pwbart: Predicting new observations with a previously fitted BART model

Description

BART is a Bayesian “sum-of-trees” model.
For a numeric response $y$, we have $y = f(x) + \epsilon$, where $\epsilon \sim N(0,\sigma^2)$.

$f$ is the sum of many tree models. The goal is to have very flexible inference for the uknown function $f$.

In the spirit of “ensemble models”, each tree is constrained by a prior to be a weak learner so that it contributes a small amount to the overall fit.

Usage

pwbart( x.test, treedraws, mu=0, mc.cores=1L, transposed=FALSE,
        dodraws=TRUE,
        nice=19L ## mc.pwbart only
      )
mc.pwbart( x.test, treedraws, mu=0, mc.cores=2L, transposed=FALSE,
           dodraws=TRUE,
           nice=19L ## mc.pwbart only
         )

Value

Returns a matrix of predictions corresponding to x.test.

Arguments

x.test: Matrix of covariates to predict $y$ for.
treedraws: $treedraws returned from wbart or pbart.
mu: Mean to add on to $y$ prediction.
mc.cores: Number of threads to utilize.
transposed: When running pwbart or mc.pwbart in parallel, it is more memory-efficient to transpose x.test prior to calling the internal versions of these functions.
dodraws: Whether to return the draws themselves (the default), or whether to return the mean of the draws as specified by dodraws=FALSE.
nice: Set the job niceness. The default niceness is 19: niceness goes from 0 (highest) to 19 (lowest).

Details

BART is an Bayesian MCMC method. At each MCMC interation, we produce a draw from the joint posterior $(f,\sigma) | (x,y)$ in the numeric $y$ case and just $f$ in the binary $y$ case.

Thus, unlike a lot of other modelling methods in R, we do not produce a single model object from which fits and summaries may be extracted. The output consists of values $f^*(x)$ (and $\sigma^*$ in the numeric case) where * denotes a particular draw. The $x$ is either a row from the training data (x.train) or the test data (x.test).

Examples

Run this code

##simulate data (example from Friedman MARS paper)
f = function(x){
10*sin(pi*x[,1]*x[,2]) + 20*(x[,3]-.5)^2+10*x[,4]+5*x[,5]
}
sigma = 1.0  #y = f(x) + sigma*z , z~N(0,1)
n = 100      #number of observations
set.seed(99)
x=matrix(runif(n*10),n,10) #10 variables, only first 5 matter
y=f(x)

##test BART with token run to ensure installation works
set.seed(99)
post = wbart(x,y,nskip=5,ndpost=5)
x.test = matrix(runif(500*10),500,10)

if (FALSE) {
##run BART
set.seed(99)
post = wbart(x,y)
x.test = matrix(runif(500*10),500,10)
pred = pwbart(post$treedraws, x.test, mu=mean(y))

plot(apply(pred, 2, mean), f(x.test))

}