Related papers: Bayesian generalized fused lasso modeling via NEG …

We consider the problem of learning a structured multi-task regression, where the output consists of multiple responses that are related by a graph and the correlated response variables are dependent on the common inputs in a sparse but…

The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…

We consider penalized regression models under a unified framework where the particular method is determined by the form of the penalty term. We propose a fully Bayesian approach that incorporates both sparse and dense settings and show how…

In this paper, we introduce a new sparsity-promoting prior, namely, the "normal product" prior, and develop an efficient algorithm for sparse signal recovery under the Bayesian framework. The normal product distribution is the distribution…

rdering of regression or classification coefficients occurs in many real-world applications. Fused Lasso exploits this ordering by explicitly regularizing the differences between neighboring coefficients through an $\ell_1$ norm…

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…

Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

Sparsity of the solution of a linear regression model is a common requirement, and many prior distributions have been designed for this purpose. A combination of the sparsity requirement with smoothness of the solution is also common in…

We study the theoretical properties of the fused lasso procedure originally proposed by \cite{tibshirani2005sparsity} in the context of a linear regression model in which the regression coefficient are totally ordered and assumed to be…

The paper addresses joint sparsity selection in the regression coefficient matrix and the error precision (inverse covariance) matrix for high-dimensional multivariate regression models in the Bayesian paradigm. The selected sparsity…

The lasso and elastic net linear regression models impose a double-exponential prior distribution on the model parameters to achieve regression shrinkage and variable selection, allowing the inference of robust models from large data sets.…

In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the…

This work considers variational Bayesian inference as an inexpensive and scalable alternative to a fully Bayesian approach in the context of sparsity-promoting priors. In particular, the priors considered arise from scale mixtures of Normal…

Our goal is to develop a Bayesian model averaging technique in linear regression models that accommodates heavier tailed error densities than the normal distribution. Motivated by the use of the Huber loss function in the presence of…

The Bayesian lasso is well-known as a Bayesian alternative for Lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be…

Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…

Functional brain networks are well described and estimated from data with Gaussian Graphical Models (GGMs), e.g. using sparse inverse covariance estimators. Comparing functional connectivity of subjects in two populations calls for…

We propose a method to fuse posterior distributions learned from heterogeneous datasets. Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors and proceeds using a simple…