Last updated: 2020-01-30
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select random rotation matrix via oob
library(rpart)
library(BART)Loading required package: nlmeLoading required package: nnetLoading required package: survivalas.numeric.factor <- function(x) {as.numeric(levels(x))[x]}
random_rotation = function(p,screening,r){
Q=qr.Q(qr(matrix(rnorm(p^2),p,p)))
if(screening){
active.var = rbinom(p,1,r)
Q[-which(active.var==1),]=0
}
Q
}
rotate_tree = function(x,y,x.oob,y.oob,xtest,ytest,n_rotate,control,screening,r){
p = ncol(x)
n = nrow(x)
fit = rpart(y~.,data = data.frame(y=y,x=x),method='class',control = control)
ypred = predict(fit,data.frame(x=x.oob),type='class')
best.accuracy = sum(ypred==y.oob)/length(y.oob)
best.fit = fit
best.Rotation = 'identity'
best.yhat = predict(fit,data.frame(x=x),type='class')
for(rot in 1:n_rotate){
Rmat = random_rotation(p,screening,r)
if(sum(Rmat)!=0){
x.train = x%*%Rmat
x.test = x.oob%*%Rmat
fit = rpart(y~.,data = data.frame(y=y,x=x.train), method='class',control = control)
ypred = predict(fit,data.frame(x=x.test),type='class')
accuracy = (sum(ypred==y.oob)/length(ypred))
if(accuracy > best.accuracy){
best.accuracy = accuracy
best.fit = fit
best.Rotation = Rmat
best.yhat = predict(fit,data.frame(x=x.train),type='class')
}
}
}
return(list(best.accuracy = best.accuracy,
best.fit = best.fit,
best.Rotation = best.Rotation,
best.yhat = best.yhat))
}
rrrforest = function(x,y,xtest=NULL,ytest=NULL,ntree=100, mtry=floor(sqrt(ncol(x))),
replace=TRUE,samplesize = if (replace) nrow(x) else ceiling(.632*nrow(x)),
control = rpart.control(),screening = TRUE,eb.screen = TRUE,
delta=max(c(0,(1+log(ncol(x)/nrow(x)))/2)),
keepforest = FALSE,n_rotate=30,printevery=100){
x = as.matrix(x)
xtest = as.matrix(xtest)
y = as.factor(y)
ytest = as.factor(ytest)
p = ncol(x)
n = nrow(x)
if (mtry >= p) stop("mtry should be smaller than the number of columns in x")
forest = list()
if(screening){
ms.idx = which(y==1)
ms = apply(x,2,function(z){(mean(z[ms.idx])-mean(z[-ms.idx]))})
if(eb.screen){
sds = sqrt(apply(x,2,function(z){var(z[ms.idx])/length(ms.idx)+var(z[-ms.idx])/(n-length(ms.idx))}))
pn.res = ebnm::ebnm(ms,sds,'point_normal')$posterior$mean
r = abs(pn.res)/max(abs(pn.res))
}else{
r = abs(ms)/max(abs(ms))
}
r = r^delta
}else{
r=rep(1,p)
}
yhat = matrix(nrow=n,ncol=ntree)
ypred = matrix(nrow=n,ncol=ntree)
oob_accuracy = c()
for(t in 1:ntree){
if(t%%printevery==0){print(sprintf("done %d (out of %d)",t,ntree))}
#select variables to split
var_idx = sample(1:p,mtry)
#select samples
sample_idx = sample(1:n,samplesize,replace = replace)
x_t = x[sample_idx,var_idx]
y_t = y[sample_idx]
x_t_oob = x[-unique(sample_idx),var_idx]
y_t_oob = y[-unique(sample_idx)]
tree.fit = rotate_tree(x_t,y_t,x_t_oob,y_t_oob,n_rotate=n_rotate,control=control,screening,r[var_idx])
oob_accuracy[t] = tree.fit$best.accuracy
yhat[sample_idx,t] = as.numeric.factor(tree.fit$best.yhat)
if(!is.null(xtest)){
if(is.character(tree.fit$best.Rotation)){
ypred[,t] = as.numeric.factor(predict(tree.fit$best.fit, data.frame(x=xtest[,var_idx]),type='class'))
}else{
ypred[,t] = as.numeric.factor(predict(tree.fit$best.fit, data.frame(x=xtest[,var_idx]%*%tree.fit$best.Rotation),type='class'))
}
}
