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In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

Machine Learning · Statistics 2026-02-27 Gracielle Antunes de Araújo , Flávio B. Gonçalves

Bayesian neural networks offer better estimates of model uncertainty compared to frequentist networks. However, inference involving Bayesian models requires multiple instantiations or sampling of the network parameters, requiring…

Neural and Evolutionary Computing · Computer Science 2024-01-30 Prabodh Katti , Anagha Nimbekar , Chen Li , Amit Acharyya , Bashir M. Al-Hashimi , Bipin Rajendran

We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…

Machine Learning · Statistics 2020-10-27 Trung Trinh , Samuel Kaski , Markus Heinonen

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…

Computation · Statistics 2026-01-09 Elliot Maceda , Emily C. Hector , Amanda Lenzi , Brian J. Reich

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…

Machine Learning · Statistics 2019-05-28 Aliaksandr Hubin , Geir Storvik

We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates…

Machine Learning · Statistics 2011-10-21 Andrew Gordon Wilson , David A. Knowles , Zoubin Ghahramani

Isotropic Gaussian priors are the de facto standard for modern Bayesian neural network inference. However, it is unclear whether these priors accurately reflect our true beliefs about the weight distributions or give optimal performance. To…

The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…

Disordered Systems and Neural Networks · Physics 2023-08-01 Chi-Ken Lu

Probability density function estimation with weighted samples is the main foundation of all adaptive importance sampling algorithms. Classically, a target distribution is approximated either by a non-parametric model or within a parametric…

Machine Learning · Computer Science 2023-10-16 Julien Demange-Chryst , François Bachoc , Jérôme Morio , Timothé Krauth

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a…

Machine Learning · Computer Science 2018-10-24 Cheng Zhang , Judith Butepage , Hedvig Kjellstrom , Stephan Mandt

In multimedia forensics, learning-based methods provide state-of-the-art performance in determining origin and authenticity of images and videos. However, most existing methods are challenged by out-of-distribution data, i.e., with…

Machine Learning · Computer Science 2020-07-29 Anatol Maier , Benedikt Lorch , Christian Riess

Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…

Machine Learning · Statistics 2023-01-19 Ali Siahkoohi , Gabrio Rizzuti , Rafael Orozco , Felix J. Herrmann

Sampling complex free energy surfaces is one of the main challenges of modern atomistic simulation methods. The presence of kinetic bottlenecks in such surfaces often renders a direct approach useless. A popular strategy is to identify a…

Computational Physics · Physics 2019-09-25 Luigi Bonati , Yue-Yu Zhang , Michele Parrinello

Computer vision tasks are difficult because of the large variability in the data that is induced by changes in light, background, partial occlusion as well as the varying pose, texture, and shape of objects. Generative approaches to…

Computer Vision and Pattern Recognition · Computer Science 2018-11-30 Adam Kortylewski , Mario Wieser , Andreas Morel-Forster , Aleksander Wieczorek , Sonali Parbhoo , Volker Roth , Thomas Vetter

There is significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware neural networks (NNs), based on learning…

Machine Learning · Computer Science 2022-02-25 Nis Meinert , Alexander Lavin

Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…

Machine Learning · Computer Science 2024-03-15 Tim Rensmeyer , Oliver Niggemann

The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…

Machine Learning · Computer Science 2022-03-31 Andrew Gordon Wilson , Pavel Izmailov

The need for function estimation in label-limited settings is common in the natural sciences. At the same time, prior knowledge of function values is often available in these domains. For example, data-free biophysics-based models can be…

Machine Learning · Computer Science 2022-10-17 Hunter Nisonoff , Yixin Wang , Jennifer Listgarten

Bayesian neural networks (BNN) promise to combine the predictive performance of neural networks with principled uncertainty modeling important for safety-critical systems and decision making. However, posterior uncertainty estimates depend…

Machine Learning · Computer Science 2025-06-06 Tristan Cinquin , Robert Bamler

The determination of the physical parameters of gravitational wave events is a fundamental pillar in the analysis of the signals observed by the current ground-based interferometers. Typically, this is done using Bayesian inference…

General Relativity and Quantum Cosmology · Physics 2023-11-07 M. Andrés-Carcasona , M. Martinez , Ll. M. Mir