mbart: Multinomial BART for categorical outcomes with fewer...

In BART: Bayesian Additive Regression Trees

Multinomial BART for categorical outcomes with fewer categories

Description

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

Usage

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
        )

Arguments

x.train	Explanatory variables for training (in sample) data. May be a matrix or a data frame, with (as usual) rows corresponding to observations and columns to variables. If a variable is a factor in a data frame, it is replaced with dummies. Note that q dummies are created if q>2 and one dummy is created if q=2, where q is the number of levels of the factor. mbart will generate draws of f(x) for each x which is a row of x.train.
y.train	Categorical dependent variable for training (in sample) data.
x.test	Explanatory variables for test (out of sample) data. Should have same structure as x.train. mbart will generate draws of f(x) for each x which is a row of x.test.
type	You can use this argument to specify the type of fit. 'pbart' for probit BART or 'lbart' for logit BART.
ntype	The integer equivalent of type where 'pbart' is 2 and 'lbart' is 3.
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 xinfo argument to specify a list (matrix) where the items (rows) are the covariates and the contents of the items (columns) are the cutpoints.
usequants	If usequants=FALSE, then the cutpoints in xinfo are generated uniformly; otherwise, if TRUE, uniform quantiles are used for the cutpoints.
rm.const	Whether or not to remove constant variables.
k	For categorical y.train, k is the number of prior standard deviations f(x) is away from +/-3.
power	Power parameter for tree prior.
base	Base parameter for tree prior.
tau.num	The numerator in the tau definition, i.e., tau=tau.num/(k*sqrt(ntree)).
offset	With Multinomial BART, the centering is P(yj=1 | x) = F(fj(x) + offset[j]) where offset defaults to F^{-1}(mean(y.train)). You can use the offset parameter to over-ride these defaults.
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 mbart in parallel, it is more memory-efficient to transpose x.train and x.test, if any, prior to calling mc.mbart.
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 TRUE.
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).

Details

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).

Value

mbart returns an object of type mbart which is essentially a list.

yhat.train	A matrix with ndpost rows and nrow(x.train)*K columns. Each row corresponds to a draw f^* from the posterior of f and each column corresponds to an estimate for a row of x.train. For the ith row of x.train, we provide the corresponding (i-1)*K+jth column of yhat.train where j=1,...,K indexes the categories. Burn-in is dropped.
yhat.train.mean	train data fits = mean of yhat.train columns.
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.

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].

See Also

gbart, alligator

Examples

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)

BART documentation built on June 22, 2024, 11:33 a.m.