# Fits the SoftBart model Runs the Markov chain for the semiparametric Gaussian model [REMOVE_ME]$$ Y = r(X) +\epsilonY = r(X) + epsilon [REMOVE_ME_2]$$ and collects the output, where $r(x)$ is modeled using a soft BART model. ```r softbart(X, Y, X_test, hypers = NULL, opts = Opts(), verbose = TRUE) ``` ## Arguments - `X`: A matrix of training data covariates. - `Y`: A vector of training data responses. - `X_test`: A matrix of test data covariates - `hypers`: A list of hyperparameter values obtained from `Hypers` function - `opts`: A list of MCMC chain settings obtained from `Opts` function - `verbose`: If `TRUE`, progress of the chain will be printed to the console. ## Returns Returns a list with the following components: * `y_hat_train`: predicted values for the training data for each iteration of the chain. * `y_hat_test`: predicted values for the test data for each iteration of the chain. * `y_hat_train_mean`: predicted values for the training data, averaged over iterations. * `y_hat_test_mean`: predicted values for the test data, averaged over iterations. * `sigma`: posterior samples of the error standard deviations. * `sigma_mu`: posterior samples of `sigma_mu`, the standard deviation of the leaf node parameters. * `s`: posterior samples of `s`. * `alpha`: posterior samples of `alpha`. * `beta`: posterior samples of `beta`. * `gamma`: posterior samples of `gamma`. * `k`: posterior samples of `k = 0.5 / (sqrt(num_tree) * sigma_mu)` * `num_leaves_final`: the number of leaves for each tree at the final iteration. ## Description Runs the Markov chain for the semiparametric Gaussian model $$ Y = r(X) +\epsilonY = r(X) + epsilon $$ and collects the output, where $r(x)$ is modeled using a soft BART model. ## Examples ```r ## NOTE: SET NUMBER OF BURN IN AND SAMPLE ITERATIONS HIGHER IN PRACTICE num_burn <- 10 ## Should be ~ 5000 num_save <- 10 ## Should be ~ 5000 set.seed(1234) f_fried <- function(x) 10 * sin(pi * x[,1] * x[,2]) + 20 * (x[,3] - 0.5)^2 + 10 * x[,4] + 5 * x[,5] gen_data <- function(n_train, n_test, P, sigma) { X <- matrix(runif(n_train * P), nrow = n_train) mu <- f_fried(X) X_test <- matrix(runif(n_test * P), nrow = n_test) mu_test <- f_fried(X_test) Y <- mu + sigma * rnorm(n_train) Y_test <- mu_test + sigma * rnorm(n_test) return(list(X = X, Y = Y, mu = mu, X_test = X_test, Y_test = Y_test, mu_test = mu_test)) } ## Simiulate dataset sim_data <- gen_data(250, 100, 1000, 1) ## Fit the model fit <- softbart(X = sim_data$X, Y = sim_data$Y, X_test = sim_data$X_test, hypers = Hypers(sim_data$X, sim_data$Y, num_tree = 50, temperature = 1), opts = Opts(num_burn = num_burn, num_save = num_save, update_tau = TRUE)) ## Plot the fit (note: interval estimates are not prediction intervals, ## so they do not cover the predictions at the nominal rate) plot(fit) ## Look at posterior model inclusion probabilities for each predictor. plot(posterior_probs(fit)[["post_probs"]], col = ifelse(posterior_probs(fit)[["post_probs"]] > 0.5, scales::muted("blue"), scales::muted("green")), pch = 20) rmse(fit$y_hat_test_mean, sim_data$mu_test) rmse(fit$y_hat_train_mean, sim_data$mu) ```

softbart function