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In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

Machine Learning · Computer Science 2019-04-03 Konstantin Posch , Jürgen Pilz

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

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks.…

Machine Learning · Computer Science 2023-05-24 Lucas Clarté , Bruno Loureiro , Florent Krzakala , Lenka Zdeborová

Quantifying the uncertainty of supervised learning models plays an important role in making more reliable predictions. Epistemic uncertainty, which usually is due to insufficient knowledge about the model, can be reduced by collecting more…

Machine Learning · Computer Science 2022-01-27 Xinlei Zhou , Han Liu , Farhad Pourpanah , Tieyong Zeng , Xizhao Wang

The bias-variance trade-off is a central concept in supervised learning. In classical statistics, increasing the complexity of a model (e.g., number of parameters) reduces bias but also increases variance. Until recently, it was commonly…

Machine Learning · Statistics 2022-03-25 Jason W. Rocks , Pankaj Mehta

We study the problem of non-Bayesian social learning with uncertain models, in which a network of agents seek to cooperatively identify the state of the world based on a sequence of observed signals. In contrast with the existing…

Optimization and Control · Mathematics 2019-09-11 César A. Uribe , James Z. Hare , Lance Kaplan , Ali Jadbabaie

Farquhar et al. [2021] show that correcting for active learning bias with underparameterised models leads to improved downstream performance. For overparameterised models such as NNs, however, correction leads either to decreased or…

Machine Learning · Computer Science 2021-12-15 Chelsea Murray , James U. Allingham , Javier Antorán , José Miguel Hernández-Lobato

Bayesian Neural Networks (BNNs) often result uncalibrated after training, usually tending towards overconfidence. Devising effective calibration methods with low impact in terms of computational complexity is thus of central interest. In…

Machine Learning · Computer Science 2020-08-18 Hector J. Hortua , Luigi Malago , Riccardo Volpi

Bayesian analyses are often performed using so-called noninformative priors, with a view to achieving objective inference about unknown parameters on which available data depends. Noninformative priors depend on the relationship of the data…

Methodology · Statistics 2013-08-14 Nicholas Lewis

Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for…

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…

Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…

Machine Learning · Computer Science 2019-05-28 Manikanta Srikar Yellapragada , Chandra Prakash Konkimalla

This is a review of asymptotic and non-asymptotic behaviour of Bayesian methods under model specification. In particular we focus on consistency, i.e. convergence of the posterior distribution to the point mass at the best parametric…

Statistics Theory · Mathematics 2023-11-21 Natalia Bochkina

State-of-the-art deep-learning systems use decision rules that are challenging for humans to model. Explainable AI (XAI) attempts to improve human understanding but rarely accounts for how people typically reason about unfamiliar agents. We…

Artificial Intelligence · Computer Science 2021-04-27 Scott Cheng-Hsin Yang , Wai Keen Vong , Ravi B. Sojitra , Tomas Folke , Patrick Shafto

In many parameter estimation problems, the exact model is unknown and is assumed to belong to a set of candidate models. In such cases, a predetermined data-based selection rule selects a parametric model from a set of candidates before the…

Signal Processing · Electrical Eng. & Systems 2025-04-25 Nadav Harel , Tirza Routtenberg

The inability of artificial neural networks to assess the uncertainty of their predictions is an impediment to their widespread use. We distinguish two types of learnable uncertainty: model uncertainty due to a lack of training data and…

Machine Learning · Computer Science 2022-06-14 Hans Weytjens , Jochen De Weerdt

Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward:…

Machine Learning · Statistics 2019-02-19 Sebastian Farquhar , Yarin Gal

The recent success of machine learning models, especially large-scale classifiers and language models, relies heavily on training with massive data. These data are often collected from online sources. This raises serious concerns about the…

Artificial Intelligence · Computer Science 2025-11-12 Ruihan Zhang , Jun Sun , Ee-Peng Lim , Peixin Zhang

Bayesian neural networks allow us to keep track of uncertainties, for example in top tagging, by learning a tagger output together with an error band. We illustrate the main features of Bayesian versions of established deep-learning…

High Energy Physics - Phenomenology · Physics 2020-01-22 Sven Bollweg , Manuel Haussmann , Gregor Kasieczka , Michel Luchmann , Tilman Plehn , Jennifer Thompson

There is significant growth and interest in the use of synthetic data as an enabler for machine learning in environments where the release of real data is restricted due to privacy or availability constraints. Despite a large number of…

Machine Learning · Computer Science 2020-11-25 Harrison Wilde , Jack Jewson , Sebastian Vollmer , Chris Holmes