m_step_regression

A wrapper function providing the quantities related to the M-step for \(\alpha_0\) and \(\sigma^2\).

Implements an efficient and powerful Bayesian approach for sparse high-dimensional linear regression. It uses minimal prior assumptions on the parameters through plug-in empirical Bayes estimates of hyperparameters. An efficient Parameter-Expanded Expectation-Conditional-Maximization (PX-ECM) algorithm estimates maximum a posteriori (MAP) values of regression parameters and variable selection probabilities. The PX-ECM results in a robust computationally efficient coordinate-wise optimization, which adjusts for the impact of other predictor variables. The E-step is motivated by the popular two-group approach to multiple testing. The result is a PaRtitiOned empirical Bayes Ecm (PROBE) algorithm applied to sparse high-dimensional linear regression, implemented using one-at-a-time or all-at-once type optimization. More information can be found in McLain, Zgodic, and Bondell (2022) <arXiv:2209.08139>.

Alexander McLain

probe

Sparse High-Dimensional Linear Regression with PROBE

Anja Zodiac

m_step_regression function

<dl><dt>Y</dt>
<dd>A matrix containing the outcome <code>Y</code></dd>
<dt>W</dt>
<dd>Quantity \(E(W_0)\) as outlined in citation, output from W_update_fun</dd>
<dt>W2</dt>
<dd>Quantity \(E(W^2_0)\) as outlined in citation, output from W_update_fun</dd>
<dt>Z</dt>
<dd>A matrix or dataframe of other predictors to account for</dd>
<dt>a</dt>
<dd>(optional) parameter for changing the hyperparameter \(a\) (default, \(a=-3/2\) uses \(n-2\) as denominator for MAP of \(\sigma^2\))</dd>
<dt>Int</dt>
<dd>(optional) Logical - should an intercept be used?</dd></dl>

Arguments

Function for fitting the initial part of the M-step — m_step_regression

<dl>

<dt>Y</dt>
<dd>A matrix containing the outcome <code>Y</code></dd>


<dt>W</dt>
<dd>Quantity \(E(W_0)\) as outlined in citation, output from W_update_fun</dd>


<dt>W2</dt>
<dd>Quantity \(E(W^2_0)\) as outlined in citation, output from W_update_fun</dd>


<dt>Z</dt>
<dd>A matrix or dataframe of other predictors to account for</dd>


<dt>a</dt>
<dd>(optional) parameter for changing the hyperparameter \(a\) (default, \(a=-3/2\) uses \(n-2\) as denominator for MAP of \(\sigma^2\))</dd>


<dt>Int</dt>
<dd>(optional) Logical - should an intercept be used?</dd>

</dl>

m_step_regression: Function for fitting the initial part of the M-step

Description

Usage

Value

Arguments

References