17 Estimateurs à noyau et \(k\) plus proches voisins

Estimateurs à noyau

ozone <- read.table("../donnees/ozone.txt",header=TRUE,sep=";")

ind <- order(ozone[,"T12"])
T12o <- ozone[ind,"T12"]
O3o <- ozone[ind,"O3"]

reg1 <- lm(O3o~1,weight=c(rep(1,10),rep(0,40)))
reg2 <- lm(O3o~1,weight=c(rep(0,10),rep(1,10),rep(0,30)))
reg3 <- lm(O3o~1,weight=c(rep(0,20),rep(1,10),rep(0,20)))
reg4 <- lm(O3o~1,weight=c(rep(0,30),rep(1,10),rep(0,10)))
reg5 <- lm(O3o~1,weight=c(rep(0,40),rep(1,10)))

plot(T12o,O3o,pch=20,xlab="T12",ylab="O3")
abline(v=c(14,18),col="red",lwd=2)
abline(v=c(16),col="blue",lty=2)
points(16,mean(O3o[T12o>=14 & T12o<=18]),col="blue",pch=17,cex=1.5)

library(ibr)
x <- seq(7,30,by=0.01)
par(mfrow=c(1,3))
h <- c(20,3,0.05)
for (i in h){
  plot(T12o,O3o,pch=20,xlab="T12",ylab="O3")
  tmp <- npregress(T12o,O3o,bandwidth = i)
  prev <- predict(tmp,newdata=x)
  lines(x,prev,col="blue",lwd=2)
}

Les \(k\) plus proches voisins

par(mfrow=c(1,3))
library(FNN)
k <- c(50,10,1)
for (i in k){
  mod <- knn.reg(train=T12o,test=as.matrix(x),y=O3o,k=i)
  plot(T12o,O3o,pch=20,xlab="T12",ylab="O3")
  lines(x,mod$pred,col="blue",lwd=2)
}

Sélection des paramètres

hcv <- npregress(T12o,O3o)$bandwidth
hcv

[1] 1.688373

knn.reg(train=T12o,y=O3o,k=10)$PRESS/length(T12o)

[1] 287.6629

K_cand <- 1:49
loo <- rep(0,length(K_cand))
for (i in 1:length(K_cand)){
  loo[i] <- knn.reg(train=T12o,y=O3o,k=K_cand[i])$PRESS/length(T12o)
}
K_cand[which.min(loo)]

[1] 8

mod.kppv <- knn.reg(train=T12o,test=as.matrix(x),y=O3o,k=8)
mod.noyau <- npregress(T12o,O3o,bandwidth = hcv)
prev.noyau <- predict(mod.noyau,newdata=x)
plot(T12o,O3o,pch=20,xlab="T12",ylab="O3")
lines(x,mod.kppv$pred,col="blue",lwd=2)
lines(x,prev.noyau,col="red",lty=2,lwd=2)

mod.noyau$df

[1] 5.339428