{"id":1942,"date":"2019-08-25T05:59:42","date_gmt":"2019-08-24T20:59:42","guid":{"rendered":"http:\/\/141.164.34.82\/?p=1942"},"modified":"2019-08-25T07:54:45","modified_gmt":"2019-08-24T22:54:45","slug":"%eb%aa%a8%ed%98%95%ec%9d%98-%ec%98%88%ec%b8%a1%ec%9d%84-%ed%99%9c%ec%9a%a9%ed%95%9c-eda%ec%99%80-%ec%83%88%eb%a1%9c%ec%9a%b4-%eb%b3%80%ec%88%98-%ec%83%9d%ec%84%b1","status":"publish","type":"post","link":"http:\/\/ds.sumeun.org\/?p=1942","title":{"rendered":"\ubaa8\ud615\uc758 \uc608\uce21\uc744 \ud65c\uc6a9\ud55c EDA\uc640 \ud53c\ucc98 \uc5d4\uc9c0\ub2c8\uc5b4\ub9c1"},"content":{"rendered":"

\uc608\uce21 \ubaa8\ud615\uc758 \uc758\ubbf8<\/h2>\n
library(dplyr)\nlibrary(ggplot2)\nlibrary(randomForest)\n<\/code><\/pre>\n
\uc608\uce21 \ubaa8\ud615\uc740 \uae30\ubcf8\uc801\uc73c\ub85c \\(f(\\vec{x})\\) \uc774\ub2e4.[1]<\/sup> \uc8fc\uc5b4\uc9c4 \uc124\uba85 \ubcc0\uc218 \\(\\vec{x}\\) \uc5d0 \ub300\ud574 \uacb0\uacfc \ubcc0\uc218 \\(y\\) \ub97c \uc608\uce21\ud55c\ub2e4. \uc608\uce21 \ubaa8\ud615\uc744 \ud3c9\uac00\ud558\ub294 \ubc29\ubc95\uc740 \\(\\hat{y}=f(\\vec{x})\\) \ub77c\uace0 \ud560 \ub54c, \\(|y – \\hat{y}|\\) \uc744 \uc4f8 \uc218\ub3c4 \uc788\uace0, \\((y – \\hat{y})^2\\) \ub97c \uc4f0\uae30\ub3c4 \ud558\uace0, hinge loss\ub77c\ub294 \uac83\uc744 \uc4f0\uae30\ub3c4 \ud558\uc9c0\ub9cc, \uc5b4\uca0b\ub4e0 \\(f(\\vec{x})\\) \ub97c \ub9cc\ub4e4\uc5b4\ub0b4\ub294 \uac83\uc774\ub2e4. <\/p>\n
\uc774\ub54c \uc5b4\ub5a4 \uac00\uc815\uc744 \ud558\ub290\ub0d0, \uc5b4\ub5a4 \uc54c\uace0\ub9ac\uc998\uc744 \uc4f0\ub290\ub0d0\uc5d0 \ub530\ub77c \ub2e4\uc911\ud68c\uadc0, \uacb0\uc815\ub098\ubb34, \ub79c\ub364\ud3ec\ub808\uc2a4\ud2b8, \uadf8\ub798\ub514\uc5b8\ud2b8\ubd80\uc2a4\ud305 \ub4f1\uc73c\ub85c \ub098\ub220\uc9c4\ub2e4. <\/p>\n
\uc774\ub54c \ub2e4\uc911\ud68c\uadc0\ubcf4\ub2e4 \ub79c\ub364\ud3ec\ub808\uc2a4\ud2b8\ub098 \uadf8\ub798\ub514\uc5b8\ud2b8 \ubd80\uc2a4\ud305\uc758 \uc131\ub2a5\uc774 \uc88b\uc740 \uc774\uc720\ub294 \ube44\uc120\ud615\uc131<\/strong>\uacfc \uc0c1\ud638\uc791\uc6a9<\/strong>\uc744 \uc7a1\uc544\ub0bc \uc218 \uc788\uae30 \ub54c\ubb38\uc774\ub2e4. <\/p>\n
[1]:<\/sup> \ubaa8\uc9d1\ub2e8\uc5d0\uc11c \\((y – \\hat{y})^2\\) \uc744 \ucd5c\uc801\ud654\ud558\ub294 \ud568\uc218 \\(f(x)\\) \uc640 \uc774 \ud568\uc218\uc758 \ucd94\uc815\ud568\uc218 \\(\\hat{f(x)}\\) \ub97c \uad6c\ubd84\ud558\uae30 \uc704\ud574 \uc608\uce21 \ubaa8\ud615\uc744 \\(\\hat{f(x)}\\) \ub85c \ub098\ud0c0\ub0b4\uae30\ub3c4 \ud55c\ub2e4. <\/p>\n
EDA<\/h2>\n
\uc0ac\ub78c\uc740 \uc544\ubb34\ub9ac \ube44\uc0c1\ud55c \uba38\ub9ac\ub97c \uc9c0\ub154\ub2e4\uace0 \ud560\uc9c0\ub77c\ub3c4 3\ucc28\uc6d0 \uc774\uc0c1\uc758 \uadf8\ub798\ud504\ub97c \uc0c1\uc0c1\ud558\uae30 \ud798\ub4e4\ub2e4. \ub9cc\uc57d \uc124\uba85\ubcc0\uc218\uc640 \uacb0\uacfc \ubcc0\uc218\uc758 \uad00\uacc4\uac00 \uc124\uba85\ubcc0\uc218 2\uac1c \uc774\uc0c1\uc758 \uc0c1\ud638\uc791\uc6a9\uc744 \ud3ec\ud568\ud55c\ub2e4\uba74, EDA\ub85c\ub294 \uadf8 \uad00\uacc4\ub97c \uc7a1\uc544\ub0b4\uae30\uac00 \ud798\ub4e4\ub2e4.<\/p>\n
\ubcf5\uc7a1\ud55c \uc124\uba85\ubcc0\uc218\uc640 \uacb0\uacfc \ubcc0\uc218\uc758 \uad00\uacc4<\/h3>\n
\ub2e4\uc74c\uc758 \uc608\ub97c \ubcf4\uc790. dat<\/code>\uc5d0\ub294 \ubaa8\ub450 10\uac1c\uc758 \ubcc0\uc218\uac00 \uc788\ub2e4. <\/p>\n
\uc2e4\uc81c \ub370\uc774\ud130 \uc0dd\uc131 \ubaa8\ud615\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4. \uc774\ub54c \\(x_3\\) \uc740 \\(-1\\), \\(+1\\) \uac12\ub9cc \uac00\uc9c8 \uc218 \uc788\uace0, \ub098\uba38\uc9c0 \ubcc0\uc218\ub4e4\uc740 \ubaa8\ub450 \uc5f0\uc18d\ud615\uc774\ub2e4.<\/p>\n
