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Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…

Machine Learning · Statistics 2023-12-29 Tim G. J. Rudner , Zonghao Chen , Yee Whye Teh , Yarin Gal

A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…

Computation · Statistics 2019-11-21 Xuejun Yu , David J. Nott , Minh-Ngoc Tran , Nadja Klein

Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…

Machine Learning · Statistics 2026-02-27 Arsalan Jawaid , Abdullah Karatas , Jörg Seewig

We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…

Methodology · Statistics 2025-09-16 Gregor Zens , Mark F. J. Steel

We show that Bayesian inference, like that used in statistical mechanics, can guide the systematic construction of Fourier dark-field methods for localizing periodicity in near-field (e.g. scanning-tunneling and electron-phase-contrast)…

Statistical Mechanics · Physics 2016-08-31 P. Fraundorf

We challenge the longstanding assumption that the mean-field approximation for variational inference in Bayesian neural networks is severely restrictive, and show this is not the case in deep networks. We prove several results indicating…

Machine Learning · Computer Science 2021-03-11 Sebastian Farquhar , Lewis Smith , Yarin Gal

We consider the problem of estimating complex statistical latent variable models using variational Bayes methods. These methods are used when exact posterior inference is either infeasible or computationally expensive, and they approximate…

Methodology · Statistics 2025-02-28 David Gunawan , David Nott , Robert Kohn

We introduce a flexible empirical Bayes approach for fitting Bayesian generalized linear models. Specifically, we adopt a novel mean-field variational inference (VI) method and the prior is estimated within the VI algorithm, making the…

Machine Learning · Statistics 2026-01-30 Dongyue Xie , Wanrong Zhu , Matthew Stephens

Sparse variational approximations are popular methods for scaling up inference and learning in Gaussian processes to larger datasets. For $N$ training points, exact inference has $O(N^3)$ cost; with $M \ll N$ features, state of the art…

Machine Learning · Statistics 2024-04-15 Talay M Cheema , Carl Edward Rasmussen

How can one perform Bayesian inference on stochastic simulators with intractable likelihoods? A recent approach is to learn the posterior from adaptively proposed simulations using neural network-based conditional density estimators.…

Machine Learning · Computer Science 2019-05-21 David S. Greenberg , Marcel Nonnenmacher , Jakob H. Macke

Bayesian synthetic likelihood is a widely used approach for conducting Bayesian analysis in complex models where evaluation of the likelihood is infeasible but simulation from the assumed model is tractable. We analyze the behaviour of the…

Statistics Theory · Mathematics 2026-04-17 David T. Frazier , Christopher Drovandi , David J. Nott

We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the…

Machine Learning · Computer Science 2024-07-24 Marvin Schmitt , Desi R. Ivanova , Daniel Habermann , Ullrich Köthe , Paul-Christian Bürkner , Stefan T. Radev

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…

Computation · Statistics 2016-04-27 Joseph B. Nagel , Bruno Sudret

Penalized B-splines are routinely used in additive models to describe smooth changes in a response with quantitative covariates. It is typically done through the conditional mean in the exponential family using generalized additive models…

Methodology · Statistics 2020-05-12 Philippe Lambert

Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…

Statistics Theory · Mathematics 2009-08-25 Ao Yuan

Bayesian and frequentist inference are two fundamental paradigms in statistical estimation. Bayesian methods treat hypotheses as random variables, incorporating priors and updating beliefs via Bayes' theorem, whereas frequentist methods…

Machine Learning · Computer Science 2025-02-18 Sarthak Mittal , Yoshua Bengio , Nikolay Malkin , Guillaume Lajoie

The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes…

Machine Learning · Computer Science 2024-12-17 Weibin Chen , Azhir Mahmood , Michel Tsamados , So Takao

While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…

Machine Learning · Computer Science 2012-07-02 Max Welling , Sridevi Parise

We provide a general solution to a fundamental open problem in Bayesian inference, namely poor uncertainty quantification, from a frequency standpoint, of Bayesian methods in misspecified models. While existing solutions are based on…

Methodology · Statistics 2023-02-14 David T. Frazier , Robert Kohn , Christopher Drovandi , David Gunawan

We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…

Statistics Theory · Mathematics 2009-08-26 A. W. van der Vaart , J. H. van Zanten