Related papers: Incorporating prior information and borrowing info…
High-dimensional data often arise from clinical genomics research to infer relevant predictors of a particular trait. A way to improve the predictive performance is to include information on the predictors derived from prior knowledge or…
Recently, a number of mostly $\ell_1$-norm regularized least squares type deterministic algorithms have been proposed to address the problem of \emph{sparse} adaptive signal estimation and system identification. From a Bayesian perspective,…
In this work, we offer a thorough analytical investigation into the role of shared hyperparameters in a hierarchical Bayesian model, examining their impact on information borrowing and posterior inference. Our approach is rooted in a…
Seemingly unrelated regression is a natural framework for regressing multiple correlated responses on multiple predictors. The model is very flexible, with multiple linear regression and covariance selection models being special cases.…
Bounded continuous responses -- such as proportions -- arise frequently in diverse scientific fields including climatology, biostatistics, and finance. Beta regression is a widely adopted framework for modeling such data, due to the…
Sparse regression problems, where the goal is to identify a small set of relevant predictors, often require modeling not only main effects but also meaningful interactions through other variables. While the pliable lasso has emerged as a…
In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity,…
Predictive inference in the sparse Gaussian sequence model has received considerably less attention than its non-sparse, finite-sample counterpart. Existing work has largely been confined to discrete mixture priors. In this paper, we study…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
Bayesian fused lasso is one of the sparse Bayesian methods, which shrinks both regression coefficients and their successive differences simultaneously. In this paper, we propose a Bayesian fused lasso modeling via horseshoe prior. By…
Modeling of the dependence structure across heterogeneous data is crucial for Bayesian inference since it directly impacts the borrowing of information. Despite the extensive advances over the last two decades, most available proposals…
Frequentist robust variable selection has been extensively investigated in high-dimensional regression. Despite success, developing the corresponding statistical inference procedures remains a challenging task. Recently, tackling this…
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
In this paper, we use augmented the hierarchical latent variable model to model multi-period time series, where the dynamics of time series are governed by factors or trends in multiple periods. Previous methods based on stacked recurrent…
We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…
We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed…
Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address…
The horseshoe prior has proven to be a noteworthy alternative for sparse Bayesian estimation, but has previously suffered from two problems. First, there has been no systematic way of specifying a prior for the global shrinkage…
We study variable selection (also called support recovery) in high-dimensional sparse linear regression when one has external information on which variables are likely to be associated with the response. Consistent recovery is only possible…