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We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

Machine Learning · Statistics 2019-03-11 Konstantin Posch , Jan Steinbrener , Jürgen Pilz

Modern neural networks tend to be overconfident on unseen, noisy or incorrectly labelled data and do not produce meaningful uncertainty measures. Bayesian deep learning aims to address this shortcoming with variational approximations (such…

Machine Learning · Statistics 2018-05-28 Nick Pawlowski , Andrew Brock , Matthew C. H. Lee , Martin Rajchl , Ben Glocker

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…

Compression and computational efficiency in deep learning have become a problem of great significance. In this work, we argue that the most principled and effective way to attack this problem is by adopting a Bayesian point of view, where…

Machine Learning · Statistics 2017-11-07 Christos Louizos , Karen Ullrich , Max Welling

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

Machine Learning · Statistics 2020-02-27 Tim Pearce , Felix Leibfried , Alexandra Brintrup , Mohamed Zaki , Andy Neely

Bayesian neural networks provide a direct and natural way to extend standard deep neural networks to support probabilistic deep learning through the use of probabilistic layers that, traditionally, encode weight (and bias) uncertainty. In…

Machine Learning · Computer Science 2021-07-16 Daniel T. Chang

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…

Machine Learning · Computer Science 2021-03-30 Zhijie Deng , Yucen Luo , Jun Zhu , Bo Zhang

Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian…

Machine Learning · Computer Science 2019-10-23 Xinjie Lan , Kenneth E. Barner

Domain generalization is challenging due to the domain shift and the uncertainty caused by the inaccessibility of target domain data. In this paper, we address both challenges with a probabilistic framework based on variational Bayesian…

Machine Learning · Computer Science 2021-07-16 Zehao Xiao , Jiayi Shen , Xiantong Zhen , Ling Shao , Cees G. M. Snoek

In this work we investigate the reasons why Batch Normalization (BN) improves the generalization performance of deep networks. We argue that one major reason, distinguishing it from data-independent normalization methods, is randomness of…

Machine Learning · Computer Science 2018-11-05 Alexander Shekhovtsov , Boris Flach

Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on…

Machine Learning · Computer Science 2022-09-30 Satya Borgohain , Klaus Ackermann , Ruben Loaiza-Maya

Bayesian Neural Networks (BNNs) provide a tool to estimate the uncertainty of a neural network by considering a distribution over weights and sampling different models for each input. In this paper, we propose a method for uncertainty…

Machine Learning · Computer Science 2024-10-28 Illia Oleksiienko , Dat Thanh Tran , Alexandros Iosifidis

In this work, we introduce a novel probabilistic representation of deep learning, which provides an explicit explanation for the Deep Neural Networks (DNNs) in three aspects: (i) neurons define the energy of a Gibbs distribution; (ii) the…

Machine Learning · Computer Science 2019-08-27 Xinjie Lan , Kenneth E. Barner

Recently, combinations of generative and Bayesian machine learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated…

Machine Learning · Computer Science 2024-11-21 Sebastian Bieringer , Sascha Diefenbacher , Gregor Kasieczka , Mathias Trabs

Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…

Artificial Intelligence · Computer Science 2019-01-08 Robert Leppert , Karl-Heinz Zimmermann

Bayesian optimization is an effective methodology for the global optimization of functions with expensive evaluations. It relies on querying a distribution over functions defined by a relatively cheap surrogate model. An accurate model for…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

Methodology · Statistics 2025-07-23 Cheng Zeng , Eleni Dilma , Jason Xu , Leo L Duan

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

Artificial Intelligence · Computer Science 2018-11-14 Zhenyu A. Liao , Charupriya Sharma , James Cussens , Peter van Beek

Bayesian inference provides a principled probabilistic framework for quantifying uncertainty by updating beliefs based on prior knowledge and observed data through Bayes' theorem. In Bayesian deep learning, neural network weights are…

Machine Learning · Computer Science 2024-10-22 Yijie Zhang

Understanding how feature learning affects generalization is among the foremost goals of modern deep learning theory. Here, we study how the ability to learn representations affects the generalization performance of a simple class of…

Machine Learning · Computer Science 2022-06-17 Jacob A. Zavatone-Veth , William L. Tong , Cengiz Pehlevan