vb_lap_global

A variational Bayesian algorithm is proposed for multi-source heterogeneous models under the Laplace
Spike-and-Slab prior, enabling simultaneous variable selection for both homogeneous and #' heterogeneous covariates.

A Variational Bayesian algorithm for high-dimensional multi-source
heterogeneous linear models. More details have been written up in a paper
submitted to the journal Statistics in Medicine, and the details of variational
Bayesian methods can be found in Ray and Szabo (2021) <doi:10.1080/01621459.2020.1847121>.
It simultaneously performs parameter estimation and variable selection. The
algorithm supports two model settings: (1) local models, where variable selection
is only applied to homogeneous coefficients, and (2) global models, where variable
selection is also performed on heterogeneous coefficients. Two forms of
Spike-and-Slab priors are available: the Laplace distribution and the Gaussian
distribution as the Slab component.

Lu Luo

VBMS

Variational Bayesian Algorithm for Multi-Source Heterogeneous
Models

Huiqiong Li

vb_lap_global function

<dl><dt>X</dt>
<dd>Homogeneous covariates</dd>
<dt>Z</dt>
<dd>Heterogeneous covariates</dd>
<dt>Y</dt>
<dd>Response covariates</dd>
<dt>max_iter</dt>
<dd>Maximum number of iterations, Defaut:1000</dd>
<dt>tol</dt>
<dd>Algorithm convergence tolerance, Defaut:1e-6</dd>
<dt>a</dt>
<dd>A prior of Beta distribution, Defaut:1</dd>
<dt>b</dt>
<dd>A prior of Beta distribution, Defaut:10</dd>
<dt>lambda</dt>
<dd>A prior of Laplace distribution, Defaut:1</dd></dl>

Arguments

Global Laplace VB — vb_lap_global

<dl>

<dt>X</dt>
<dd>Homogeneous covariates</dd>


<dt>Z</dt>
<dd>Heterogeneous covariates</dd>


<dt>Y</dt>
<dd>Response covariates</dd>


<dt>max_iter</dt>
<dd>Maximum number of iterations, Defaut:1000</dd>


<dt>tol</dt>
<dd>Algorithm convergence tolerance, Defaut:1e-6</dd>


<dt>a</dt>
<dd>A prior of Beta distribution, Defaut:1</dd>


<dt>b</dt>
<dd>A prior of Beta distribution, Defaut:10</dd>


<dt>lambda</dt>
<dd>A prior of Laplace distribution, Defaut:1</dd>

</dl>

vb_lap_global: Global Laplace VB

Description

Usage

Value

Arguments