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Related papers: Horseshoe Priors and MDP

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We present a new algorithm based on posterior sampling for learning in constrained Markov decision processes (CMDP) in the infinite-horizon undiscounted setting. The algorithm achieves near-optimal regret bounds while being advantageous…

Machine Learning · Computer Science 2023-09-28 Danil Provodin , Pratik Gajane , Mykola Pechenizkiy , Maurits Kaptein

In this article densities (and their derivatives) of subordinators and inverse subordinators are considered. Under minor restrictions, generally milder than the existing in the literature, using a useful modification of the saddle point…

Probability · Mathematics 2024-02-12 Giacomo Ascione , Mladen Savov , Bruno Toaldo

We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior…

Statistics Theory · Mathematics 2021-02-12 Qiyang Han

In this paper, the use of the Generalized Beta Mixture (GBM) and Horseshoe distributions as priors in the Bayesian Compressive Sensing framework is proposed. The distributions are considered in a two-layer hierarchical model, making the…

Information Theory · Computer Science 2014-11-11 Zahra Sabetsarvestani , Hamidreza Amindavar

The large variety of functions encountered in nonparametric statistics, calls for methods that are flexible enough to achieve optimal or near-optimal performance over a wide variety of functional classes, such as Besov balls, as well as…

Statistics Theory · Mathematics 2026-02-04 Sergios Agapiou , Ismaël Castillo , Paul Egels

Precision matrix estimation in a multivariate Gaussian model is fundamental to network estimation. Although there exist both Bayesian and frequentist approaches to this, it is difficult to obtain good Bayesian and frequentist properties…

Statistics Theory · Mathematics 2022-01-19 Ksheera Sagar , Sayantan Banerjee , Jyotishka Datta , Anindya Bhadra

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…

Statistics Theory · Mathematics 2012-12-27 Anirban Bhattacharya , Debdeep Pati , Natesh S. Pillai , David B. Dunson

We present a locally adaptive nonparametric curve fitting method that operates within a fully Bayesian framework. This method uses shrinkage priors to induce sparsity in order-k differences in the latent trend function, providing a…

Methodology · Statistics 2017-02-10 James R. Faulkner , Vladimir N. Minin

Prior choice can strongly influence Bayesian Dirichlet ARMA (B-DARMA) inference for compositional time-series. Using simulations with (i) correct lag order, (ii) overfitting, and (iii) underfitting, we assess five priors:…

Methodology · Statistics 2025-07-08 Harrison Katz , Liz Medina , Robert E. Weiss

Consider a situation of analyzing high-dimensional count data containing an excess of near-zero counts with a small number of moderate or large counts. Assuming that the observations are modeled by a Poisson distribution, we are interested…

Statistics Theory · Mathematics 2025-11-27 Sayantan Paul , Arijit Chakrabarti

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…

Statistics Theory · Mathematics 2014-01-22 Anirban Bhattacharya , Debdeep Pati , Natesh S. Pillai , David B. Dunson

Bayesian hierarchical models are commonly employed for inference in count datasets, as they account for multiple levels of variation by incorporating prior distributions for parameters at different levels. Examples include Beta-Binomial,…

Methodology · Statistics 2024-11-04 Yuexi Wang , Nicholas G. Polson

Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection---even choosing the number of nodes---remains an open question. In…

Machine Learning · Statistics 2017-05-31 Soumya Ghosh , Finale Doshi-Velez

The Horseshoe is a widely used and popular continuous shrinkage prior for high-dimensional Bayesian linear regression. Recently, regularized versions of the Horseshoe prior have also been introduced in the literature. Various Gibbs sampling…

Statistics Theory · Mathematics 2021-01-05 Suman K. Bhattacharya , Kshitij Khare , Subhadip Pal

This paper studies the sparse normal mean models under the empirical Bayes framework. We focus on the mixture priors with an atom at zero and a density component centered at a data driven location determined by maximizing the marginal…

Methodology · Statistics 2017-02-20 Xianyang Zhang , Anirban Bhattacharya

In the Bayes paradigm and for a given loss function, we propose the construction of a new type of posterior distributions, that extends the classical Bayes one, for estimating the law of an $n$-sample. The loss functions we have in mind are…

Statistics Theory · Mathematics 2024-01-05 Yannick Baraud

We revisit the problem of simultaneously testing the means of $n$ independent normal observations under sparsity. We take a Bayesian approach to this problem by introducing a scale-mixture prior known as the normal-beta prime (NBP) prior.…

Methodology · Statistics 2020-07-29 Ray Bai , Malay Ghosh

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.…

Methodology · Statistics 2019-07-23 Yunfan Li , Jyotishka Datta , Bruce A. Craig , Anindya Bhadra

Since the advent of the horseshoe priors for regularization, global-local shrinkage methods have proved to be a fertile ground for the development of Bayesian methodology in machine learning, specifically for high-dimensional regression and…

Methodology · Statistics 2019-11-25 Anindya Bhadra , Jyotishka Datta , Yunfan Li , Nicholas G. Polson

We continue the development, started in of the asymptotic description of certain stochastic neural networks. We use the Large Deviation Principle (LDP) and the good rate function H announced there to prove that H has a unique minimum mu_e,…

Probability · Mathematics 2014-07-10 Olivier Faugeras , James MacLaurin