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Penalized linear regression is of fundamental importance in high-dimensional statistics and has been routinely used to regress a response on a high-dimensional set of predictors. In many scientific applications, there exists external…

In many regression settings the unknown coefficients may have some known structure, for instance they may be ordered in space or correspond to a vectorized matrix or tensor. At the same time, the unknown coefficients may be sparse, with…

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…

In this paper we analyze, for a model of linear regression with gaussian covariates, the performance of a Bayesian estimator given by the mean of a log-concave posterior distribution with gaussian prior, in the high-dimensional limit where…

One of the most criticized features of Bayesian statistics is the fact that credible intervals, especially when open likelihoods are involved, may strongly depend on the prior shape and range. Many analyses involving open likelihoods are…

We develop a data-driven algorithm for automatically selecting the regularisation parameter in Bayesian inversion under random tree Besov priors. One of the key challenges in Bayesian inversion is the construction of priors that are both…

Traditional approaches to Bayes net structure learning typically assume little regularity in graph structure other than sparseness. However, in many cases, we expect more systematicity: variables in real-world systems often group into…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

Neural networks (NNs) are primarily developed within the frequentist statistical framework. Nevertheless, frequentist NNs lack the capability to provide uncertainties in the predictions, and hence their robustness can not be adequately…

Bayesian model selection procedures based on nonlocal alternative prior densities are extended to ultrahigh dimensional settings and compared to other variable selection procedures using precision-recall curves. Variable selection…

Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However,…

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…

We discuss Bayesian nonparametric procedures for the regression analysis of compositional responses, that is, data supported on a multivariate simplex. The procedures are based on a modified class of multivariate Bernstein polynomials and…

We propose and develop a Bayesian plaid model for biclustering that accounts for the prior dependency between genes (and/or conditions) through a stochastic relational graph. This work is motivated by the need for improved understanding of…

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…

Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems.…

Substantial research on structured sparsity has contributed to analysis of many different applications. However, there have been few Bayesian procedures among this work. Here, we develop a Bayesian model for structured sparsity that uses a…

In this work we apply the methodology of integral priors to handle Bayesian model selection in binomial regression models with a general link function. These models are very often used to investigate associations and risks in…

Skewed generalizations of the normal distribution have been a topic of great interest in the statistics community due to their diverse applications across several domains. One of the most popular skew normal distributions, due to its…

This paper develops a class of Bayesian non- and semiparametric methods for estimating regression curves and surfaces. The main idea is to model the regression as locally linear, and then place suitable local priors on the local parameters.…