Capitulo 8: Arboles
Arboles de clasificación
library(tree)
## Warning: package 'tree' was built under R version 3.1.2
library(ISLR)
attach(Carseats)
High=ifelse(Sales<=8,"No","Yes")
Carseats=data.frame(Carseats,High)
tree.carseats=tree(High~.-Sales,Carseats)
summary(tree.carseats)
##
## Classification tree:
## tree(formula = High ~ . - Sales, data = Carseats)
## Variables actually used in tree construction:
## [1] "ShelveLoc" "Price" "Income" "CompPrice" "Population"
## [6] "Advertising" "Age" "US"
## Number of terminal nodes: 27
## Residual mean deviance: 0.458 = 171 / 373
## Misclassification error rate: 0.09 = 36 / 400
plot(tree.carseats)
text(tree.carseats,pretty=0)
tree.carseats
## node), split, n, deviance, yval, (yprob)
## * denotes terminal node
##
## 1) root 400 500 No ( 0.59 0.41 )
## 2) ShelveLoc: Bad,Medium 315 400 No ( 0.69 0.31 )
## 4) Price < 92.5 46 60 Yes ( 0.30 0.70 )
## 8) Income < 57 10 10 No ( 0.70 0.30 )
## 16) CompPrice < 110.5 5 0 No ( 1.00 0.00 ) *
## 17) CompPrice > 110.5 5 7 Yes ( 0.40 0.60 ) *
## 9) Income > 57 36 40 Yes ( 0.19 0.81 )
## 18) Population < 207.5 16 20 Yes ( 0.38 0.62 ) *
## 19) Population > 207.5 20 8 Yes ( 0.05 0.95 ) *
## 5) Price > 92.5 269 300 No ( 0.75 0.25 )
## 10) Advertising < 13.5 224 200 No ( 0.82 0.18 )
## 20) CompPrice < 124.5 96 40 No ( 0.94 0.06 )
## 40) Price < 106.5 38 30 No ( 0.84 0.16 )
## 80) Population < 177 12 20 No ( 0.58 0.42 )
## 160) Income < 60.5 6 0 No ( 1.00 0.00 ) *
## 161) Income > 60.5 6 5 Yes ( 0.17 0.83 ) *
## 81) Population > 177 26 8 No ( 0.96 0.04 ) *
## 41) Price > 106.5 58 0 No ( 1.00 0.00 ) *
## 21) CompPrice > 124.5 128 200 No ( 0.73 0.27 )
## 42) Price < 122.5 51 70 Yes ( 0.49 0.51 )
## 84) ShelveLoc: Bad 11 7 No ( 0.91 0.09 ) *
## 85) ShelveLoc: Medium 40 50 Yes ( 0.38 0.62 )
## 170) Price < 109.5 16 7 Yes ( 0.06 0.94 ) *
## 171) Price > 109.5 24 30 No ( 0.58 0.42 )
## 342) Age < 49.5 13 20 Yes ( 0.31 0.69 ) *
## 343) Age > 49.5 11 7 No ( 0.91 0.09 ) *
## 43) Price > 122.5 77 60 No ( 0.88 0.12 )
## 86) CompPrice < 147.5 58 20 No ( 0.97 0.03 ) *
## 87) CompPrice > 147.5 19 30 No ( 0.63 0.37 )
## 174) Price < 147 12 20 Yes ( 0.42 0.58 )
## 348) CompPrice < 152.5 7 6 Yes ( 0.14 0.86 ) *
## 349) CompPrice > 152.5 5 5 No ( 0.80 0.20 ) *
## 175) Price > 147 7 0 No ( 1.00 0.00 ) *
## 11) Advertising > 13.5 45 60 Yes ( 0.44 0.56 )
## 22) Age < 54.5 25 30 Yes ( 0.20 0.80 )
## 44) CompPrice < 130.5 14 20 Yes ( 0.36 0.64 )
## 88) Income < 100 9 10 No ( 0.56 0.44 ) *
## 89) Income > 100 5 0 Yes ( 0.00 1.00 ) *
## 45) CompPrice > 130.5 11 0 Yes ( 0.00 1.00 ) *
## 23) Age > 54.5 20 20 No ( 0.75 0.25 )
## 46) CompPrice < 122.5 10 0 No ( 1.00 0.00 ) *
## 47) CompPrice > 122.5 10 10 No ( 0.50 0.50 )
## 94) Price < 125 5 0 Yes ( 0.00 1.00 ) *
## 95) Price > 125 5 0 No ( 1.00 0.00 ) *
## 3) ShelveLoc: Good 85 90 Yes ( 0.22 0.78 )
## 6) Price < 135 68 50 Yes ( 0.12 0.88 )
## 12) US: No 17 20 Yes ( 0.35 0.65 )
## 24) Price < 109 8 0 Yes ( 0.00 1.00 ) *
## 25) Price > 109 9 10 No ( 0.67 0.33 ) *
## 13) US: Yes 51 20 Yes ( 0.04 0.96 ) *
## 7) Price > 135 17 20 No ( 0.65 0.35 )
## 14) Income < 46 6 0 No ( 1.00 0.00 ) *
## 15) Income > 46 11 20 Yes ( 0.45 0.55 ) *
set.seed(2)
train=sample(1:nrow(Carseats), 200)
Carseats.test=Carseats[-train,]
High.test=High[-train]
tree.carseats=tree(High~.-Sales,Carseats,subset=train)
tree.pred=predict(tree.carseats,Carseats.test,type="class")
table(tree.pred,High.test)
## High.test
## tree.pred No Yes
## No 86 27
## Yes 30 57
(86+57)/200
## [1] 0.715
set.seed(3)
cv.carseats=cv.tree(tree.carseats,FUN=prune.misclass)
names(cv.carseats)
## [1] "size" "dev" "k" "method"
cv.carseats