\\[y = x_1^2 + \\frac{x_2}{|x_1|+0.1} + \\Big(I(x_2<0)+I(x_2<1)\\times x_3\\Big) \\times \\frac{1}{5}(x_4+x_5+x_6+x_7+x_8)+e\\]<\/p>\n
\\[e\\sim\\mathcal{N}(0,1)\\]<\/p>\n
iseed=100\nset.seed(iseed)\n\nN = 1000\n\nsdErr = 1\n\nx1 <- runif(N, -3, 3)\nx11 <- x1^2 \n\nx2 <- runif(N, -3, 3)\nx3 <- sample(c(-1, 1), N, replace=TRUE)\n\nncolMatX <- 5\nncolMatX2 <- 2\n\nlibrary(mvtnorm)\nsigma <- matrix(\n  rep(0.97, ncolMatX*ncolMatX),\n  ncolMatX, ncolMatX)\ndiag(sigma) = 1\n\nmatX <- rmvnorm(N, mean=rep(0,ncolMatX), sigma=sigma)\nx40 <- apply(matX, 1, mean)\/ncolMatX\ncolnames(matX) <- paste0('x', 4:(ncolMatX+3))\n\nmatX2 <- rmvnorm(N, mean=rep(0,ncolMatX2), sigma=diag(ncolMatX2))\ncolnames(matX2) <- paste0('x', (ncolMatX+4):(ncolMatX+ncolMatX2+3))\n\ny <- x11 + x2\/(abs(x1)+0.1) + (x2 < 0)*x40 + (x2<1)*x3 * x40 + rnorm(N, 0, sdErr)\n\ndat <- data.frame(y, x1, x2, x3, matX, matX2)\n\ngenData = function(N=1000, iseed=100) {\n  set.seed(iseed)\n  sdErr = 1\n\n  x1 <- runif(N, -3, 3)\n  x11 <- x1^2 \n\n  x2 <- runif(N, -3, 3)\n  x3 <- sample(c(-1, 1), N, replace=TRUE)\n\n  ncolMatX <- 5\n  ncolMatX2 <- 2\n\n  require(mvtnorm)\n  sigma <- matrix(\n    rep(0.97, ncolMatX*ncolMatX),\n    ncolMatX, ncolMatX)\n  diag(sigma) = 1\n\n  matX <- rmvnorm(N, mean=rep(0,ncolMatX), sigma=sigma)\n  x40 <- apply(matX, 1, mean)\/ncolMatX\n  colnames(matX) <- paste0('x', 4:(ncolMatX+3))\n\n  matX2 <- rmvnorm(N, mean=rep(0,ncolMatX2), sigma=diag(ncolMatX2))\n  colnames(matX2) <- paste0('x', (ncolMatX+4):(ncolMatX+ncolMatX2+3))\n\n  y <- x11 + x2\/(abs(x1)+0.1) + (x2 < 0)*x40 + (x2<1)*x3 * x40 + rnorm(N, 0, sdErr)\n\n  return(data.frame(y, x1, x2, x3, matX, matX2))\n}\n<\/code><\/pre>\n
dat<\/code>\uc5d0\ub294 \uacb0\uacfc \ubcc0\uc218 y<\/code>\uc640 \uc124\uba85\ubcc0\uc218 (\ud6c4\ubcf4) x1<\/code> ~ x10<\/code>\uc774 \uc800\uc7a5\ub418\uc5b4 \uc788\ub2e4. \uacb0\uacfc \ubcc0\uc218 y<\/code>\uc640 \uc124\uba85\ubcc0\uc218 x1<\/code> ~ x10<\/code>\uc758 \uad00\uacc4\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n
pairs(dat)\n<\/code><\/pre>\n
\"plot<\/p>\n
pairs(dat[,c("y", "x1", "x2", "x3")])\n<\/code><\/pre>\n
\"plot<\/p>\n
pairs(dat[,c("y", paste0("x", 4:10))])\n<\/code><\/pre>\n
\"plot<\/p>\n
\uc704\uc758 \uc0b0\uc810\ub3c4\ub97c \ubcf4\uba74 \uc54c\uaca0\uc9c0\ub9cc, x1<\/code>\uacfc x2<\/code>\ub97c \uc81c\uc678\ud558\uace0\uc11c\ub294 y<\/code>\uc640 \uc124\uba85\ubcc0\uc218\uc758 \uad00\uacc4\ub97c \ub69c\ub837\uc774 \uc54c\uc544\ub0b4\uae30\ub294 \ud798\ub4e4\ub2e4. \uadf8\ub9ac\uace0 x1<\/code>\uacfc y<\/code>\uc758 \uad00\uacc4\ub3c4 \uc0ac\uc2e4 \uc5b4\ub5a4 \uad00\uacc4\ub77c\uace0 \ub69c\ub837\uc774 \uc124\uba85\ud558\uae30 \ud798\ub4e4\ub2e4. \uc0b0\uc810\ub3c4\uc640 \ud68c\uadc0\uc120\uc744 \uadf8\ub824\ubcf4\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4. <\/p>\n
dat %>% ggplot(aes(x=x1, y=y)) + geom_point() + geom_smooth(method='loess', span=0.3)\n<\/code><\/pre>\n
\"plot<\/p>\n
\uc77c\ub2e8 \ud68c\uadc0\ubd84\uc11d\uc744 \ud55c \ubc88 \ub3cc\ub824\ubcf8\ub2e4. <\/p>\n
fit <- lm(y ~ ., data=dat)\nsummary(fit)\n<\/code><\/pre>\n
