rbartpackages.BART.mc_gbart

class rbartpackages.BART.mc_gbart(x_train, y_train, x_test=None, *, type='wbart', sparse=False, theta=0.0, omega=1.0, a=0.5, b=1.0, augment=False, rho=None, xinfo=None, usequants=False, rm_const=True, sigest=None, sigdf=3.0, sigquant=0.9, k=2.0, power=2.0, base=0.95, lambda_=None, tau_num=None, offset=None, w=None, ntree=None, numcut=100, ndpost=1000, nskip=100, keepevery=None, printevery=100, transposed=False, hostname=False, mc_cores=2, nice=19, seed=99)[source]

Fit BART to continuous or binary outcomes with multiple MCMC chains.

Python interface to R’s BART::mc.gbart, which runs mc_cores MCMC chains in forked R processes and pools their draws. Arguments left to None are omitted from the R call, so R computes its own defaults, described below; ‘continuous’ refers to type='wbart' fits and ‘binary’ to type='pbart'/'lbart' fits.

Parameters:

  • x_train (Float64[ndarray, 'n p'] | DataFrame) – Covariates for training; rows are observations. A dataframe’s factor columns are expanded into indicator columns; missing values are imputed by hot decking.

  • y_train (Float64[ndarray, 'n']) – Dependent variable for training: continuous, or binary coded as 0/1 (requires setting type).

  • x_test (Float64[ndarray, 'm p'] | DataFrame | None, default: None) – Covariates for test data, with the same structure as x_train.

  • type (Literal['wbart', 'pbart', 'lbart'], default: 'wbart') – The type of fit: ‘wbart’ (continuous), ‘pbart’ (probit binary) or ‘lbart’ (logit binary).

  • sparse (bool, default: False) – Whether to replace the uniform splitting-variable choice with the sparse Dirichlet (DART) variable-selection prior.

  • theta (float, default: 0.0) – theta parameter of the DART prior; 0 means random.

  • omega (float, default: 1.0) – omega parameter of the DART prior; 0 means random.

  • a (float, default: 0.5) – Shape parameter of the Beta(a, b) prior on the DART sparsity, between 0.5 and 1; lower values induce more sparsity.

  • b (float, default: 1.0) – Shape parameter of the Beta(a, b) prior on the DART sparsity.

  • augment (bool, default: False) – Whether to perform data augmentation in the sparse variable selection.

  • rho (float | None, default: None) – Concentration of the DART prior; default the number of variables (after factor expansion), set it lower for more sparsity.

  • xinfo (Float64[ndarray, 'p numcut'] | None, default: None) – Cutpoints to use, one row per variable; by default they are computed from x_train (see numcut and usequants).

  • usequants (bool, default: False) – Whether the computed cutpoints are quantiles of the data rather than uniformly spaced over its range.

  • rm_const (bool, default: True) – Whether to drop constant covariates.

  • sigest (float | None, default: None) – Rough estimate of the error SD that anchors the sigma prior; default the residual SD of a linear fit (the SD of y_train if p >= n). Continuous only.

  • sigdf (float, default: 3.0) – Degrees of freedom of the (scaled inverse chi-squared) sigma prior. Continuous only.

  • sigquant (float, default: 0.9) – Quantile of the sigma prior placed at sigest; closer to 1 puts more prior weight below sigest. Continuous only.

  • k (float, default: 2.0) – Number of prior SDs between f’s mean and the data extremes (+/-0.5 of the rescaled y for continuous, +/-3 on the latent scale for binary); bigger is more conservative.

  • power (float, default: 2.0) – Exponent of the tree depth prior P(split node at depth d) = base / (1 + d)**power.

  • base (float, default: 0.95) – Scale of the tree depth prior (see power).

  • lambda_ (float | None, default: None) – Scale of the sigma prior (R’s lambda); the default derives it from sigest and sigquant. 0 would fix the error SD at sigest, but R then crashes summarizing the sigma draws it no longer makes. Continuous only.

  • tau_num (float | None, default: None) – Numerator of the leaf-value prior SD tau_num / (k * sqrt(ntree)); default (max(y_train) - min(y_train)) / 2 for continuous, 3 for ‘pbart’ and 6 for ‘lbart’.

  • offset (float | None, default: None) – Centering subtracted from y_train; default its mean, mapped through the inverse link for binary outcomes.

  • w (Float64[ndarray, 'n'] | None, default: None) – Per-observation weights multiplying the error SD. Continuous only.

