, w=116, b=399: 5189.6",[11,3406,3407],{},"Quase 20 vezes menos custo só de acertar melhor os parâmetros. Mexe você mesmo nos sliders e tenta chegar perto desses ~5189 (repara: não dá pra zerar, o mínimo real é isso mesmo, dado real tem ruído):",[3409,3410],"housing-cost-explorer",{},[3412,3413,3414],"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":1816,"searchDepth":1829,"depth":1829,"links":3416},[3417,3418,3419,3420,3421,3422,3423,3424],{"id":783,"depth":1829,"text":784},{"id":795,"depth":1829,"text":796},{"id":1808,"depth":1829,"text":1809},{"id":1983,"depth":1829,"text":1984},{"id":2484,"depth":1829,"text":2485},{"id":2805,"depth":1829,"text":2806},{"id":3003,"depth":1829,"text":3004},{"id":3306,"depth":1829,"text":3307},null,"2026-08-18","Como colocar um número no quanto um modelo erra: J(w,b), por que ao quadrado, por que dividir por 2m, e por que a superfície de custo é sempre uma tigela.","md",{},"\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab03-cost-function","machine-learning-specialization",{"title":6,"description":3427},"published","pt\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab03-cost-function",[3436,3437,3438],"funcao-de-custo","erro-quadratico","fundamentos","k9789tpYfYGNTWE35KZvCQyXFElCaL20opMAjLZWyUI",1787338983631]