LRQVB (version 1.0.0)

vbms: Low Rank Correction Variational Bayesian Algorithm for Multi-Source Heterogeneous Models.

Description

This package implements a variational Bayesian algorithm for high-dimensional multi-source quantile heterogeneous linear models. 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 parameter estimation are output: one is the standard variational #' Bayesian estimation, and the other is the variational Bayesian estimation corrected with low-rank adjustment.

Usage

vbms(X, Z, y, global, tau, eps = 0.001)

Value

mu_hom

The mean of the homogeneous coefficients

lr_mu_hom

The low rank correction estimation of homogeneous coefficients

sigma_hom

The variance of homogeneous coefficients

gamma_hom

Selection indicators for homogeneous coefficients

mu_het

The mean of the heterogeneous coefficients

lr_mu_het

The low rank correction estimation of heterogeneous coefficients

sigma_het

The variance of heterogeneous coefficients

gamma_het

Selection indicators for heterogeneous coefficients (NULL for local models)

Arguments

X

Homogeneous covariates

Z

Heterogeneous covariates

y

Response covariates

global

Indicates whether variable selection is required for het coefficients, if TRUE, Variable selection will be made for het coefficients.

tau

Quantile Levels

eps

Algorithm convergence tolerance, Defaut:1e-3

Examples

# Simulate multi-source heterogeneous data
n <- 50  # number of samples per source
K <- 3   # number of sources
p <- 100  # number of homogeneous covariates
q <- 5    # number of heterogeneous covariates
tau <- 0.5

set.seed(1)
theta <- matrix(c(c(-1,0.5,1,-0.5,2),rep(0,p-5)), ncol = 1)
beta <- matrix(1, nrow = q, ncol = K)
for (k in 1:K) {
  beta[,k] <- matrix(c(rep(log(k+1),5),rep(0,q-5)), ncol = 1)
}

zdata <- MASS::mvrnorm(K*n, rep(0,q), diag(q))
Z <- array(data=zdata,dim=c(n,q,K))
xdata <- MASS::mvrnorm(K*n, rep(0,p), diag(p))
X <- array(data=xdata,dim=c(n,p,K))
Y <- matrix(0, nrow = n, ncol = K)

for (k in 1:K) {
  Y[,k] <- MASS::mvrnorm(1, X[,,k]%*%theta+Z[,,k]%*%beta[,k], diag(n))
}

# Fit local model with Laplace prior
res <- vbms(X, Z, Y, global=FALSE, tau=tau)

# View results
print(head(res$mu_hom))      # Homogeneous coefficients mean
print(head(res$lr_mu_hom))      # Low rank correction estimation
print(head(res$gamma_hom))   # Homogeneous variable selection
print(res$mu_het)            # Heterogeneous coefficients mean