  • ntree (int | None, default: None) – Number of trees in the sum; default 200 for continuous and 50 for binary outcomes.

  • numcut (int | Integer[ndarray, 'p'], default: 100) – Number of candidate cutpoints, for all variables or per column (the per-column form requires transposed: R’s preprocessing mishandles it otherwise).

  • ndpost (int, default: 1000) – Number of posterior draws to keep, after burn-in and thinning (rounded up to a whole number of draws per chain).

  • nskip (int, default: 100) – Number of burn-in MCMC iterations discarded, per chain.

  • keepevery (int | None, default: None) – Thinning: keep one draw out of keepevery; default 1 for continuous and 10 for binary outcomes.

  • printevery (int, default: 100) – Interval, in MCMC iterations, of the progress messages.

  • transposed (bool, default: False) – Whether x_train and x_test are already preprocessed (see bartModelMatrix) and transposed to (p, n), as mc_gbart does when handing the data to its workers.

  • hostname (bool, default: False) – Whether to record the hostname the fit runs on (per chain for mc.gbart), to track the nodes of a cluster.

  • mc_cores (int, default: 2) – Number of MCMC chains, run in forked R processes, capped at the detected core count. gbart runs a single chain in-process and ignores it.

  • nice (int, default: 19) – Unix niceness of the chain processes, from 0 (highest priority) to 19 (lowest). gbart ignores it.

  • seed (int | None, default: 99) – Seed of the chains’ L’Ecuyer-CMRG RNG streams; None seeds from the clock and process ID. gbart ignores it: seed R directly with set.seed.

Notes

The R argument ntype (an internal device to compute the type-dependent defaults) is not exposed.

R documentation

title
-----

Generalized BART for continuous and binary outcomes

name
----

gbart

alias
-----

mc.gbart

keyword
-------

nonlinear

description
-----------

 BART is a Bayesian  sum-of-trees  model.
 For a numeric response  y , we have
 y = f(x) + \epsilon y = f(x) + e ,
 where  \epsilon \sim N(0,\sigma^2) 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.


usage
-----


 gbart(
       x.train, y.train,
       x.test=matrix(0,0,0), type='wbart',
       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,
       sigest=NA, sigdf=3, sigquant=0.90,
       k=2, power=2, base=0.95,
        %sigmaf=NA,
       lambda=NA, tau.num=c(NA, 3, 6)[ntype],  %tau.interval=0.9973,
       offset=NULL, w=rep(1, length(y.train)),
       ntree=c(200L, 50L, 50L)[ntype], numcut=100L,
        %ntree=200L, numcut=100L,
       ndpost=1000L, nskip=100L,  %keepevery=1L,
       keepevery=c(1L, 10L, 10L)[ntype],
       printevery=100L, transposed=FALSE,
       hostname=FALSE,
       mc.cores = 1L, ## mc.gbart only
       nice = 19L,    ## mc.gbart only
       seed = 99L     ## mc.gbart only
 )

 mc.gbart(
          x.train, y.train,
          x.test=matrix(0,0,0), type='wbart',
          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,
          sigest=NA, sigdf=3, sigquant=0.90,
          k=2, power=2, base=0.95,
           %sigmaf=NA,
          lambda=NA, tau.num=c(NA, 3, 6)[ntype],  %tau.interval=0.9973,
          offset=NULL, w=rep(1, length(y.train)),
           %ntree=200L, numcut=100L,
          ntree=c(200L, 50L, 50L)[ntype], numcut=100L,
          ndpost=1000L, nskip=100L,  %keepevery=1L,
          keepevery=c(1L, 10L, 10L)[ntype],
          printevery=100L, transposed=FALSE,
          hostname=FALSE,
          mc.cores = 2L, nice = 19L, seed = 99L
 )



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
     created if  q=2  where  q  is the number of levels of the
     factor.   gbart  will generate draws of  f(x)  for each
      x  which is a row of  x.train .

     y.train
    Continuous or binary dependent variable for training (in sample) data.
 If  y  is numeric, then a continuous BART model is fit (Normal errors).
 If  y  is binary (has only 0's and 1's), then a binary BART model
 with a probit link is fit by default: you can over-ride the default via the
 argument  type  to specify a logit BART model.


     x.test  Explanatory variables for test (out of sample)
    data. Should have same structure as  x.train .
     gbart  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.
     'wbart'  for continuous BART,  'pbart'  for probit BART or
     'lbart'  for logit BART.

   ntype  The integer equivalent of  type  where
    'wbart'  is 1,  '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.

     sigest  The prior for the error variance
    ( sigma^2 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
     sigest=NA  then the rough estimate will be the usual least squares
    estimator.  Otherwise the supplied value will be used.
    Not used if  y  is binary.


