probe: Fitting PaRtitiOned empirical Bayes Ecm (PROBE) algorithm to...

In probe: Sparse High-Dimensional Linear Regression with PROBE

Fitting PaRtitiOned empirical Bayes Ecm (PROBE) algorithm to sparse high-dimensional linear models.

Description

A wrapper function for the all-at-once variant of the PROBE algorithm.

Usage

probe(Y, X, Z = NULL, ep = 0.1, maxit = 10000, Y_test = NULL, X_test = NULL, 
Z_test = NULL, verbose = FALSE, signal = NULL, eta_i = NULL, alpha = 0.05, 
plot_ind = FALSE, adj = 5)

Arguments

Y	The outcome variable.
X	An n x M matrix of sparse predictors variables.
Z	(optional) An n x p matrix or dataframe of other predictors not subjected to the sparsity assumption.
ep	Value against which to compare convergence criterion (default = 0.1).
maxit	Maximum number of iterations the algorithm will run for (default = 10000).
Y_test	(optional) Test Y data used plotting purposes only (doesn't impact results).
X_test	(optional) Test X data used plotting purposes only (doesn't impact results).
Z_test	(optional) Test Z data used plotting purposes only (doesn't impact results).
verbose	A logical (true/false) value whether to print algorithm iteration progress and summary quantities (default = FALSE).
signal	(optional) A vector of indicies of the true non-null coefficients. This is used to calculate the true and false discovery rates by iteration for simulated data. Used plotting purposes only (doesn't impact results).
eta_i	(optional) A vector of the true signal. This is used to calculate the MSE by iteration for simulated data. Used plotting purposes only (doesn't impact results).
alpha	(optional) significance level
plot_ind	A logical values (True/False) for whether to output plots on algorithm results and progress (default = FALSE)
adj	Bandwidth parameter for empirical Bayes E-step. The bandwidth will be equal to adj times Silverman's 'rule of thumb' (default = 2).

Value

A list including

beta_ast_hat MAP estimates of the regression coefficients (\beta^\ast),

beta_hat, beta_hat_var MAP estimates of the posterior expectation (beta_hat) and variance (beta_hat_var) of the prior mean (\beta) of the regression coefficients assuming \gamma=1,

gamma_hat the posterior expectation of the latent \gamma variables,

sigma2_est MAP estimate of the residual variance,

E_step full results of the final E_step,

Calb_mod results of first (\alpha_0) part of the M-step,

count the total number of iterations before convergence.

References

McLain, A. C., Zgodic, A., & Bondell, H. (2022). Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm. arXiv preprint arXiv:2209.08139..

See Also

predict_probe_func to obtain predictions, credible intervals and prediction intervals from PROBE.

Examples

### Example
data(Sim_data)
data(Sim_data_test)
attach(Sim_data)
attach(Sim_data_test)
alpha <- 0.05
plot_ind <- TRUE
adj <- 10

# Run the analysis. Y_test and X_test are included for plotting purposes only
full_res <- probe( Y = Y, X = X, Y_test = Y_test, 
X_test = X_test, alpha = alpha, plot_ind = plot_ind, adj = adj)

# Predicting for test data
pred_res <- predict_probe_func(full_res, X = X_test)
sqrt(mean((Y_test - pred_res$Pred)^2))

# Estimate of the residual variance and true value
full_res$sigma2_est
sigma2_tr

# RMSE of estimated beta coefficients
beta_ast_est <- full_res$beta_ast_hat
sqrt(mean((beta_ast_est - beta_tr)^2))

# Posterior expectation of gamma by true
gamma_est <- full_res$E_step$gamma
sum(gamma_est)
sum(gamma_est[beta_tr>0])

### Examples that incorporate additional covariate data (Z) 
### not subjected to the sparsity assumption available on Github.

probe documentation built on Nov. 2, 2023, 5:49 p.m.