mbart {BART} | R Documentation |
BART is a Bayesian “sum-of-trees” model.
For numeric response y, we have y = f(x) +ε
y = f(x) + e, where e ~ N(0, 1).
For a multinomial response y, P(Y=y | x) = F(f(x)),
where F denotes the standard Normal CDF (probit link) or the
standard Logistic CDF (logit link).
In both cases, 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.
mbart( x.train, y.train, x.test=matrix(0,0,0), type='pbart', ntype=as.integer( factor(type, levels=c('wbart', 'pbart', 'lbart'))), sparse=FALSE, theta=0, omega=1, a=0.5, b=1, augment=FALSE, rho=NULL, xinfo=matrix(0,0,0), usequants=FALSE, rm.const=TRUE, k=2, power=2, base=0.95, tau.num=c(NA, 3, 6)[ntype], offset=NULL, ntree=c(200L, 50L, 50L)[ntype], numcut=100L, ndpost=1000L, nskip=100L, keepevery=c(1L, 10L, 10L)[ntype], printevery=100L, transposed=FALSE, hostname=FALSE, mc.cores = 2L, ## mc.bart only nice = 19L, ## mc.bart only seed = 99L ## mc.bart only ) mc.mbart( x.train, y.train, x.test=matrix(0,0,0), type='pbart', ntype=as.integer( factor(type, levels=c('wbart', 'pbart', 'lbart'))), sparse=FALSE, theta=0, omega=1, a=0.5, b=1, augment=FALSE, rho=NULL, xinfo=matrix(0,0,0), usequants=FALSE, rm.const=TRUE, k=2, power=2, base=0.95, tau.num=c(NA, 3, 6)[ntype], offset=NULL, ntree=c(200L, 50L, 50L)[ntype], numcut=100L, ndpost=1000L, nskip=100L, keepevery=c(1L, 10L, 10L)[ntype], printevery=100L, transposed=FALSE, hostname=FALSE, mc.cores = 2L, ## mc.bart only nice = 19L, ## mc.bart only seed = 99L ## mc.bart only )
x.train |
Explanatory variables for training (in sample) data. |
y.train |
Categorical dependent variable for training (in sample) data. |
x.test |
Explanatory variables for test (out of sample) data. |
type |
You can use this argument to specify the type of fit.
|
ntype |
The integer equivalent of |
sparse |
Whether to perform variable selection based on a sparse Dirichlet prior rather than simply uniform; see Linero 2016. |
theta |
Set theta parameter; zero means random. |
omega |
Set omega parameter; zero means random. |
a |
Sparse parameter for Beta(a, b) prior: 0.5<=a<=1 where lower values inducing more sparsity. |
b |
Sparse parameter for Beta(a, b) prior; typically, b=1. |
rho |
Sparse parameter: typically rho=p where p is the number of covariates under consideration. |
augment |
Whether data augmentation is to be performed in sparse variable selection. |
xinfo |
You can provide the cutpoints to BART or let BART
choose them for you. To provide them, use the |
usequants |
If |
rm.const |
Whether or not to remove constant variables. |
k |
For categorical |
power |
Power parameter for tree prior. |
base |
Base parameter for tree prior. |
tau.num |
The numerator in the |
offset |
With Multinomial
BART, the centering is P(yj=1 | x) = F(fj(x) + offset[j]) where
|
ntree |
The number of trees in the sum. |
numcut |
The number of possible values of c (see usequants). If a single number if given, this is used for all variables. Otherwise a vector with length equal to ncol(x.train) is required, where the i^th element gives the number of c used for the i^th variable in x.train. If usequants is false, numcut equally spaced cutoffs are used covering the range of values in the corresponding column of x.train. If usequants is true, then min(numcut, the number of unique values in the corresponding columns of x.train - 1) c values are used. |
ndpost |
The number of posterior draws returned. |
nskip |
Number of MCMC iterations to be treated as burn in. |
keepevery |
Every keepevery draw is kept to be returned to the user. |
printevery |
As the MCMC runs, a message is printed every printevery draws. |
transposed |
When running |
hostname |
When running on a cluster occasionally it is useful
to track on which node each chain is running; to do so
set this argument to |
seed |
Setting the seed required for reproducible MCMC. |
mc.cores |
Number of cores to employ in parallel. |
nice |
Set the job niceness. The default niceness is 19: niceness goes from 0 (highest) to 19 (lowest). |
BART is an Bayesian MCMC method. At each MCMC interation, we produce a draw from f in the categorical 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) where * denotes a particular draw. The x is either a row from the training data (x.train).
mbart
returns an object of type mbart
which is
essentially a list.
yhat.train |
A matrix with |
yhat.train.mean |
train data fits = mean of |
varcount |
a matrix with |
In addition, the list
has a offset
vector giving the value used.
Note that in the multinomial y case yhat.train
is
f(x) + offset[j].
Robert McCulloch: robert.e.mcculloch@gmail.com,
Rodney Sparapani: rsparapa@mcw.edu,
Robert Gramacy: rbg@vt.edu.
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>.
Friedman, J.H. (1991) Multivariate adaptive regression splines. The Annals of Statistics, 19, 1–67.
Gramacy, RB and Polson, NG (2012) Simulation-based regularized logistic regression. Bayesian Analysis, 7, 567–590.
Holmes, C and Held, L (2006) Bayesian auxiliary variable models for binary and multinomial regression. Bayesian Analysis, 1, 145–68.
Linero, A.R. (2018) Bayesian regression trees for high dimensional prediction and variable selection. JASA, 113, 626–36.
N=500 set.seed(12) x1=runif(N) x2=runif(N, max=1-x1) x3=1-x1-x2 x.train=cbind(x1, x2, x3) y.train=0 for(i in 1:N) y.train[i]=sum((1:3)*rmultinom(1, 1, x.train[i, ])) table(y.train)/N ##test mbart with token run to ensure installation works set.seed(99) post = mbart(x.train, y.train, nskip=1, ndpost=1) ## Not run: set.seed(99) post=mbart(x.train, y.train, x.train) ##mc.post=mbart(x.train, y.train, x.test, mc.cores=8, seed=99) K=3 i=seq(1, N*K, K)-1 for(j in 1:K) print(cor(x.train[ , j], post$prob.test.mean[i+j])^2) ## End(Not run)