## \n## Call:\n## lm(formula = y ~ ., data = dat)\n## \n## Residuals:\n##     Min      1Q  Median      3Q     Max \n## -19.193  -2.197  -0.563   2.354  21.039 \n## \n## Coefficients:\n##             Estimate Std. Error t value Pr(>|t|)    \n## (Intercept)  3.03042    0.11826  25.626   <2e-16 ***\n## x1           0.02624    0.06872   0.382   0.7026    \n## x2           1.12308    0.06730  16.688   <2e-16 ***\n## x3          -0.03158    0.11846  -0.267   0.7898    \n## x4           0.33754    0.59900   0.564   0.5732    \n## x5          -0.60503    0.62142  -0.974   0.3305    \n## x6          -0.45517    0.61745  -0.737   0.4612    \n## x7          -0.37385    0.62504  -0.598   0.5499    \n## x8           1.19926    0.61419   1.953   0.0511 .  \n## x9          -0.11433    0.11667  -0.980   0.3273    \n## x10          0.17648    0.12464   1.416   0.1571    \n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n## \n## Residual standard error: 3.726 on 989 degrees of freedom\n## Multiple R-squared:  0.2252, Adjusted R-squared:  0.2174 \n## F-statistic: 28.75 on 10 and 989 DF,  p-value: < 2.2e-16\n<\/pre>\n
\uadf8\ub807\uad70!<\/a><\/p>\n
\uc774\ubc88\uc5d4 \ub79c\ub364\ud3ec\uc2a4\ud2b8\ub85c \ub3cc\ub824\uc11c \ubcc0\uc218 \uc911\uc694\ub3c4\ub97c \uc54c\uc544\ubcf8\ub2e4. <\/p>\n
library(randomForest)\n\nfitRF <- \n  randomForest(y ~ ., \n               data = dat, \n               importance = TRUE)\nfitRF0 <- fitRF # \ub098\uc911\uc5d0 \ube44\uad50\ub97c \uc704\ud574\n\nprint(fitRF)\n<\/code><\/pre>\n
## \n## Call:\n##  randomForest(formula = y ~ ., data = dat, importance = TRUE) \n##                Type of random forest: regression\n##                      Number of trees: 500\n## No. of variables tried at each split: 3\n## \n##           Mean of squared residuals: 5.280945\n##                     % Var explained: 70.19\n<\/pre>\n
varImpPlot(fitRF)\n<\/code><\/pre>\n
\"plot<\/p>\n
\uc608\uce21\uc5d0 \uac00\uc7a5 \uc911\uc694\ud55c \ubcc0\uc218 x1<\/code>, x2<\/code>, x4<\/code>\uac00 \uacb0\uacfc\ubcc0\uc218\uc5d0 \uc5b4\ub5a4 \ubc29\uc2dd\uc73c\ub85c \uc601\ud5a5\uc744 \ubbf8\uce58\ub294\uc9c0 \uc54c\uc544\ubcf4\ub294 \ubc29\ubc95\uc740 \uac01 \ubcc0\uc218\uc758 \ubcc0\ud654\uc5d0 \ub530\ub978 \ub79c\ub364\ud3ec\ub808\uc2a4\ud2b8\uc758 \uc608\uce21\uac12\uc774 \uc5b4\ub5bb\uac8c \ubcc0\ud654\ud558\ub294\uc9c0 \uadf8\ub824\ubcf4\ub294 \uac83\uc774\ub2e4. \uc544\ub798\uc5d0\uc11c\ub294 \uc124\uba85\ubcc0\uc218 x1<\/code>, x2<\/code>, x4<\/code>\ub97c \uc81c\uc678\ud55c \ub098\uba38\uc9c0 \ubcc0\uc218\ub294 \ubaa8\ub450 \ud3c9\uade0\uc73c\ub85c \uace0\uc815\ud588\uc744 \ub54c<\/strong>, x1<\/code>, x2<\/code>, x4<\/code>\uac00 \ub2ec\ub77c\uc9d0\uc5d0 \ub530\ub77c \ub79c\ub364\ud3ec\ub808\uc2a4\ud2b8\uc758 \uc608\uce21\uc774 \uc5b4\ub5bb\uac8c \ubcc0\ud654\ud558\ub294\uc9c0 \ubcf4\uc5ec\uc900\ub2e4. <\/p>\n
library(ggplot2)\nlibrary(dplyr)\nk=1\n#k=0.5\ndatx <- dat %>% select(-y, -x1, -x2, -x4)\ndatx %>% summarise_all(mean) -> datMean\ndatx %>% summarise_all(sd) -> datSD\n\nnewdat1 = datMean\nnewdat2 = expand.grid(x1=seq(min(dat$x1), max(dat$x1), length.out=20),\n            x2=seq(min(dat$x2), max(dat$x2), length.out=20),\n            x4=seq(min(dat$x4), max(dat$x4), length.out=20))\nnewdat = cbind(newdat1, newdat2)\n\nnewdat$y = predict(fitRF, newdat)\n\nnewdat %>% ggplot(aes(x=x1, y=y)) + geom_point(color='gray50', shape='x') + \n  geom_smooth(method='loess', span=0.3) +\n  facet_grid(cut(x2,3) ~ cut(x4, 3))\n<\/code><\/pre>\n
\"plot<\/p>\n
\ud558\uc9c0\ub9cc \uc608\uce21\uc774\ub780 \ud56d\uc0c1 \uc815\ud655\ud558\uc9c0 \uc54a\ub2e4. \ub79c\ub364\ud3ec\ub808\uc2a4\ud2b8\uc758 \uc54c\uace0\ub9ac\uc998\uc740 \ud2b9\uc815\ud55c \uad00\uacc4\ub97c \uc7a1\uc544\ub0b4\ub294\ub370 \uc88b\uc9c0\ub9cc, \ub2e4\ub978 \uad00\uacc4\ub97c \uc7a1\uc544\ub0b4\ub294\ub370\uc5d0\ub294 \uc88b\uc9c0 \uc54a\ub2e4. \ub79c\ub364\ud3ec\uc2a4\ud2b8\uc758 \uc608\uce21\uc774 \ud56d\uc0c1 \uc5b4\ub5a4 \ud615\ud0dc\ub97c \ub744\uac8c \ub418\ub294\uc9c0 \uc0dd\uac01\ud574\ubcf4\ub77c. x1<\/code>, x2<\/code>, x4<\/code>\ub97c \uc81c\uc678\ud55c \uc124\uba85\ubcc0\uc218\ub97c \ud3c9\uade0\uc5d0\uc11c k=1<\/code> \ud45c\uc900\ud3b8\ucc28 \uc774\ub0b4 \uc790\ub8cc\uc5d0 \ub300\ud574 x1<\/code>, x2<\/code>, x4<\/code>\uc5d0 \ub530\ub978 \uc2e4\uc81c y<\/code>\uc758 \uc591\uc0c1\uc744 \ubcf4\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4. k<\/code>\ub97c \uc880 \ub354 \uc791\uac8c \ud639\uc740 \ud06c\uac8c \ud574\uc11c\ub3c4 \uadf8\ub824\ubcf4\uc790.<\/p>\n