## $size
## [1] 19 17 14 13 9 7 3 2 1
##
## $dev
## [1] 55 55 53 52 50 56 69 65 80
##
## $k
## [1] -Inf 0.0000 0.6667 1.0000 1.7500 2.0000 4.2500 5.0000 23.0000
##
## $method
## [1] "misclass"
##
## attr(,"class")
## [1] "prune" "tree.sequence"
par(mfrow=c(1,2))
plot(cv.carseats$size,cv.carseats$dev,type="b")
plot(cv.carseats$k,cv.carseats$dev,type="b")
prune.carseats=prune.misclass(tree.carseats,best=9)
plot(prune.carseats)
text(prune.carseats,pretty=0)
tree.pred=predict(prune.carseats,Carseats.test,type="class")
table(tree.pred,High.test)
## High.test
## tree.pred No Yes
## No 94 24
## Yes 22 60
(94+60)/200
## [1] 0.77
prune.carseats=prune.misclass(tree.carseats,best=15)
plot(prune.carseats)
text(prune.carseats,pretty=0)
tree.pred=predict(prune.carseats,Carseats.test,type="class")
table(tree.pred,High.test)
## High.test
## tree.pred No Yes
## No 86 22
## Yes 30 62
(86+62)/200
## [1] 0.74
Arboles de regresión
library(MASS)
set.seed(1)
train = sample(1:nrow(Boston), nrow(Boston)/2)
tree.boston=tree(medv~.,Boston,subset=train)
summary(tree.boston)
##
## Regression tree:
## tree(formula = medv ~ ., data = Boston, subset = train)
## Variables actually used in tree construction:
## [1] "lstat" "rm" "dis"
## Number of terminal nodes: 8
## Residual mean deviance: 12.6 = 3100 / 245
## Distribution of residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -14.100 -2.040 -0.054 0.000 1.960 12.600
plot(tree.boston)
text(tree.boston,pretty=0)
cv.boston=cv.tree(tree.boston)
plot(cv.boston$size,cv.boston$dev,type='b')
par(mfrow=c(2,3))
plot(tree.boston)
title("Arbol completo")
prune.boston4=prune.tree(tree.boston,best=4)
plot(prune.boston4)
title("best=4")
prune.boston5=prune.tree(tree.boston,best=5)
plot(prune.boston5)
title("best=5")
prune.boston6=prune.tree(tree.boston,best=6)
plot(prune.boston6)
title("best=6")
prune.boston7=prune.tree(tree.boston,best=7)
plot(prune.boston7)
title("best=7")
prune.boston8=prune.tree(tree.boston,best=8)
plot(prune.boston8)
title("best=8")
par(mfrow=c(1,1))
plot(prune.boston5)
text(prune.boston5,pretty=0)
yhat=predict(tree.boston,newdata=Boston[-train,])
boston.test=Boston[-train,"medv"]
plot(boston.test,yhat)
mean((yhat-boston.test)^2)
## [1] 25.05
Bagging y Random Forest
library(randomForest)
## Warning: package 'randomForest' was built under R version 3.1.2
## randomForest 4.6-10
## Type rfNews() to see new features/changes/bug fixes.
set.seed(1)
bag.boston=randomForest(medv~.,data=Boston,subset=train,mtry=13,importance=TRUE)
bag.boston
##
## Call:
## randomForest(formula = medv ~ ., data = Boston, mtry = 13, importance = TRUE, subset = train)
## Type of random forest: regression
## Number of trees: 500
## No. of variables tried at each split: 13
##
## Mean of squared residuals: 11.03
## % Var explained: 86.65
yhat.bag = predict(bag.boston,newdata=Boston[-train,])
plot(yhat.bag, boston.test)
abline(0,1)
mean((yhat.bag-boston.test)^2)
## [1] 13.47
bag.boston=randomForest(medv~.,data=Boston,subset=train,mtry=13,ntree=25)
yhat.bag = predict(bag.boston,newdata=Boston[-train,])
mean((yhat.bag-boston.test)^2)
## [1] 13.43
set.seed(1)
rf.boston=randomForest(medv~.,data=Boston,subset=train,mtry=6,importance=TRUE)
yhat.rf = predict(rf.boston,newdata=Boston[-train,])
mean((yhat.rf-boston.test)^2)
## [1] 11.48
importance(rf.boston)
## %IncMSE IncNodePurity
## crim 12.548 1094.65
## zn 1.375 64.40
## indus 9.304 1086.09
## chas 2.519 76.37
## nox 12.836 1008.74
## rm 31.646 6705.03
## age 9.970 575.14
## dis 12.774 1351.02
## rad 3.912 93.78
## tax 7.624 453.19
## ptratio 12.008 919.07
## black 7.376 358.97
## lstat 27.667 6927.98
varImpPlot(rf.boston)