     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  sigest ) is placed at.  The closer the quantile is to 1, the more
    aggresive the fit will be as you are putting more prior weight on
    error standard deviations ( sigma ) less than the rough
    estimate.  Not used if  y  is binary.

     k  For numeric  y ,  k  is the number of prior
    standard deviations  E(Y|x) = f(x)  is away from +/-0.5.  For
    binary  y ,  k  is the number of prior standard deviations
     f(x)  is away from +/-3.  The bigger  k  is, the more
    conservative the fitting will be.

     power
    Power parameter for tree prior.


     base
    Base parameter for tree prior.


     %% \item{sigmaf}{
     %% The SD of \eqn{f}.  Not used if \eqn{y} is binary.
     %% }

     lambda
    The scale of the prior for the variance.  If  lambda  is zero,
      then the variance is to be considered fixed and known at the given
      value of  sigest .  Not used if  y  is binary.


   tau.num  The numerator in the  tau  definition, i.e.,
     tau=tau.num/(k*sqrt(ntree)) .
     %% \item{tau.interval}{
     %%   The width of the interval to scale the variance for the terminal
     %%   leaf values.  Only used if \eqn{y} is binary.}

     offset  Continous BART operates on  y.train  centered by
     offset  which defaults to  mean(y.train) .  With binary
    BART, the centering is  P(Y=1 | x) = F(f(x) + offset)  where
     offset  defaults to  F^{-1}(mean(y.train)) .  You can use
    the  offset  parameter to over-ride these defaults.

     w  Vector of weights which multiply the standard deviation.
    Not used if  y  is binary.

     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} i^th
    element gives the number of  c  used for the  i^{th} 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)  values are used.

     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.
     %% A \dQuote{draw} will consist of values of the error standard deviation (\eqn{\sigma}{sigma})
     %% and \eqn{f^*(x)}{f*(x)}
     %% at \eqn{x} = rows from the train(optionally) and test data, where \eqn{f^*}{f*} denotes
     %% the current draw of \eqn{f}.


     transposed
    When running  gbart  in parallel, it is more memory-efficient
    to transpose  x.train  and  x.test , if any, prior to
    calling  mc.gbart .


   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 a Bayesian MCMC method.
    At each MCMC interation, we produce a draw from the joint posterior
     (f,\sigma) | (x,y) (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) f*(x)  (and
     \sigma^* 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,  gbart
    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.gbart  runs multiple  gbart  threads in
    parallel,  mc.gbart  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 .



value
-----


     %% The \code{plot} method sets mfrow to c(1,2) and makes two plots.\cr
     %% The first plot is the sequence of kept draws of \eqn{\sigma}{sigma}
     %% including the burn-in draws.  Initially these draws will decline as BART finds fit
     %% and then level off when the MCMC has burnt in.\cr
     %% The second plot has \eqn{y} on the horizontal axis and posterior intervals for
     %% the corresponding \eqn{f(x)} on the vertical axis.

     gbart  returns an object of type  gbart  which is
    essentially a list.  % assigned class \sQuote{bart}.
    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^* f*  from the posterior of  f
    and each column corresponds to a row of x.train.
    The  (i,j)  value is  f^*(x) f*(x)  for the  i^{th} i\^th  kept draw of  f
    and the  j^{th} j\^th  row of x.train.
    Burn-in is dropped.


     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 sigma ) used in the prior.



seealso
-------


 pbart


examples
--------


 ##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)


 ##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))
hostname: Bool[ndarray, 'mc_cores'] | String[ndarray, 'mc_cores']

Per-chain hostname if fitted with hostname=True, else per-chain False.

prob_test: None | Float64[ndarray, 'ndpost/mc_cores m'] = None

Test-point success-probability draws (binary outcomes only).

mc.gbart with mc_cores > 1 forgets to combine the chains, leaving only the first chain’s draws.

prob_test_mean: None | Float64[ndarray, 'm'] = None

Posterior mean of prob_test.

prob_train: None | Float64[ndarray, 'ndpost/mc_cores n'] = None

Training-point success-probability draws (binary outcomes only).

mc.gbart with mc_cores > 1 forgets to combine the chains, leaving only the first chain’s draws.

prob_train_mean: None | Float64[ndarray, 'n'] = None

Posterior mean of prob_train.

sigma: Float64[ndarray, 'nskip+ndpost*keepevery'] | Float64[ndarray, 'nskip+ndpost*keepevery/mc_cores mc_cores'] | None = None

Error-SD draws, continuous outcomes only (per chain for mc.gbart).