k=1\ndat01r = datMean-k*datSD\ndat02r = datMean+k*datSD\ndat01 = dat01r[rep(1,nrow(dat)),]\ndat02 = dat02r[rep(1,nrow(dat)),]\nir <- apply(as.matrix(datx >=dat01 & datx <=dat02),1,all)\nsum(ir)\n<\/code><\/pre>\n
## [1] 135\n<\/pre>\n
datPlot <- dat %>% filter(ir)\n\ndatPlot %>% ggplot(aes(x=x1, y=y)) + \n  geom_point() +  \n  #geom_smooth(method='loess', span=0.3) + \n  facet_grid(cut(x2,3) ~ cut(x4,3)) \n<\/code><\/pre>\n
\"plot<\/p>\n
\uc124\uba85\ubcc0\uc218\uc758 \uc870\uac74\uc744 \uc880 \ub354 \ud0c0\uc774\ud2b8\ud558\uac8c \ub9cc\ub4e0\ub2e4\uba74 \uc880 \ub354 \ud655\uc2e4\ud55c \uad00\uacc4\ub97c \ud30c\uc545\ud560 \uc218 \uc788\uc744\uc9c0 \ubaa8\ub978\ub2e4. \ud558\uc9c0\ub9cc \ub370\uc774\ud130\uc758 \uac2f\uc218\uac00 \uc791\uc744 \uc218\ub85d loess \ud68c\uadc0\uc120\uc740 \ubd88\ud655\uc2e4\ud558\ub2e4. <\/p>\n
k=c(1, rep(0.8, ncol(datMean)-1)) # x3 is either -1, or 1 so...\ndat01r = datMean-k*datSD\ndat02r = datMean+k*datSD\ndat01 = dat01r[rep(1,nrow(dat)),]\ndat02 = dat02r[rep(1,nrow(dat)),]\nir <- apply(as.matrix(datx >=dat01 & datx <=dat02),1,all)\nsum(ir)\n<\/code><\/pre>\n
## [1] 72\n<\/pre>\n
datPlot <- dat %>% filter(ir)\n\ndatPlot %>% ggplot(aes(x=x1, y=y)) + \n  geom_point() +  \n  #geom_smooth(method='loess', span=0.3) + \n  facet_grid(cut(x2,3) ~ cut(x4,3))\n<\/code><\/pre>\n
\"plot<\/p>\n
#datPlot %>% ggplot(aes(x=x1, y=y)) + \n#  geom_point() +  \n#  geom_smooth(method='loess', span=0.3, se=FALSE) + \n#  facet_grid(cut(x2,3) ~ cut(x4,3)) \n<\/code><\/pre>\n
\uc774\uc81c \ub79c\ub364\ud3ec\ub808\uc2a4\ud2b8\uc758 \uc608\uce21\uacfc \uc2e4\uc81c \ub370\uc774\ud130\ub97c \uac19\uc774 \uadf8\ub824\ubcf4\uc790. <\/p>\n
brx1 = quantile(datPlot$x1, prob=seq(0,1,length.out=20))\nbrx2 = quantile(datPlot$x2, prob=seq(0,1,length.out=20))\nbrx4 = quantile(datPlot$x4, prob=seq(0,1,length.out=20))\n\nnewdat1 = datMean\nnewdat2 = expand.grid(x1=brx1,\n                      x2=brx2,\n                      x4=brx4)\nnewdat = cbind(newdat1, newdat2)\n\nnewdat$y = predict(fitRF, newdat)\n\ndatPlot %>% mutate(x1Cut = cut(x1, breaks=brx1),\n                   x2Cut = cut(x2, breaks=brx2),\n                   x4Cut = cut(x4, breaks=brx4)) -> datPlot\ndatPlot$err <- datPlot$y - predict(fitRF, datPlot)\ndatPlot$se <- (datPlot$err)^2\n\nnewdat %>% mutate(x1Cut = cut(x1, breaks=brx1),\n                  x2Cut = cut(x2, breaks=brx2),\n                  x4Cut = cut(x4, breaks=brx4)) -> newdatCut\n\nggplot(datPlot) + \n  geom_point(data=newdatCut, mapping=aes(x=x1, y=y), shape='x', col='gray50') + \n  geom_smooth(data=newdatCut, mapping=aes(x=x1, y=y), method='loess', span=0.3, col='gray80') + \n  geom_point(data=datPlot, mapping=aes(x=x1,y=y)) + \n  facet_grid(cut(x2,breaks=3) ~ cut(x4,breaks=3))\n<\/code><\/pre>\n
\"plot<\/p>\n
