# Variational Bayesian Algorithm for Multi-Source Heterogeneous Models. This package implements a variational Bayesian algorithm for high-dimensional multi-source 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 Spike-and-Slab priors are available: the #' Laplace distribution and the Gaussian distribution as the Slab component. ```r vbms( X, Z, Y, global, prior, max_iter = 1000, tol = 1e-06, a = 1, b = 10, lambda = 1 ) ``` ## 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. - `prior`: Forms of Slab distribution in Spike-and-Slab prior, "laplace" or "gauss". - `max_iter`: Maximum number of iterations, Defaut:1000 - `tol`: Algorithm convergence tolerance, Defaut:1e-6 - `a`: A prior of Beta distribution, Defaut:1 - `b`: A prior of Beta distribution, Defaut:10 - `lambda`: A prior of Laplace distribution, Defaut:1 ## Returns - **mu_hom**: The mean of the homogeneous coefficients - **sigma_hom**: The variance of homogeneous coefficients - **gamma_hom**: Selection indicators for homogeneous coefficients - **mu_het**: The mean of the heterogeneous coefficients - **sigma_het**: The variance of heterogeneous coefficients - **gamma_het**: Selection indicators for heterogeneous coefficients (NULL for local models) ## Examples ```r # 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 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, prior='laplace') # View results print(head(res$mu_hom)) # Homogeneous coefficients mean print(head(res$gamma_hom)) # Homogeneous variable selection print(res$mu_het) # Heterogeneous coefficients mean ```

vbms function