Related papers: Variational Bernstein-von Mises theorem with incre…
The Bayesian estimation of GARCH-family models has been typically addressed through Monte Carlo sampling. Variational Inference is gaining popularity and attention as a robust approach for Bayesian inference in complex machine learning…
The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from…
Approximate Bayesian inference for models with computationally expensive, black-box likelihoods poses a significant challenge, especially when the posterior distribution is complex. Many inference methods struggle to explore the parameter…
Semiparametric mixture models are parametric models with latent variables. They are defined kernel, $p_\theta(x | z)$, where z is the unknown latent variable, and $\theta$ is the parameter of interest. We assume that the latent variables…
The Variational Bayesian method (VB) is used to solve the probability distributions of latent variables with the minimum free energy criterion. This criterion is not easy to understand, and the computation is complex. For these reasons,…
Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL)…
The major goal of this paper is to study the second order frequentist properties of the marginal posterior distribution of the parametric component in semiparametric Bayesian models, in particular, a second order semiparametric…
Non-linear hierarchical models are commonly used in many disciplines. However, inference in the presence of non-nested effects and on large datasets is challenging and computationally burdensome. This paper provides two contributions to…
Optimal data detection in massive multiple-input multiple-output (MIMO) systems often requires prohibitively high computational complexity. A variety of detection algorithms have been proposed in the literature, offering different…
Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…
We continue the investigation of Bernstein-von Mises theorems for nonparametric Bayes procedures from [Ann. Statist. 41 (2013) 1999-2028]. We introduce multiscale spaces on which nonparametric priors and posteriors are naturally defined,…
Bernstein-von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete…
One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation…
Varying coefficient models are popular for estimating nonlinear regression functions in functional data models. Their Bayesian variants have received limited attention in large data applications, primarily due to prohibitively slow…
Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…
Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…
In a smooth semi-parametric model, the marginal posterior distribution for a finite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of any efficient point-estimator. The assertion…
Variational Bayesian Monte Carlo (VBMC) is a recently introduced framework that uses Gaussian process surrogates to perform approximate Bayesian inference in models with black-box, non-cheap likelihoods. In this work, we extend VBMC to deal…
Markov Chain Monte Carlo (MCMC), Laplace approximation (LA) and variational inference (VI) methods are popular approaches to Bayesian inference, each with trade-offs between computational cost and accuracy. However, a theoretical…
We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing tail,…