BART (version 2.8)

predict.wbart: 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

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

Arguments

object

object returned from previous BART fit.

newdata

Matrix of covariates to predict \(y\) for.

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 a matrix of 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 \(f^*(x)\) (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).

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

wbart, mc.wbart, pwbart, mc.pwbart, mc.cores.openmp

Examples

# NOT RUN {
##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)

# }
# NOT RUN {
##run BART
set.seed(99)
post = wbart(x,y)
x.test = matrix(runif(500*10),500,10)
pred = predict(post, x.test, mu=mean(y))

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

# }