\uc774\ub97c \ud1b5\ud574 \ubaa8\ud615\uc774 \uc798 \uc7a1\uc544\ub0b4\uc9c0 \ubabb\ud558\ub294 \ubd80\ubd84\uc744 \ud655\uc778\ud560 \uc218 \uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4 x2<\/code> \\(\\in\\) (-2.91, -0.935]<\/code>\uc5d0\uc11c\ub294 x1<\/code>\uc774 0\uacfc \uac00\uae4c\uc6b4 \ubd80\ubd84\uc5d0\uc11c \uc2e4\uc81c y<\/code>\uac00 \uc608\uce21\uac12\ubcf4\ub2e4 \ub9e4\uc6b0 \ub0ae\uc740 \uacbd\uc6b0\ub4e4\uc774 \uc788\uace0, x2<\/code> \\(\\in\\) (1.03,3]<\/code>\uc5d0\uc11c\ub294 \uc2e4\uc81c y<\/code>\uac00 \uc608\uce21\uac12\ubcf4\ub2e4 \ucee4\uc9c0\ub294 \ubd80\ubd84\uc774 \uc788\ub2e4\ub294 \uc0ac\uc2e4\uc744 \ud655\uc778\ud560 \uc218 \uc788\ub2e4.<\/p>\n
\uc544\ub798\uc640 \uac19\uc774 \ub2e4\ub978 \ubc29\uc2dd\uc73c\ub85c \uadf8\ub824\ubcfc \uc218\ub3c4 \uc788\ub2e4. <\/p>\n
ggplot(datPlot) + \n  geom_point(data=newdatCut, mapping=aes(x=x2, y=y), shape='x', col='gray50') + \n  geom_smooth(data=newdatCut, mapping=aes(x=x2, y=y), method='loess', span=0.3, col='gray80') + \n  geom_point(data=datPlot, mapping=aes(x=x2,y=y)) +\n  facet_grid(cut(x4,breaks=3) ~ cut(x1,breaks=3))\n<\/code><\/pre>\n
\"plot<\/p>\n
\ud558\uc9c0\ub9cc \ubaa8\ud615\uc774 \uc2e4\uc81c \ub370\uc774\ud130\ub97c \uc815\ud655\ud788 \uc608\uce21\ud558\uc9c0 \ubabb\ud558\ub294 \ubd80\ubd84\uc774 \ub2e8\uc21c\ud788 \uc6b0\uc5f0\uc778\uc9c0 \uc544\ub2c8\uba74 \uc2e4\uc81c \uad00\uacc4\ub97c \ub098\ud0c0\ub0b4\ub294 \ubd80\ubd84\uc778\uc9c0\ub294 \ud655\uc2e0\ud560 \uc218 \uc5c6\ub2e4. \uc65c\ub0d0\ud558\uba74 \ub370\uc774\ud130\uc758 \uc218\uac00 \uc791\uae30 \ub54c\ubb38\uc774\ub2e4. <\/p>\n
\uc774 \ubd80\ubd84\uc744 \ud655\uc2e4\ud788 \uc54c\uae30 \uc704\ud574\uc11c\ub294 \ub370\uc774\ud130\uac00 \ub9ce\uc544\uc57c \ud558\ub294\ub370, \uc124\uba85\ubcc0\uc218\uc758 \uac2f\uc218\uac00 \uc99d\uac00\ud568\uc5d0 \ub530\ub77c \ud655\uc2e4\ud55c \uad00\uacc4\ub97c \uc54c\uae30 \uc704\ud574 \ud544\uc694\ud55c \ub370\uc774\ud130\uc758 \uc218\ub294 \uae30\ud558\uae09\uc218\uc801\uc73c\ub85c \uc99d\uac00\ud558\uae30 \ub54c\ubb38\uc5d0 \uc6b0\ub9ac\uac00 \ud754\ud788 \ub9d0\ud558\ub294 \uace0\ucc28\uc6d0\uc758 \uc800\uc8fc \ud604\uc0c1\uc744 \uacbd\ud5d8\ud558\uac8c \ub41c\ub2e4.<\/p>\n
\uc704\uc758 \uadf8\ub798\ud504\uc5d0\uc11c \uace0\ucc28\uc6d0\uc758 \uc800\uc8fc\ub780 \uc124\uba85\ubcc0\uc218\uc758 \uac2f\uc218\uac00 \uc99d\uac00\ud560 \uc218\ub85d \uac01 \ubcc0\uc218\uc5d0 \uc77c\uc815\ud55c \uc870\uac74(\ud3c9\uade0 \uadfc\ucc98\ub77c\ub358\uc9c0)\uc744 \uc8fc\uc5c8\uc744 \ub54c, \uc704\uc758 \uac01 \uaca9\uc790\uc5d0 \ub4e4\uc5b4\uac00\ub294 \uc810\uc758 \uac2f\uc218\ub294 \uc810\uc810 \ub354 \uc801\uc5b4\uc9c0\uace0, \uadf8\uc5d0 \ub530\ub77c \\(f(x)\\) \uc758 \ucd94\uc815\ub3c4 \uc2e4\uc81c \ub370\uc774\ud130\uac00 \uc544\ub2c8\ub77c \uc5ec\ub7ec \uac00\uc9c0 \uac00\uc815\uc5d0 \uae30\ubc18\ud558\uac8c \ub428\uc744 \uc758\ubbf8\ud55c\ub2e4. <\/p>\n
\ub9cc\uc57d \uc704\uc758 \ub3d9\uc77c\ud55c \uc2e4\uc81c \ubaa8\ud615\uc5d0\uc11c \ub370\uc774\ud130\uc758 \uc218\uac00 10\ubc30 \uc99d\uac00\ud55c\ub2e4\uba74 \uc5b4\ub5bb\uac8c \ub420\uae4c?<\/p>\n
dat <- genData(N=10000)\n<\/code><\/pre>\n
library(randomForest)\n\nfitRF <- \n  randomForest(y ~ ., \n               data = dat, \n               importance = TRUE)\nvarImpPlot(fitRF)\n<\/code><\/pre>\n
\"plot<\/p>\n
library(ggplot2)\nlibrary(dplyr)\nk=1\n#k=0.5\ndatx <- dat %>% select(-y, -x1, -x2, -x4)\ndatx %>% summarise_all(mean) -> datMean\ndatx %>% summarise_all(sd) -> datSD\n\nnewdat1 = datMean\nnewdat2 = expand.grid(x1=seq(min(dat$x1), max(dat$x1), length.out=20),\n            x2=seq(min(dat$x2), max(dat$x2), length.out=20),\n            x4=seq(min(dat$x4), max(dat$x4), length.out=20))\nnewdat = cbind(newdat1, newdat2)\n\nnewdat$y = predict(fitRF, newdat)\n\nnewdat %>% ggplot(aes(x=x1, y=y)) + geom_point(color='gray50', shape='x') + \n  geom_smooth(method='loess', span=0.3) +\n  facet_grid(cut(x2,3) ~ cut(x4, 3))\n<\/code><\/pre>\n
