Performs variable selection by cross-validating over the three threshold-based procedures outlined in Bleich et al. (2013) and selecting the single procedure that returns the lowest cross-validation RMSE.

```
var_selection_by_permute_cv(bart_machine, k_folds = 5,
num_reps_for_avg = 5, num_permute_samples = 100,
num_trees_for_permute = 20, alpha = 0.05, num_trees_pred_cv = 50)
```

bart_machine

An object of class ``bartMachine''.

k_folds

Number of folds to be used in cross-validation.

num_reps_for_avg

Number of replicates to over over to for the BART model's variable inclusion proportions.

num_permute_samples

Number of permutations of the response to be made to generate the ``null'' permutation distribution.

num_trees_for_permute

Number of trees to use in the variable selection procedure. As with `investigate_var_importance`

, a small number of trees should be used to force variables to compete for entry into the model. Note that this number is used to estimate both the ``true'' and ``null'' variable inclusion proportions.

alpha

Cut-off level for the thresholds.

num_trees_pred_cv

Number of trees to use for prediction on the hold-out portion of each fold. Once variables have been selected using the training portion of each fold, a new model is built using only those variables with `num_trees_pred_cv`

trees in the sum-of-trees model. Forecasts for the holdout sample are made using this model. A larger number of trees is recommended to exploit the full forecasting power of BART.

Returns a list with the following components:

The name of the best variable selection procedure, as chosen via cross-validation.

The variables chosen by the `best_method`

above.

See Bleich et al. (2013) for a complete description of the procedures outlined above as well as the corresponding vignette for a brief summary with examples.

J Bleich, A Kapelner, ST Jensen, and EI George. Variable Selection Inference for Bayesian Additive Regression Trees. ArXiv e-prints, 2013.

Adam Kapelner, Justin Bleich (2016). bartMachine: Machine Learning with Bayesian Additive Regression Trees. Journal of Statistical Software, 70(4), 1-40. doi:10.18637/jss.v070.i04

# NOT RUN { #generate Friedman data set.seed(11) n = 150 p = 100 ##95 useless predictors X = data.frame(matrix(runif(n * p), ncol = p)) y = 10 * sin(pi* X[ ,1] * X[,2]) +20 * (X[,3] -.5)^2 + 10 * X[ ,4] + 5 * X[,5] + rnorm(n) ##build BART regression model (not actually used in variable selection) bart_machine = bartMachine(X, y) #variable selection via cross-validation var_sel_cv = var_selection_by_permute_cv(bart_machine, k_folds = 3) print(var_sel_cv$best_method) print(var_sel_cv$important_vars_cv) # } # NOT RUN { # }