BART (version 2.5)

predict.mbart: 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 $y=f(x)+ϵ$, where $ϵ\sim N(0,{\sigma }^2)$.

$f$ 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

# S3 method for mbart
predict(object, newdata, mc.cores=1, openmp=(mc.cores.openmp()>0), ...)
# S3 method for mbart2
predict(object, newdata, mc.cores=1, openmp=(mc.cores.openmp()>0), ...)

Arguments

object

object returned from previous BART fit with mbart or mbart2.

newdata

Matrix of covariates to predict the distribution of $t$.

mc.cores

Number of threads to utilize.

openmp

Logical value dictating whether OpenMP is utilized for parallel processing. Of course, this depends on whether OpenMP is available on your system which, by default, is verified with mc.cores.openmp.

...

Other arguments which will be passed on to pwbart.

Value

Returns an object of type mbart with predictions corresponding to newdata.

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 $f^{\ast }(x)$ (and ${\sigma }^{\ast }$ 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).

References

Chipman, H., George, E., and McCulloch R. (2010) Bayesian Additive Regression Trees. The Annals of Applied Statistics, 4,1, 266-298 <doi:10.1214/09-AOAS285>.

Chipman, H., George, E., and McCulloch R. (2006) Bayesian Ensemble Learning. Advances in Neural Information Processing Systems 19, Scholkopf, Platt and Hoffman, Eds., MIT Press, Cambridge, MA, 265-272.

Friedman, J.H. (1991) Multivariate adaptive regression splines. The Annals of Statistics, 19, 1--67.

See Also

mbart, mbart2

Examples

# NOT RUN {
## load the advanced lung cancer example
data(lung)

group <- -which(is.na(lung[ , 7])) ## remove missing row for ph.karno
times <- lung[group, 2]   ##lung$time
delta <- lung[group, 3]-1 ##lung$status: 1=censored, 2=dead
                          ##delta: 0=censored, 1=dead

## this study reports time in days rather than months like other studies
## coarsening from days to months will reduce the computational burden
times <- ceiling(times/30)

summary(times)
table(delta)

x.train <- as.matrix(lung[group, c(4, 5, 7)]) ## matrix of observed covariates

## lung$age:        Age in years
## lung$sex:        Male=1 Female=2
## lung$ph.karno:   Karnofsky performance score (dead=0:normal=100:by=10)
##                  rated by physician

dimnames(x.train)[[2]] <- c('age(yr)', 'M(1):F(2)', 'ph.karno(0:100:10)')

summary(x.train[ , 1])
table(x.train[ , 2])
table(x.train[ , 3])

x.test <- matrix(nrow=84, ncol=3) ## matrix of covariate scenarios

dimnames(x.test)[[2]] <- dimnames(x.train)[[2]]

i <- 1

for(age in 5*(9:15)) for(sex in 1:2) for(ph.karno in 10*(5:10)) {
    x.test[i, ] <- c(age, sex, ph.karno)
    i <- i+1
}

## this x.test is relatively small, but often you will want to
## predict for a large x.test matrix which may cause problems
## due to consumption of RAM so we can predict separately

## mcparallel/mccollect do not exist on windows
if(.Platform$OS.type=='unix') {
##test BART with token run to ensure installation works
    set.seed(99)
    post <- surv.bart(x.train=x.train, times=times, delta=delta, nskip=5, ndpost=5, keepevery=1)

    pre <- surv.pre.bart(x.train=x.train, times=times, delta=delta, x.test=x.test)

    pred <- predict(post, pre$tx.test)
    ##pred. <- surv.pwbart(pre$tx.test, post$treedraws, post$binaryOffset)
}

# }
# NOT RUN {
## run one long MCMC chain in one process
set.seed(99)
post <- surv.bart(x.train=x.train, times=times, delta=delta)

## run "mc.cores" number of shorter MCMC chains in parallel processes
## post <- mc.surv.bart(x.train=x.train, times=times, delta=delta,
##                      mc.cores=5, seed=99)

pre <- surv.pre.bart(x.train=x.train, times=times, delta=delta, x.test=x.test)

pred <- predict(post, pre$tx.test)

## let's look at some survival curves
## first, a younger group with a healthier KPS
## age 50 with KPS=90: males and females
## males: row 17, females: row 23
x.test[c(17, 23), ]

low.risk.males <- 16*post$K+1:post$K ## K=unique times including censoring
low.risk.females <- 22*post$K+1:post$K

plot(post$times, pred$surv.test.mean[low.risk.males], type='s', col='blue',
     main='Age 50 with KPS=90', xlab='t', ylab='S(t)', ylim=c(0, 1))
points(post$times, pred$surv.test.mean[low.risk.females], type='s', col='red')

# }