Related papers: Joint Variable Selection of both Fixed and Random …
A mean field variational Bayes approach to support vector machines (SVMs) using the latent variable representation on Polson & Scott (2012) is presented. This representation allows circumvention of many of the shortcomings associated with…
Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning…
We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed…
Identifying co-varying causal elements in very high dimensional feature space with internal structures, e.g., a space with as many as millions of linearly ordered features, as one typically encounters in problems such as whole genome…
The ability to manipulate complex systems, such as the brain, to modify specific outcomes has far-reaching implications, particularly in the treatment of psychiatric disorders. One approach to designing appropriate manipulations is to…
This paper deals with variable selection in multivariate linear regression model when the data are observations on a spatial domain being a grid of sites in $\mathbb{Z}^d$ with $d\geqslant 2$. We use a criterion that allows to characterize…
Spatial generalized linear mixed-effects models are popularly used to analyze spatially indexed univariate responses. However, with modern technology, it is common to observe vector-valued mixed-type responses, e.g., a combination of…
Varying coefficient models are useful in applications where the effect of the covariate might depend on some other covariate such as time or location. Various applications of these models often give rise to case-specific prior distributions…
Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…
Classification and probability estimation are fundamental tasks with broad applications across modern machine learning and data science, spanning fields such as biology, medicine, engineering, and computer science. Recent development of…
We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…
This work proposes a scalable probabilistic latent variable model based on Gaussian processes (Lawrence, 2004) in the context of multiple observation spaces. We focus on an application in astrophysics where data sets typically contain both…
Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…
In practical regression applications, multiple covariates are often measured, but not all may be associated with the response variable. Identifying and including only the relevant covariates in the model is crucial for improving prediction…
We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the…
This paper presents approaches to compute sparse solutions of Generalized Singular Value Problem (GSVP). The GSVP is regularized by $\ell_1$-norm and $\ell_q$-penalty for $0<q<1$, resulting in the $\ell_1$-GSVP and $\ell_q$-GSVP…
Gaussian process (GP) regression is a flexible, nonparametric approach to regression that naturally quantifies uncertainty. In many applications, the number of responses and covariates are both large, and a goal is to select covariates that…
Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design…
We consider Bayesian variable selection for binary outcomes under a probit link with a spike-and-slab prior on the regression coefficients. Motivated by the computational challenges encountered by Markov chain Monte Carlo (MCMC) samplers in…
Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly…