Related papers: Multi-Goal Prior Selection: A Way to Reconcile Bay…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

Sparse modeling for signal processing and machine learning has been at the focus of scientific research for over two decades. Among others, supervised sparsity-aware learning comprises two major paths paved by: a) discriminative methods and…

In algorithmically fair prediction problems, a standard goal is to ensure the equality of fairness metrics across multiple overlapping groups simultaneously. We reconsider this standard fair classification problem using a probabilistic…

Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…

This paper proposes the asymmetric linear double autoregression, which jointly models the conditional mean and conditional heteroscedasticity characterized by asymmetric effects. A sufficient condition is established for the existence of a…

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…

Bayesian methods are increasingly applied in these days in the theory and practice of statistics. Any Bayesian inference depends on a likelihood and a prior. Ideally one would like to elicit a prior from related sources of information or…

In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first…

Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach…

Machine learning algorithms may have disparate impacts on protected groups. To address this, we develop methods for Bayes-optimal fair classification, aiming to minimize classification error subject to given group fairness constraints. We…

Meta-analysis is widely used to integrate results from multiple experiments to obtain generalized insights. Since meta-analysis datasets are often heteroscedastic due to varying subgroups and temporal heterogeneity arising from experiments…

This paper introduces Bayesian frameworks for tackling various aspects of multi-criteria decision-making (MCDM) problems, leveraging a probabilistic interpretation of MCDM methods and challenges. By harnessing the flexibility of Bayesian…

The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…

We establish concentration rates for estimation of treatment effects in experiments that incorporate prior sources of information -- such as past pilots, related studies, or expert assessments -- whose external validity is uncertain. Each…

Dealing with uncertainty is essential for efficient reinforcement learning. There is a growing literature on uncertainty estimation for deep learning from fixed datasets, but many of the most popular approaches are poorly-suited to…

Bayesian model selection poses two main challenges: the specification of parameter priors for all models, and the computation of the resulting Bayes factors between models. There is now a large literature on automatic and objective…

The interpretation of data in terms of multi-parameter models of new physics, using the Bayesian approach, requires the construction of multi-parameter priors. We propose a construction that uses elements of Bayesian reference analysis. Our…

We introduce non-stationary Mat\'ern field priors with stochastic partial differential equations, and construct correlation length-scaling with hyperpriors. We model both the hyperprior and the Mat\'ern prior as continuous-parameter random…

Variants of fluctuation theorems recently discovered in the statistical mechanics of non-equilibrium processes may be used for the efficient determination of high-dimensional integrals as typically occurring in Bayesian data analysis. In…

Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…