English
Related papers

Related papers: Wide Mean-Field Bayesian Neural Networks Ignore th…

200 papers

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…

Comparing Bayesian neural networks (BNNs) with different widths is challenging because, as the width increases, multiple model properties change simultaneously, and, inference in the finite-width case is intractable. In this work, we…

Machine Learning · Statistics 2022-11-29 Jiayu Yao , Yaniv Yacoby , Beau Coker , Weiwei Pan , Finale Doshi-Velez

Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better…

Machine Learning · Statistics 2023-05-25 Insung Kong , Dongyoon Yang , Jongjin Lee , Ilsang Ohn , Gyuseung Baek , Yongdai Kim

Overparameterised deep neural networks (DNNs) are highly expressive and so can, in principle, generate almost any function that fits a training dataset with zero error. The vast majority of these functions will perform poorly on unseen…

Machine Learning · Computer Science 2021-04-13 Chris Mingard , Guillermo Valle-Pérez , Joar Skalse , Ard A. Louis

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…

Bayesian neural networks (BNNs) have become a principal approach to alleviate overconfident predictions in deep learning, but they often suffer from scaling issues due to a large number of distribution parameters. In this paper, we discover…

Machine Learning · Computer Science 2021-12-14 Shiye Lei , Zhuozhuo Tu , Leszek Rutkowski , Feng Zhou , Li Shen , Fengxiang He , Dacheng Tao

One of the most popular estimation methods in Bayesian neural networks (BNN) is mean-field variational inference (MFVI). In this work, we show that neural networks with ReLU activation function induce posteriors, that are hard to fit with…

Machine Learning · Statistics 2022-07-28 Piotr Tempczyk , Ksawery Smoczyński , Philip Smolenski-Jensen , Marek Cygan

We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning…

Machine Learning · Statistics 2021-06-01 Sebastian Farquhar , Michael Osborne , Yarin Gal

Currently, it is hard to reap the benefits of deep learning for Bayesian methods, which allow the explicit specification of prior knowledge and accurately capture model uncertainty. We present Prior-Data Fitted Networks (PFNs). PFNs…

Machine Learning · Computer Science 2024-08-14 Samuel Müller , Noah Hollmann , Sebastian Pineda Arango , Josif Grabocka , Frank Hutter

Bayesian neural networks are theoretically well-understood only in the infinite-width limit, where Gaussian priors over network weights yield Gaussian priors over network outputs. Recent work has suggested that finite Bayesian networks may…

Machine Learning · Computer Science 2022-05-16 Jacob A. Zavatone-Veth , Cengiz Pehlevan

Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…

Computation · Statistics 2018-05-28 Minh-Ngoc Tran , Nghia Nguyen , David Nott , Robert Kohn

Quantifying uncertainty in neural networks is a highly relevant problem which is essential to many applications. The two predominant paradigms to tackle this task are Bayesian neural networks (BNNs) and deep ensembles. Despite some…

Machine Learning · Computer Science 2025-01-31 Gabriel Loaiza-Ganem , Valentin Villecroze , Yixin Wang

We establish novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters (weights and biases) and Lipschitz activation functions, in the wide limit. Our bounds apply for the joint output of a network…

Statistics Theory · Mathematics 2023-12-20 Dario Trevisan

Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior…

Computer Vision and Pattern Recognition · Computer Science 2021-03-26 Gianni Franchi , Andrei Bursuc , Emanuel Aldea , Severine Dubuisson , Isabelle Bloch

Bayesian neural networks (BNNs) offer a natural probabilistic formulation for inference in deep learning models. Despite their popularity, their optimality has received limited attention through the lens of statistical decision theory. In…

Statistics Theory · Mathematics 2026-04-07 Daniel Andrew Coulson , Martin T. Wells

A key property of neural networks driving their success is their ability to learn features from data. Understanding feature learning from a theoretical viewpoint is an emerging field with many open questions. In this work we capture…

Disordered Systems and Neural Networks · Physics 2024-05-20 Kirsten Fischer , Javed Lindner , David Dahmen , Zohar Ringel , Michael Krämer , Moritz Helias

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

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 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

The asymptotic properties of Bayesian Neural Networks (BNNs) have been extensively studied, particularly regarding their approximations by Gaussian processes in the infinite-width limit. We extend these results by showing that posterior…

Machine Learning · Statistics 2025-02-07 Francesco Caporali , Stefano Favaro , Dario Trevisan