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Gaussian variational approximations are widely used for summarizing posterior distributions in Bayesian models, especially in high-dimensional settings. However, a drawback of such approximations is the inability to capture skewness or more…

Methodology · Statistics 2026-04-02 Lucas Kock , Linda S. L. Tan , Prateek Bansal , David J. Nott

We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…

Artificial Intelligence · Computer Science 2013-01-30 Kevin Murphy

Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…

Statistics Theory · Mathematics 2020-08-05 Moumita Chakraborty , Subhashis Ghosal

Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…

Methodology · Statistics 2026-04-20 Yucong Liu , Zilai Si , Alexander Strang

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

Stochastic variational Bayes algorithms have become very popular in the machine learning literature, particularly in the context of nonparametric Bayesian inference. These algorithms replace the true but intractable posterior distribution…

Methodology · Statistics 2024-10-04 Pedro Regueiro , Abel Rodríguez , Juan Sosa

Language models often show a preference for using information from specific positions in the input regardless of semantic relevance. While positional bias has been studied in various contexts, from attention sinks to task performance…

Computation and Language · Computer Science 2026-01-08 Maryam Rahimi , Mahdi Nouri , Yadollah Yaghoobzadeh

Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…

Machine Learning · Statistics 2019-06-21 Atanas Mirchev , Baris Kayalibay , Maximilian Soelch , Patrick van der Smagt , Justin Bayer

As a computational alternative to Markov chain Monte Carlo approaches, variational inference (VI) is becoming more and more popular for approximating intractable posterior distributions in large-scale Bayesian models due to its comparable…

Machine Learning · Statistics 2023-06-05 Anirban Bhattacharya , Debdeep Pati , Yun Yang

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…

Machine Learning · Computer Science 2018-03-08 Francesco Locatello , Rajiv Khanna , Joydeep Ghosh , Gunnar Rätsch

We consider the optimal approximate posterior over the top-layer weights in a Bayesian neural network for regression, and show that it exhibits strong dependencies on the lower-layer weights. We adapt this result to develop a correlated…

Machine Learning · Statistics 2021-06-23 Sebastian W. Ober , Laurence Aitchison

Despite the popularism of Bayesian neural networks in recent years, its use is somewhat limited in complex and big data situations due to the computational cost associated with full posterior evaluations. Variational Bayes (VB) provides a…

Machine Learning · Statistics 2020-06-30 Shrijita Bhattacharya , Tapabrata Maiti

In Bayesian analysis, the posterior follows from the data and a choice of a prior and a likelihood. One hopes that the posterior is robust to reasonable variation in the choice of prior and likelihood, since this choice is made by the…

Methodology · Statistics 2015-12-09 Ryan Giordano , Tamara Broderick , Michael Jordan

Deep neural networks have revolutionized medical image analysis and disease diagnosis. Despite their impressive performance, it is difficult to generate well-calibrated probabilistic outputs for such networks, which makes them…

Machine Learning · Computer Science 2020-05-29 Pranav Poduval , Hrushikesh Loya , Amit Sethi

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…

Statistics Theory · Mathematics 2019-04-23 Pierre Alquier , James Ridgway

We propose a general framework using spike-and-slab prior distributions to aid with the development of high-dimensional Bayesian inference. Our framework allows inference with a general quasi-likelihood function. We show that highly…

Statistics Theory · Mathematics 2019-08-21 Yves Atchade , Anwesha Bhattacharyya

This paper studies the influence of perturbations of conjugate priors in Bayesian inference. A perturbed prior is defined inside a larger family, local mixture models, and the effect on posterior inference is studied. The perturbation, in…

Methodology · Statistics 2015-09-01 Vahed Maroufy , Paul Marriott

Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…

Analysis of PDEs · Mathematics 2019-11-11 Olivier Zahm , Paul Constantine , Clémentine Prieur , Youssef Marzouk

Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…

Methodology · Statistics 2020-07-10 Michael A. Chappell , Mark W. Woolrich

Variational Bayes methods are popular due to their computational efficiency and adaptability to diverse applications. In specifying the variational family, mean-field classes are commonly used, which enables efficient algorithms such as…

Statistics Theory · Mathematics 2025-11-26 Shitao Fan , Ilsang Ohn , David Dunson , Lizhen Lin