Related papers: Posterior contraction in group sparse logit models…
We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…
Sparse recovery in linear systems underpins applications from signal processing to high-dimensional regression. Sparse Bayesian Learning, grounded in the principle of automatic relevance determination (ARD), offers a practical Bayesian…
This paper considers generalized linear models in the presence of many controls. We lay out a general methodology to estimate an effect of interest based on the construction of an instrument that immunize against model selection mistakes…
Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods…
Most of the consistency analyses of Bayesian procedures for variable selection in regression refer to pairwise consistency, that is, consistency of Bayes factors. However, variable selection in regression is carried out in a given class of…
We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…
We consider Bayesian inference of sparse covariance matrices and propose a post-processed posterior. This method consists of two steps. In the first step, posterior samples are obtained from the conjugate inverse-Wishart posterior without…
We consider support recovery in the quadratic logistic regression setting - where the target depends on both p linear terms $x_i$ and up to $p^2$ quadratic terms $x_i x_j$. Quadratic terms enable prediction/modeling of higher-order effects…
Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This…
Longitudinal studies with binary or ordinal responses are widely encountered in various disciplines, where the primary focus is on the temporal evolution of the probability of each response category. Traditional approaches build from the…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
We focus on the increasingly important area of sparse regression problems where there are many variables and the effects of a large subset of these are negligible. This paper describes the construction of hierarchical prior distributions…
In the sparse normal means model, coverage of adaptive Bayesian posterior credible sets associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…
We study central limit theorems for linear statistics in high-dimensional Bayesian linear regression with product priors. Unlike the existing literature where the focus is on posterior contraction, we work under a non-contracting regime…
Penalized regression methods, such as $L_1$ regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is…
Consider a set of categorical variables where at least one of them is binary. The log-linear model that describes the counts in the resulting contingency table implies a specific logistic regression model, with the binary variable as the…
We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…
In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG…
Generalized linear models (GLMs) are routinely used for modeling relationships between a response variable and a set of covariates. The simple form of a GLM comes with easy interpretability, but also leads to concerns about model…
Categorical predictors are omnipresent in everyday regression practice: in fact, most regression data involve some categorical predictors, and this tendency is increasing in modern applications with more complex structures and larger data…