One draw per MCMC iteration: burn-in and the thinned-away iterations are included.

varcount: Int32[ndarray, 'ndpost p']

Per-draw count of splits on each variable, summed over trees.

varcount_mean: Float64[ndarray, 'p']

Posterior mean of varcount per variable.

varprob: Float64[ndarray, 'ndpost p']

Per-draw probability assigned to each variable for splitting.

varprob_mean: Float64[ndarray, 'p']

Posterior mean of varprob per variable.

yhat_test: Float64[ndarray, 'ndpost m']

Test-point posterior function draws (latent scale for binary).

Always present: R’s cgbart allocates it unconditionally, so without test data it is an empty array rather than None (with the rows of the first chain only for mc.gbart, which combines the chains just when there is test data).

yhat_test_mean: Float64[ndarray, 'm'] | None = None

Posterior mean of yhat_test (continuous with test data only).

yhat_train: Float64[ndarray, 'ndpost n']

Training-point posterior function draws (latent scale for binary).

yhat_train_mean: Float64[ndarray, 'n'] | None = None

Posterior mean of yhat_train (continuous only).

LPML: float

Log pseudo-marginal likelihood; unstable for BART.

Always computed, even without burn-in. Miscomputed by R for binary mc.gbart fits with mc_cores > 1 (the chains’ probabilities are not combined before the computation).

ndpost: int

Number of posterior draws kept, after burn-in and thinning.

offset: float

Data centering value for the response (link scale for binary).

proc_time: ProcTime

Timing of the fit, from R’s proc.time.

rm_const: Int32[ndarray, '<=p']

0-based indices of the x_train columns kept (constant columns dropped).

mc.gbart with mc_cores=1 relabels the kept columns to 0 .. kept-1, losing which original columns were dropped.

sigma_mean: float | None = None

Mean of the first ndpost post-burn-in sigma draws (continuous only).

treedraws: TreeDraws

Sampled trees, as a per-variable cutpoint grid and the serialized ensemble.

predict(newdata, *, mc_cores=None, openmp=None, dodraws=None, nice=None)[source]

Compute predictions at new covariate points.

Python interface to R’s predict method for the fit, dispatched on the fit type. For continuous (‘wbart’) fits the result is the matrix of posterior latent-function draws (their mean with dodraws=False); for binary (‘pbart’/’lbart’) fits R returns a list, exposed here as a PredictBinary dict. Arguments left to None are omitted from the R call, so R computes its own defaults, described below.

Parameters:

  • newdata (Float64[ndarray, 'm p'] | DataFrame) – Covariates to predict at; rows are observations, with one column per kept x_train column (see rm_const). A dataframe’s factor columns are expanded into indicator columns.

  • mc_cores (int | None, default: None) – Number of OpenMP threads or forked R processes (see openmp) computing the predictions; default 1.

  • openmp (bool | None, default: None) – Whether mc_cores counts OpenMP threads rather than forked R processes; default whether BART was compiled with OpenMP.

  • dodraws (bool | None, default: None) – Whether to return the posterior draws (the default) rather than only their mean. ‘wbart’ fits only (the binary methods accept it but then crash summarizing the mean-only result).

  • nice (int | None, default: None) – Unix niceness of the forked processes, from 0 (highest priority) to 19 (lowest, the default); ignored unless forking.

Returns:

Float64[ndarray, 'ndpost m'] | Float64[ndarray, 'm'] | PredictBinary – The function draws at newdata for continuous fits (their mean with dodraws=False), or a PredictBinary dict for binary fits.

Notes

For mc.gbart fits with mc_cores > 1 that dropped constant columns, R miscounts the kept columns and fails to update the header of the serialized ensemble, so only the first chain’s draws are returned.

The R arguments mu (the method already fills it with the fit’s offset, and a second value would be a duplicate-argument error) and transposed (a pre-transposed newdata cannot pass the method’s own column-count check) are not exposed.