if(keepforest){
forest[[t]] = tree.fit
}
}
vote_hat = 1*(apply(yhat,1,mean,na.rm=TRUE) > 0.5)
vote_pred = 1*(apply(ypred,1,mean,na.rm=TRUE) > 0.5)
accuracy_train = sum(y == vote_hat)/n
accuracy_test = ifelse(is.null(ytest),ytest,sum(ytest==vote_pred)/length(ytest))
return(list(accuracy_train=accuracy_train,
accuracy_test =accuracy_test,
yhat = yhat,
ypred = ypred,
vote_hat = vote_hat,
vote_pred = vote_pred,
oob_accuracy = oob_accuracy,
forest = forest))
}f_linear = function(x){
ey=-2.50*x[,1] + 2.0*x[,2] -1.60*x[,3] + 1.2*x[,4] +0.9*x[,5]
as.factor(rbinom(nrow(x),1,pnorm(ey)))
}
f_friedman=function(x){
ey = (((sin(pi*x[,1]*x[,2]) + 2*(x[,3]-.5)^2+x[,4]-2*x[,5])))
as.factor(rbinom(nrow(x),1,pnorm(ey)))
}
set.seed(1234)
n=100
p=100
x = matrix(runif(n*p),nrow=n)
y = f_linear(x)
xtest = matrix(runif(n*p),nrow=n)
ytest = f_linear(xtest)
round((apply(x,2,function(z){abs(mean(z[y==1])-mean(z[y==0]))}))/max((apply(x,2,function(z){abs(mean(z[y==1])-mean(z[y==0]))}))),2)
round(abs(apply(x,2,cor,as.numeric.factor(y)))/max(abs(apply(x,2,cor,as.numeric.factor(y)))),2)
ms = (apply(x,2,function(z){(mean(z[y==1])-mean(z[y==0]))}))
sds = sqrt(apply(x,2,function(z){(var(z)/sum(as.numeric.factor(y))+var(z)/(n-sum(as.numeric.factor(y))))}))
library(ebnm)
pn.res = ebnm(ms,sds,'point_normal')
round(abs(pn.res$posterior$mean)/max(abs(pn.res$posterior$mean)),2)
library(randomForest)
rf = randomForest(x,y,xtest,ytest,ntree=100)
rrrf = rrrforest(x,y,xtest,ytest,ntree=100,n_rotate = 30,replace = F)
rrf = rotationForest(data.frame(x),y,L=100)
rprf = rprforest(x,y,xtest,ytest)
library(pROC)
library(rotationForest)
roc_obj <- roc(as.numeric.factor(ytest), as.numeric.factor(rf$test$predicted))
auc(roc_obj)
accuracy_calc = function(a,b){
sum(a==b)/length(a)
}
roc_obj <- roc(as.numeric.factor(ytest), rrrf$vote_pred)
auc(roc_obj)
roc_obj <- roc(as.numeric.factor(ytest), 1*(predict(rrf,data.frame(xtest)) > 0.5))
auc(roc_obj)
ypred = rrrf$ypred
err.rate = c()
for(i in 1:ncol(ypred)){
err.rate[i] = sum(ytest!= (1*(apply(ypred[,1:i,drop=FALSE],1,mean) > 0.5)))/length(ytest)
}
plot(1-rf$test$err.rate[,1],type='l')
lines(1-err.rate,col=4)
# correlation of oob accuracy and accu on test data
acc.rate = c()
for(i in 1:ncol(ypred)){
acc.rate[i] = sum(ytest == ypred[,i])/length(ytest)
}
cor(acc.rate,rrrf$oob_accuracy)random projection
# generate sparse random projection
#'@param p,q random projection matrix of dimension p*q
#'@param r a vector of length p indicate variables weights
#'@param s parameter in sprase random projection, see https://web.stanford.edu/~hastie/Papers/Ping/KDD06_rp.pdf
random_projection = function(p,q,r,s){
active.var = rbinom(p,1,r)
rp.mat = matrix(sqrt(s)*rbinom(p*q,1,1/s)*(2*rbinom(p*q,1,0.5)-1),nrow=p)
rp.mat[-which(active.var==1),] = 0
rp.mat
}
project_tree = function(x,y,x.oob,y.oob,n_project,control,r,q,s){
p = ncol(x)
n = nrow(x)
rp1 = random_projection(p,q,r,s)
fit = rpart(y~.,data = data.frame(y=y,x=x%*%rp1),method='class',control = control)
ypred = predict(fit,data.frame(x=x.oob%*%rp1),type='class')
best.accuracy = sum(ypred==y.oob)/length(y.oob)
best.fit = fit
best.project = rp1
best.yhat = predict(fit,data.frame(x=x%*%rp1),type='class')
for(rot in 1:n_project){
Rmat = random_projection(p,q,r,s)