\"plot<\/p>\n
k=1\ndat01r = datMean-k*datSD\ndat02r = datMean+k*datSD\ndat01 = dat01r[rep(1,nrow(dat)),]\ndat02 = dat02r[rep(1,nrow(dat)),]\nir <- apply(as.matrix(datx >=dat01 & datx <=dat02),1,all)\nsum(ir)\n<\/code><\/pre>\n
## [1] 1401\n<\/pre>\n
datPlot <- dat %>% filter(ir)\n\ndatPlot %>% ggplot(aes(x=x1, y=y)) + \n  geom_point() +  \n  geom_smooth(method='loess', span=0.3) + \n  facet_grid(cut(x2,3) ~ cut(x4,3)) \n<\/code><\/pre>\n
\"plot<\/p>\n
brx1 = quantile(datPlot$x1, prob=seq(0,1,length.out=20))\nbrx2 = quantile(datPlot$x2, prob=seq(0,1,length.out=20))\nbrx4 = quantile(datPlot$x4, prob=seq(0,1,length.out=20))\n\nnewdat1 = datMean\nnewdat2 = expand.grid(x1=brx1,\n                      x2=brx2,\n                      x4=brx4)\nnewdat = cbind(newdat1, newdat2)\n\nnewdat$y = predict(fitRF, newdat)\n\ndatPlot %>% mutate(x1Cut = cut(x1, breaks=brx1),\n                   x2Cut = cut(x2, breaks=brx2),\n                   x4Cut = cut(x4, breaks=brx4)) -> datPlot\ndatPlot$err <- datPlot$y - predict(fitRF, datPlot)\ndatPlot$se <- (datPlot$err)^2\n\nnewdat %>% mutate(x1Cut = cut(x1, breaks=brx1),\n                  x2Cut = cut(x2, breaks=brx2),\n                  x4Cut = cut(x4, breaks=brx4)) -> newdatCut\n\nggplot(datPlot) + \n  geom_point(data=datPlot, mapping=aes(x=x1,y=y)) + \n  geom_point(data=newdatCut, mapping=aes(x=x1, y=y), shape='x', col='gray50') + \n  geom_smooth(data=newdatCut, mapping=aes(x=x1, y=y), method='loess', span=0.3, col='gray80') + \n  facet_grid(cut(x4,breaks=4) ~ cut(x2,breaks=4))\n<\/code><\/pre>\n
\"plot<\/p>\n
\uc704\uc758 \uadf8\ub798\ud504\ub294 \ub370\uc774\ud130\uac00 \ub9ce\uc544\uc9d0\uc5d0 \ub530\ub77c x1<\/code>\uc640 y<\/code>\uc758 \uad00\uacc4\uac00 \ud655\uc2e4\ud574\uc9c0\uace0, \ub79c\ub364\ud3ec\ub808\uc2a4\ud2b8\ub294 \uc774\ub97c \uc5b4\ub290 \uc815\ub3c4 \uc7a1\uc544\ub0b4\uace0 \uc788\uc74c\uc744 \uc54c \uc218 \uc788\ub2e4. <\/p>\n
\uc0c8\ub85c\uc6b4 \ubcc0\uc218\uc758 \uc0dd\uc131(a.k.a feature engineering)<\/h2>\n
\ub9cc\uc57d x1<\/code>\uacfc y<\/code>\uc758 \uad00\uacc4\uac00 x2<\/code>\uac00 \uc591\uc218\uc77c \ub54c\ub294 y ~ 1\/x1<\/code>, \uc74c\uc218\uc77c\ub54c\ub294 y ~ -1\/x1<\/code>\uc758 \uad00\uacc4\uac00 \uc788\ub2e4\ub294 \uac83\uc744 \uc5b4\ub290 \uc815\ub3c4 \uc720\ucd94\ud560 \uc218 \uc788\uac70\ub098, \uc601\uc5ed \uc9c0\uc2dd(domain knowledge)\uc73c\ub85c \uc54c \uc218 \uc788\ub2e4\uba74, 1\/x1<\/code> \ub610\ub294 -1\/x1<\/code>\uc744 \uc0c8\ub85c\uc6b4 \ubcc0\uc218\ub85c \uc0ac\uc6a9\ud560 \uc218 \uc788\ub2e4. <\/p>\n
\uc774\uc81c \ub2e4\uc2dc \uc6d0\ub798 \uc790\ub8cc\ub85c \ub418\ub3cc\uc544\uac00 \ubcf4\uc790. \ub370\uc774\ud130\uac00 1000\uac1c \ubfd0\uc77c \ub54c, \ub79c\ub364\ud3ec\ub808\uc2a4\ud2b8 \uacb0\uacfc\ub294 y<\/code>\uc640 x1<\/code>\uc758 \uc870\uac74\ubd80 \uad00\uacc4\ub97c \uc798 \uc7a1\uc544\ub0b4\uc9c0 \ubabb\ud588\uc9c0\ub9cc, y ~ 1\/x<\/code>\uc758 \uad00\uacc4\uac00 \uc758\uc2ec\ub41c\ub2e4\uba74 \uc774 \uad00\uacc4\ub97c \uc880 \ub354 \uc27d\uac8c \ud3ec\ucc29\ud560 \uc218 \uc788\ub3c4\ub85d \uc0c8\ub85c\uc6b4 \ubcc0\uc218\ub97c \ub9cc\ub4e4\uc5b4 \uc904 \uc218 \uc788\ub2e4. <\/p>\n
dat <- genData(N=1000)\n<\/code><\/pre>\n
#dat$ov1x1 = 1\/dat$x1\n#dat$ov2x1 = -1\/dat$x1\n\nov1x1 = function(x) { return(1\/x) }\ndat$ov1x1 = ov1x1(dat$x1)\n\nfitRF <- \n  randomForest(y ~ ., \n               data = dat, \n               importance = TRUE,\n               mtry=3) # fitRF0\uacfc \ub3d9\uc77c\ud55c \uc870\uac74\uc73c\ub85c..\n<\/code><\/pre>\n
