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Bayesian low-rank matrix factorization techniques have become an essential tool for relational data analysis and matrix completion. A standard approach is to assign zero-mean Gaussian priors on the columns or rows of factor matrices to…
Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models…
Many modern statistical applications involve inference for complicated stochastic models for which the likelihood function is difficult or even impossible to calculate, and hence conventional likelihood-based inferential echniques cannot be…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
In environmental studies, realistic simulations are essential for understanding complex systems. Statistical emulation with Gaussian processes (GPs) in functional data models have become a standard tool for this purpose. Traditional…
Gaussian graphical models can capture complex dependency structures among variables. For such models, Bayesian inference is attractive as it provides principled ways to incorporate prior information and to quantify uncertainty through the…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…
Estimation of spatially-varying parameters for computationally expensive forward models governed by partial differential equations is addressed. A novel multiscale Bayesian inference approach is introduced based on deep probabilistic…
Multidimensional scaling (MDS) is widely used to reconstruct a low-dimensional representation of high-dimensional data while preserving pairwise distances. However, Bayesian MDS approaches based on Markov chain Monte Carlo (MCMC) face…
In second-order optimization, a potential bottleneck can be computing the Hessian matrix of the optimized function at every iteration. Randomized sketching has emerged as a powerful technique for constructing estimates of the Hessian which…
Variational inference methods have been shown to lead to significant improvements in the computational efficiency of approximate Bayesian inference in mixed multinomial logit models when compared to standard Markov-chain Monte Carlo (MCMC)…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…
Modern macroeconometrics often relies on time series models for which it is time-consuming to evaluate the likelihood function. We demonstrate how Bayesian computations for such models can be drastically accelerated by reweighting and…
In learned image compression, probabilistic models play an essential role in characterizing the distribution of latent variables. The Gaussian model with mean and scale parameters has been widely used for its simplicity and effectiveness.…
We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior…
Bayesian inverse problems highly rely on efficient and effective inference methods for uncertainty quantification (UQ). Infinite-dimensional MCMC algorithms, directly defined on function spaces, are robust under refinement of physical…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
While Bayesian methods are extremely popular in statistics and machine learning, their application to massive datasets is often challenging, when possible at all. Indeed, the classical MCMC algorithms are prohibitively slow when both the…