Posterior Inference on Shallow Infinitely Wide Bayesian Neural Networks under Weights with Unbounded Variance
Loading...
Access rights
openAccess
CC BY
CC BY
publishedVersion
URL
Journal Title
Journal ISSN
Volume Title
A4 Artikkeli konferenssijulkaisussa
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
Authors
Date
Department
Major/Subject
Mcode
Degree programme
Language
en
Pages
19
Series
Proceedings of Machine Learning Research, Volume 244, pp. 2331-2349
Abstract
From the classical and influential works of Neal (1996), it is known that the infinite width scaling limit of a Bayesian neural network with one hidden layer is a Gaussian process, when the network weights have bounded prior variance. Neal’s result has been extended to networks with multiple hidden layers and to convolutional neural networks, also with Gaussian process scaling limits. The tractable properties of Gaussian processes then allow straightforward posterior inference and uncertainty quantification, considerably simplifying the study of the limit process compared to a network of finite width. Neural network weights with unbounded variance, however, pose unique challenges. In this case, the classical central limit theorem breaks down and it is well known that the scaling limit is an α-stable process under suitable conditions. However, current literature is primarily limited to forward simulations under these processes and the problem of posterior inference under such a scaling limit remains largely unaddressed, unlike in the Gaussian process case. To this end, our contribution is an interpretable and computationally feasible procedure for posterior inference, using a conditionally Gaussian representation, that then allows full use of the Gaussian process machinery for tractable posterior inference and uncertainty quantification in the non-Gaussian regime.Description
Publisher Copyright: © 2024 Proceedings of Machine Learning Research. All rights reserved.
Keywords
Other note
Citation
Loría, J & Bhadra, A 2024, 'Posterior Inference on Shallow Infinitely Wide Bayesian Neural Networks under Weights with Unbounded Variance', Proceedings of Machine Learning Research, vol. 244, pp. 2331-2349. < https://proceedings.mlr.press/v244/loria24a.html >