Type:	Package
Title:	Bayesian Treed Machine Learning for Personalized Prediction
Version:	0.2.0
Date:	2026-02-01
Description:	Generalization of the Bayesian classification and regression tree (CART) model that partitions subjects into terminal nodes and tailors machine learning model to each terminal node.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Depends:	R (≥ 4.5.0), glmnet, randomForest, e1071, pROC, stats, graphics
NeedsCompilation:	no
Packaged:	2026-02-02 06:05:15 UTC; ychung36
Author:	Yunro Chung [aut, cre], Yaliang Zhang [aut]
Maintainer:	Yunro Chung <yunro.chung@asu.edu>
Repository:	CRAN
Date/Publication:	2026-02-02 06:20:02 UTC

Bayeisan Treed Machine Learning

Description

Generalized Bayesian classification and tree (BCART) model that assigns the most effective predictive model to each terminal node.

Usage

  btml(y,x,z,ynew,xnew,znew,MLlist,sparse,nwarm,niter,minsample,base,power)

Arguments

Details

The tgml function uses a stochastic search to identify the optimal decision-tree based rule that partitions subjects into distinct terminal nodes and assigns the most effective predictive model to each terminal node.

Ideally, two sets of predictors are used: x and z, where x is used to construct tree splits, and z is used to fit the predictive models within each terminal node. If this separation is not possible, the same predictors can be used to predict y based on x, e.g.,

btml(y=y, x=x, z=x, y=ynew, x=xnew, z=xnew)

In terms of node numbering, an internal node s has left and right child nodes 2*s and 2*s+1, respectively. Node 1 is the root node; nodes 2 and 3 are left and right child nodes of node 1; nodes 4 and 5 are left and right nodes of node 2; and so on.

As a default setting, one of the three predictive models in the MLlist is assigned to each terminal node: lasso(), randomForest(), and svm(...,kernel="radial") functions from the R packages cv.glmnet, randomForest, and e1071, respectively. Additional models can be flexibly incorporated; see Example 3 below for an illustration.

Value

An object of class btml, which is a list with the following components:

Author(s)

Yaliang Zhang [aut], Yunro Chung [aut, cre]

References

Yaliang Zhang and Yunro Chung, Bayesian treed machine learning model (in preperation)

Examples

set.seed(9)
###
#1. continuous y
###
n=200*2 #n=200 & 200 for training & test sets

x=matrix(rnorm(n*4),n,4)
z=matrix(rnorm(n*4),n,4)

xcut=median(x[,1])
subgr=1*(x[,1]<xcut)+2*(x[,1]>=xcut) #2 subgroups

lp=rep(NA,n)
for(i in 1:n){
  if(x[i,1]<0){
    lp[i]=1+3*z[i,1]
  }else{
    lp[i]=1+3*z[i,2]
  }
}
y=lp+rnorm(n,0,1)

idx.nex=sample(1:n,n*1/2,replace=FALSE)
ynew=y[idx.nex]
xnew=x[idx.nex,]
znew=z[idx.nex,]

y=y[-idx.nex]
x=x[-idx.nex,]
z=z[-idx.nex,]

fit1=btml(y,x,z,ynew=ynew,xnew=xnew,znew=znew,nwarm=1000,niter=1000)
fit1$mse.new
plot(fit1$y.hat.new~ynew,ylab="Predicted y",xlab="ynew")
abline(a=0,b=1,lwd=2,col="darkgray")

###
#2. binary y
###
x=matrix(rnorm(n*4),n,4)
z=matrix(rnorm(n*4),n,4)

lp=rep(NA,n)
for(i in 1:n){
  if(x[i,1]<0){
    lp[i]=1+3*z[i,1]
  }else{
    lp[i]=1+3*z[i,2]
  }
}
prob=1/(1+exp(-lp))
y=rbinom(n,1,prob)
y=as.factor(y)

idx.nex=sample(1:n,n*1/2,replace=FALSE)
ynew=y[idx.nex]
xnew=x[idx.nex,]
znew=z[idx.nex,]

y=y[-idx.nex]
x=x[-idx.nex,]
z=z[-idx.nex,]

fit2=btml(y,x,z,ynew=ynew,xnew=xnew,znew=znew,nwarm=1000,niter=1000)
fit2$auc.new
plot(fit2$roc.new)

###
#3. add new ML models
#   1) write two functions:
#      c_xx & c_xx_predict if y is continuous or
#      b_xx & b_xx.predict if y is binary
#   2) MLlist includes xx, not c.xx nor b.xx.
#   3) run btml using the updated MLlist.
#   The below is an example of adding ridge regression.
###
#3.1. ridge regression for continuous y.
c_ridge=function(y,x){
  x=data.matrix(x)
  fit=NULL
  suppressWarnings(try(fit<-glmnet::cv.glmnet(x,y,alpha=0),silent=TRUE))
  return(fit)
}
c_ridge_predict=function(fit,xnew){
  y.hat=rep(NA,nrow(xnew))
  if(!is.null(fit)){
    xnew=data.matrix(xnew)
    y.hat=as.numeric(predict(fit,newx=xnew,s="lambda.min",type="response"))
  }
  return(y.hat)
}

#3.2. ridge regression for binary y.
b_ridge=function(y,x){
  x=data.matrix(x)
  fit=NULL
  suppressWarnings(try(fit<-glmnet::cv.glmnet(x,y,alpha=1,family="binomial"),silent=TRUE))
  return(fit)
}
b_ridge_predict=function(fit,xnew){
  y.hat=rep(NA,nrow(xnew))
  if(!is.null(fit)){
    xnew=data.matrix(xnew)
    y.hat=as.numeric(predict(fit,newx=xnew,s="lambda.min",type="response"))
  }
  return(y.hat)
}

#3.3. update MLlist
MLlist=c("lasso","ridge")
fit3=btml(y,x,z,ynew=ynew,xnew=xnew,znew=znew,MLlist=MLlist,nwarm=1000,niter=1000)
fit3$auc.new
plot(fit3$roc.new)