Related papers: Posterior contraction in sparse Bayesian factor mo…

Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…

We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…

In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity,…

This paper considers the posterior contraction of non-parametric Bayesian inference on non-homogeneous Poisson processes. We consider the quality of inference on a rate function $\lambda$, given non-identically distributed realisations,…

In the Bayesian literature on model comparison, Bayes factors play the leading role. In the classical statistical literature, model selection criteria are often devised used cross-validation ideas. Amalgamating the ideas of Bayes factor and…

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…

Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…

We consider Bayesian inference of banded covariance matrices and propose a post-processed posterior. The post-processing of the posterior consists of two steps. In the first step, posterior samples are obtained from the conjugate…

Recent advances in engineering technologies have enabled the collection of a large number of longitudinal features. This wealth of information presents unique opportunities for researchers to investigate the complex nature of diseases and…

We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…

Factor Analysis is a popular method for modeling dependence in multivariate data. However, determining the number of factors and obtaining a sparse orientation of the loadings are still major challenges. In this paper, we propose a…

We propose a Machine Learning approach for optimal macroeconomic density forecasting in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is general enough to encompass specific forecasting…

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…

Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…

There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…

Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…

This work addresses the problem of high-dimensional classification by exploring the generalized Bayesian logistic regression method under a sparsity-inducing prior distribution. The method involves utilizing a fractional power of the…

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…

We study posterior contraction behaviors for parameters of interest in the context of Bayesian mixture modeling, where the number of mixing components is unknown while the model itself may or may not be correctly specified. Two…