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We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior…

Machine Learning · Statistics 2022-10-24 Jeahan Jung , Minseok Choi

Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…

Machine Learning · Computer Science 2016-11-03 Hao Wang , Xingjian Shi , Dit-Yan Yeung

Bayesian method is capable of capturing real world uncertainties/incompleteness and properly addressing the over-fitting issue faced by deep neural networks. In recent years, Bayesian Neural Networks (BNNs) have drawn tremendous attentions…

Machine Learning · Computer Science 2020-05-11 Xiaotao Jia , Jianlei Yang , Runze Liu , Xueyan Wang , Sorin Dan Cotofana , Weisheng Zhao

The task of quantifying the inherent uncertainty associated with neural network predictions is a key challenge in artificial intelligence. Bayesian neural networks (BNNs) and deep ensembles are among the most prominent approaches to tackle…

Machine Learning · Computer Science 2025-05-23 Valentin Villecroze , Yixin Wang , Gabriel Loaiza-Ganem

A novel variational inference based resampling framework is proposed to evaluate the robustness and generalization capability of deep learning models with respect to distribution shift. We use Auto Encoding Variational Bayes to find a…

Machine Learning · Computer Science 2019-10-29 Xudong Sun , Alexej Gossmann , Yu Wang , Bernd Bischl

There has been increasing interest in modeling survival data using deep learning methods in medical research. In this paper, we proposed a Bayesian hierarchical deep neural networks model for modeling and prediction of survival data.…

Methodology · Statistics 2021-09-20 Dai Feng , Lili Zhao

Bayesian neural networks (BNNs) are a principled approach to modeling predictive uncertainties in deep learning, which are important in safety-critical applications. Since exact Bayesian inference over the weights in a BNN is intractable,…

Machine Learning · Statistics 2024-01-02 Tim Z. Xiao , Weiyang Liu , Robert Bamler

Predictive uncertainty quantification is crucial for reliable decision-making in various applied domains. Bayesian neural networks offer a powerful framework for this task. However, defining meaningful priors and ensuring computational…

Machine Learning · Computer Science 2024-04-30 Yijia Liu , Xiao Wang

Deep neural networks are revolutionizing the way complex systems are developed. However, these automatically-generated networks are opaque to humans, making it difficult to reason about them and guarantee their correctness. Here, we propose…

Artificial Intelligence · Computer Science 2020-08-11 Yuval Jacoby , Clark Barrett , Guy Katz

Sequential Bayesian inference over predictive functions is a natural framework for continual learning from streams of data. However, applying it to neural networks has proved challenging in practice. Addressing the drawbacks of existing…

Machine Learning · Statistics 2023-12-29 Tim G. J. Rudner , Freddie Bickford Smith , Qixuan Feng , Yee Whye Teh , Yarin Gal

Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been…

Approximate Bayesian inference for neural networks is considered a robust alternative to standard training, often providing good performance on out-of-distribution data. However, Bayesian neural networks (BNNs) with high-fidelity…

Machine Learning · Computer Science 2021-12-07 Pavel Izmailov , Patrick Nicholson , Sanae Lotfi , Andrew Gordon Wilson

Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately,…

Computation · Statistics 2025-02-18 Yiqi Tang , Ryan Martin

Bayesian neural networks perform variational inference over the weights however calculation of the posterior distribution remains a challenge. Our work builds on variational inference techniques for bayesian neural networks using the…

Machine Learning · Computer Science 2021-06-23 Abhinav Sagar

Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support…

Machine Learning · Computer Science 2024-05-09 Yucen Lily Li , Tim G. J. Rudner , Andrew Gordon Wilson

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

We study Bayesian hypernetworks: a framework for approximate Bayesian inference in neural networks. A Bayesian hypernetwork $\h$ is a neural network which learns to transform a simple noise distribution, $p(\vec\epsilon) = \N(\vec 0,\mat…

Machine Learning · Statistics 2018-04-26 David Krueger , Chin-Wei Huang , Riashat Islam , Ryan Turner , Alexandre Lacoste , Aaron Courville

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…

Machine Learning · Computer Science 2026-03-03 Wenlong Chen

Bayesian neural networks (BNNs) allow rigorous uncertainty quantification in deep learning, but often come at a prohibitive computational cost. We propose three different innovative architectures of partial trace-class Bayesian neural…

Machine Learning · Statistics 2025-11-04 Arran Carter , Torben Sell

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…

Machine Learning · Statistics 2022-12-13 Diederik P Kingma , Max Welling
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