library(ggplot2)\nlibrary(dplyr)\nk=1\n#k=0.5\n\ndatx <- dat %>% select(-y, -x1, -x2, -x4, -ov1x1)\ndatx %>% summarise_all(mean) -> datMean\ndatx %>% summarise_all(sd) -> datSD\n\nnewdat1 = datMean\nnewdat2 = expand.grid(x1=seq(min(dat$x1), max(dat$x1), length.out=20),\n            x2=seq(min(dat$x2), max(dat$x2), length.out=20),\n            x4=seq(min(dat$x4), max(dat$x4), length.out=20))\nnewdat2$ov1x1 = ov1x1(newdat2$x1)\nnewdat = cbind(newdat1, newdat2)\n\nnewdat$y = predict(fitRF, newdat)\n\nnewdat %>% ggplot(aes(x=x1, y=y)) + geom_point(color='gray50', shape='x') + geom_smooth(method='loess', span=0.3) +\n  facet_grid(cut(x2,3) ~ cut(x4, 3))\n<\/code><\/pre>\n
\"plot<\/p>\n
Voila! 1000\uac1c\uc758 \ub370\uc774\ud130\ub9cc\uc73c\ub85c\ub3c4 \uc5bc\ucd94 \uc815\ud655\ud55c \uc608\uce21\uc774 \uac00\ub2a5\ud558\ub2e4! \ubaa8\ud615\uc740 \uc9c4\ubcf4\ud588\ub2e4!<\/p>\n
print(fitRF)\n<\/code><\/pre>\n
## \n## Call:\n##  randomForest(formula = y ~ ., data = dat, importance = TRUE,      mtry = 3) \n##                Type of random forest: regression\n##                      Number of trees: 500\n## No. of variables tried at each split: 3\n## \n##           Mean of squared residuals: 3.495394\n##                     % Var explained: 80.27\n<\/pre>\n
1\/x1<\/code>\ub97c \uc81c\uc678\ud55c \ucd5c\ucd08 \ubaa8\ud615\uc740 \ub2e4\uc74c\uacfc \uac19\uc558\ub2e4.<\/p>\n
print(fitRF0)\n<\/code><\/pre>\n
## \n## Call:\n##  randomForest(formula = y ~ ., data = dat, importance = TRUE) \n##                Type of random forest: regression\n##                      Number of trees: 500\n## No. of variables tried at each split: 3\n## \n##           Mean of squared residuals: 5.280945\n##                     % Var explained: 70.19\n<\/pre>\n
\ubb3c\ub860 \uacfc\uc801\ud569\uc758 \uac00\ub2a5\uc131\uc774 \uc788\uc73c\ubbc0\ub85c \uc0c8\ub85c\uc6b4 \ub370\uc774\ud130\uc5d0 \uc801\uc6a9\ud574\ubcf4\uc790. <\/p>\n
newdat <- genData(N=1000, iseed=104)\nnewdat$ov1x1 <- 1\/newdat$x1\n<\/code><\/pre>\n
mean((predict(fitRF0, newdata=newdat) - newdat$y)^2)\n<\/code><\/pre>\n
## [1] 5.832372\n<\/pre>\n
mean((predict(fitRF, newdata=newdat) - newdat$y)^2)\n<\/code><\/pre>\n
## [1] 3.759634\n<\/pre>\n
mean(abs(predict(fitRF0, newdata=newdat) - newdat$y))\n<\/code><\/pre>\n
## [1] 1.444332\n<\/pre>\n
mean(abs(predict(fitRF, newdata=newdat) - newdat$y))\n<\/code><\/pre>\n
## [1] 1.143498\n<\/pre>\n
\ub9c8\ubb34\ub9ac<\/h2>\n
\uc5b4\uca0b\uac70\ub098 R\uc758 randomForest<\/code>\ub294 \ub108\ubb34 \ub290\ub9ac\ub2e4. \ub370\uc774\ud130\uc758 \uc218\uac00 \ub9ce\uc744 \ub54c\ub294. \ub2e4\uc74c\uc5d0\ub294 \uc880\ub354 \ube60\ub978 \uad6c\ud604\uc744 \uc54c\uc544\ubd10\uc57c\uaca0\ub2e4. ranger<\/code><\/a> \uac19\uc740…<\/p>\n
\uc7a0\uae50!<\/h3>\n
\uc704\uc758 \uc608\ub97c \ubcf4\uba74 1\/x1<\/code>\uc774\ub780 \uc0c8\ub85c\uc6b4 \ubcc0\uc218\ub97c \ub9cc\ub4e4\uc5b4 \uc8fc\uc5c8\uae30 \ub54c\ubb38\uc774\ub77c\uace0 \uc0dd\uac01\ud558\uae30 \uc27d\uc9c0\ub9cc, \uc0ac\uc2e4 \ubcc0\uc218 \ud558\ub098\uc9dc\ub9ac \uc0c8\ub85c\uc6b4 \ubcc0\uc218\ub294 \ub79c\ub364\ud3ec\ub808\uc2a4\ud2b8\uc758 \uc54c\uace0\ub9ac\uc998\uc744 \uc0b4\ud3b4\ubd24\uc744 \ub54c \ud06c\uac8c \uc758\ubbf8\uac00 \uc5c6\ub2e4. \uc2e4\uc81c\ub85c \uc704\uc758 \uc608\uc5d0\uc11c \uc0c8\ub85c\uc6b4 \ubcc0\uc218 ov1x1<\/code>\uc5d0 1\/x1<\/code>\uc774 \uc544\ub2c8\ub77c x1<\/code>\uc744 \ub300\uc785\ud574\ub3c4 \uacb0\uacfc\ub294 \ube44\uc2b7\ud558\ub2e4!<\/p>\n
\ud639\uc740 mtry=<\/code>\uc744 \uc0ac\uc6a9\ud560 \uc218\ub3c4 \uc788\ub2e4.<\/p>\n