x.train = x%*%Rmat
x.test = x.oob%*%Rmat
fit = rpart(y~.,data = data.frame(y=y,x=x.train), method='class',control = control)
ypred = predict(fit,data.frame(x=x.test),type='class')
accuracy = (sum(ypred==y.oob)/length(ypred))
if(accuracy > best.accuracy){
best.accuracy = accuracy
best.fit = fit
best.project = Rmat
best.yhat = predict(fit,data.frame(x=x.train),type='class')
}
}
return(list(best.accuracy = best.accuracy,
best.fit = best.fit,
best.project = best.project,
best.yhat = best.yhat))
}
# q: random projection dimension, could be a vector
# delta: |r|^delta
rprforest = function(x,y,xtest=NULL,ytest=NULL,ntree=100,mtry=floor(sqrt(ncol(x))),
replace=TRUE,samplesize = if (replace) nrow(x) else ceiling(.632*nrow(x)),
control = rpart.control(),
keepforest = FALSE,n_project=30,printevery=100,
q=round(seq(log(ncol(x)),mtry,length.out = ntree/10)),
#q=mtry,
s=3,delta=max(c(0,(1+log(ncol(x)/nrow(x)))/2))){
x = as.matrix(x)
xtest = as.matrix(xtest)
y = as.factor(y)
ytest = as.factor(ytest)
p = ncol(x)
n = nrow(x)
if (mtry >= p) stop("mtry should be smaller than the number of columns in x")
forest = list()
# find r
ms.idx = y==1
ms = apply(x,2,function(z){abs(mean(z[ms.idx])-mean(z[-ms.idx]))})
r = abs(ms)/max(abs(ms))
r = r^delta
yhat = matrix(nrow=n,ncol=ntree)
ypred = matrix(nrow=n,ncol=ntree)
oob_accuracy = c()
for(t in 1:ntree){
if(t%%printevery==0){print(sprintf("done %d (out of %d)",t,ntree))}
#select variables to split
var_idx = sample(1:p,mtry)
#select samples
sample_idx = sample(1:n,samplesize,replace = replace)
x_t = x[sample_idx,var_idx]
y_t = y[sample_idx]
x_t_oob = x[-unique(sample_idx),var_idx]
y_t_oob = y[-unique(sample_idx)]
if(length(q)>1){
qt = sample(q,1)
}else{
qt=q
}
tree.fit = project_tree(x_t,y_t,x_t_oob,y_t_oob,n_project=n_project,control=control,r=r[var_idx],q=qt,s=s)
oob_accuracy[t] = tree.fit$best.accuracy
yhat[sample_idx,t] = as.numeric.factor(tree.fit$best.yhat)
if(!is.null(xtest)){
ypred[,t] = as.numeric.factor(predict(tree.fit$best.fit, data.frame(x=xtest[,var_idx]%*%tree.fit$best.project),type='class'))
}
if(keepforest){
forest[[t]] = tree.fit
}
}
vote_hat = 1*(apply(yhat,1,mean,na.rm=TRUE) > 0.5)
vote_pred = 1*(apply(ypred,1,mean,na.rm=TRUE) > 0.5)
accuracy_train = sum(y == vote_hat)/n
accuracy_test = ifelse(is.null(ytest),ytest,sum(ytest==vote_pred)/length(ytest))
return(list(accuracy_train=accuracy_train,
accuracy_test =accuracy_test,
yhat = yhat,
ypred = ypred,
vote_hat = vote_hat,
vote_pred = vote_pred,
oob_accuracy = oob_accuracy,
forest = forest))
}
sessionInfo()R version 3.6.1 (2019-07-05)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.6
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] BART_2.7 survival_2.44-1.1 nnet_7.3-12 nlme_3.1-141
[5] rpart_4.1-15
loaded via a namespace (and not attached):
[1] Rcpp_1.0.2 knitr_1.25 whisker_0.4 magrittr_1.5
[5] workflowr_1.5.0 splines_3.6.1 lattice_0.20-38 R6_2.4.0
[9] rlang_0.4.0 stringr_1.4.0 tools_3.6.1 parallel_3.6.1
[13] grid_3.6.1 xfun_0.10 git2r_0.26.1 htmltools_0.4.0
[17] yaml_2.2.0 digest_0.6.21 rprojroot_1.3-2 Matrix_1.2-17
[21] later_1.0.0 promises_1.1.0 fs_1.3.1 glue_1.3.1
[25] evaluate_0.14 rmarkdown_1.16 stringi_1.4.3 compiler_3.6.1
[29] backports_1.1.5 httpuv_1.5.2