Related papers: Frequentist Asymptotics of Variational Laplace

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…

The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…

Gaussian variational inference and the Laplace approximation are popular alternatives to Markov chain Monte Carlo that formulate Bayesian posterior inference as an optimization problem, enabling the use of simple and scalable stochastic…

We study the asymptotic frequentist coverage of credible sets based on a novel Bayesian approach for a multiple linear regression model under variable selection. We initially ignore the issue of variable selection, which allows us to put a…

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…

Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…

Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…

We study the properties of variational Bayes approximations for exponential family models with missing values. It is shown that the iterative algorithm for obtaining the variational Bayesian estimator converges locally to the true value…

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…

Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…

Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs…

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…

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 introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and…

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…

Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…