dat <- genData(N=1000)\nfitRF2 <- \n  randomForest(y ~ ., \n               data = dat, \n               importance = TRUE,\n               mtry=7)\nprint(fitRF2)\n<\/code><\/pre>\n
## \n## Call:\n##  randomForest(formula = y ~ ., data = dat, importance = TRUE,      mtry = 7) \n##                Type of random forest: regression\n##                      Number of trees: 500\n## No. of variables tried at each split: 7\n## \n##           Mean of squared residuals: 2.691028\n##                     % Var explained: 84.81\n<\/pre>\n
varImpPlot(fitRF2)\n<\/code><\/pre>\n
\"plot<\/p>\n
newdat <- genData(N=1000, iseed=104)\nmean((predict(fitRF2, newdata=newdat) - newdat$y)^2)\n<\/code><\/pre>\n
## [1] 3.017949\n<\/pre>\n
mean(abs(predict(fitRF2, newdata=newdat) - newdat$y))\n<\/code><\/pre>\n
## [1] 1.079153\n<\/pre>\n
\uc9c4\uc9dc \ud53c\ucc98 \uc5d4\uc9c0\ub2c8\uc5b4\ub9c1\uc740 \uc5ec\ub7ec \ubcc0\uc218\ub97c \uac00\uc9c0\uace0 \uc0c8\ub85c\uc6b4 \ubcc0\uc218\ub97c \ub9cc\ub4e4 \ub54c<\/strong>\ubd80\ud130 \uc2dc\uc791\ud55c\ub2e4!<\/p>\n
\ub367\ubd99\uc5ec.<\/h3>\n
\ub300\ubd80\ubd84\uc758 DS, ML, AI\ub294 \uc5b4\uca0b\ub4e0 \ub370\uc774\ud130\ub97c \ub123\uc73c\uba74 \uacb0\uacfc\uac00 \ub098\uc628\ub2e4. \ubb38\uc81c\ub294 \uac70\uae30\uc5d0\uc11c \uc5b4\ub5bb\uac8c \ubaa8\ud615\uc744 \ud5a5\uc0c1\uc2dc\ud0a4\ub0d0\uc778\ub370, \uc774\ub97c \uc54c\uae30 \uc704\ud574\uc11c\ub294(\ubaa8\ud615\uc758 \ub2e8\uc810, \uc7a5\uc810\uc744 \ubaa8\ub450 \uace0\ub824\ud558\uae30 \uc704\ud574\uc11c\ub294) \ubaa8\ud615\uc774 \uc5b4\ub5a4 \uc2dd\uc73c\ub85c \uc791\ub3d9\ud558\ub294\uc9c0\uc5d0 \ub300\ud55c \uc9c0\uc2dd\uacfc \uc774\ub97c \ud65c\uc6a9\ud560 \uc218 \uc788\ub294 \ub2a5\ub825\uc774 \ud544\uc694\ud558\ub2e4.<\/p>\n","protected":false},"excerpt":{"rendered":"
\uc608\uce21 \ubaa8\ud615\uc758 \uc758\ubbf8 library(dplyr) library(ggplot2) library(randomForest) \uc608\uce21 \ubaa8\ud615\uc740 \uae30\ubcf8\uc801\uc73c\ub85c \\(f(\\vec{x})\\) \uc774\ub2e4.[1] \uc8fc\uc5b4\uc9c4 \uc124\uba85 \ubcc0\uc218 \\(\\vec{x}\\) \uc5d0 \ub300\ud574 \uacb0\uacfc \ubcc0\uc218 \\(y\\) \ub97c \uc608\uce21\ud55c\ub2e4. \uc608\uce21 \ubaa8\ud615\uc744 \ud3c9\uac00\ud558\ub294 \ubc29\ubc95\uc740 \\(\\hat{y}=f(\\vec{x})\\) \ub77c\uace0 \ud560 \ub54c, \\(|y – \\hat{y}|\\) \uc744 \uc4f8 \uc218\ub3c4 \uc788\uace0, \\((y – \\hat{y})^2\\) \ub97c \uc4f0\uae30\ub3c4 \ud558\uace0, hinge loss\ub77c\ub294 \uac83\uc744 \uc4f0\uae30\ub3c4 \ud558\uc9c0\ub9cc, \uc5b4\uca0b\ub4e0 \\(f(\\vec{x})\\) \ub97c \ub9cc\ub4e4\uc5b4\ub0b4\ub294 \uac83\uc774\ub2e4. \uc774\ub54c \uc5b4\ub5a4 […]<\/p>\n","protected":false},"author":1,"featured_media":1946,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[371,146,319],"tags":[168,368,372,367,366,338],"jetpack_featured_media_url":"http:\/\/ds.sumeun.org\/wp-content\/uploads\/2019\/08\/variableSelection02_tidy.png","_links":{"self":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/1942"}],"collection":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1942"}],"version-history":[{"count":8,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/1942\/revisions"}],"predecessor-version":[{"id":1951,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/1942\/revisions\/1951"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/media\/1946"}],"wp:attachment":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1942"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1942"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1942"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}