gbmm {BART} | R Documentation |
BART is a Bayesian “sum-of-trees” model.
For a numeric response y, we have
y = f(x) + e,
where e ~ 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.
gbmm( x.train, y.train, x.test=matrix(0,0,0), type='wbart', u.train=NULL, B=NULL, ntype=as.integer( factor(type, levels=c('wbart', 'pbart'))), 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, sigest=NA, sigdf=3, sigquant=0.90, k=2, power=2, base=0.95, lambda=NA, 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 = 1L, ## mc.gbmm only nice = 19L, ## mc.gbmm only seed = 99L ## mc.gbmm only ) mc.gbmm( x.train, y.train, x.test=matrix(0,0,0), type='wbart', u.train=NULL, B=NULL, ntype=as.integer( factor(type, levels=c('wbart', 'pbart'))), 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, sigest=NA, sigdf=3, sigquant=0.90, k=2, power=2, base=0.95, lambda=NA, 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, nice = 19L, seed = 99L )
x.train |
Explanatory variables for training (in sample)
data. |
y.train |
Continuous or binary dependent variable for training (in sample) data. |
x.test |
Explanatory variables for test (out of sample)
data. Should have same structure as |
u.train |
Integer indices specifying the random effects. |
B |
The prior for the standard deviation of the random effects is U(0, B). |
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. |
sigest |
The prior for the error variance
(sigma\^2) is inverted chi-squared (the standard
conditionally conjugate prior). The prior is specified by choosing
the degrees of freedom, a rough estimate of the corresponding
standard deviation and a quantile to put this rough estimate at. If
|
sigdf |
Degrees of freedom for error variance prior. Not used if y is binary. |
sigquant |
The quantile of the prior that the rough estimate
(see |
k |
For numeric y, |
power |
Power parameter for tree prior. |
base |
Base parameter for tree prior. |
lambda |
The scale of the prior for the variance. If |
tau.num |
The numerator in the |
offset |
Continous BART operates on |
ntree |
The number of trees in the sum. |
numcut |
The number of possible values of c (see
|
ndpost |
The number of posterior draws returned. |
nskip |
Number of MCMC iterations to be treated as burn in. |
printevery |
As the MCMC runs, a message is printed every printevery draws. |
keepevery |
Every keepevery draw is kept to be returned to the user. |
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 a 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
.
For x.train
/x.test with missing data elements, gbmm
will singly impute them with hot decking. For one or more missing
covariates, record-level hot-decking imputation deWaPann11 is
employed that is biased towards the null, i.e., nonmissing values
from another record are randomly selected regardless of the
outcome. Since mc.gbmm
runs multiple gbmm
threads in
parallel, mc.gbmm
performs multiple imputation with hot
decking, i.e., a separate imputation for each thread. This
record-level hot-decking imputation is biased towards the null, i.e.,
nonmissing values from another record are randomly selected
regardless of y.train
.
gbmm
returns an object of type gbmm
which is
essentially a list.
In the numeric y case, the list has components:
yhat.train |
A matrix with ndpost rows and nrow(x.train) columns.
Each row corresponds to a draw f* from the posterior of f
and each column corresponds to a row of x.train.
The (i,j) value is f*(x) for the i\^th kept draw of f
and the j\^th row of x.train. |
yhat.test |
Same as yhat.train but now the x's are the rows of the test data. |
yhat.train.mean |
train data fits = mean of yhat.train columns. |
yhat.test.mean |
test data fits = mean of yhat.test columns. |
sigma |
post burn in draws of sigma, length = ndpost. |
first.sigma |
burn-in draws of sigma. |
varcount |
a matrix with ndpost rows and nrow(x.train) columns. Each row is for a draw. For each variable (corresponding to the columns), the total count of the number of times that variable is used in a tree decision rule (over all trees) is given. |
sigest |
The rough error standard deviation (sigma) used in the prior. |
Robert McCulloch: robert.e.mcculloch@gmail.com,
Rodney Sparapani: rsparapa@mcw.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>.
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.
De Waal, T., Pannekoek, J. and Scholtus, S. (2011) Handbook of statistical data editing and imputation. John Wiley & Sons, Hoboken, NJ.
Friedman, J.H. (1991) Multivariate adaptive regression splines. The Annals of Statistics, 19, 1–67.
Linero, A.R. (2018) Bayesian regression trees for high dimensional prediction and variable selection. JASA, 113(522), 626–636.
##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 Ey = f(x) y=Ey+sigma*rnorm(n) lmFit = lm(y~.,data.frame(x,y)) #compare lm fit to BART later ##test BART with token run to ensure installation works set.seed(99) bartFit = wbart(x,y,nskip=5,ndpost=5) ## Not run: ##run BART set.seed(99) bartFit = wbart(x,y) ##compare BART fit to linear matter and truth = Ey fitmat = cbind(y,Ey,lmFit$fitted,bartFit$yhat.train.mean) colnames(fitmat) = c('y','Ey','lm','bart') print(cor(fitmat)) ## End(Not run)