mbart {BART} | R Documentation

## 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) +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.

### 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 `i`th row of `x.train`, we provide the corresponding `(i-1)*K+j`th 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].

### Author(s)

Robert McCulloch: robert.e.mcculloch@gmail.com,
Rodney Sparapani: rsparapa@mcw.edu,
Robert Gramacy: rbg@vt.edu.

### 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>.

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.

### 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)

[Package BART version 2.5 Index]