Variational Gaussian Process Diffusion Processes

Prakhar Verma, Vincent Adam, Arno Solin

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

Abstract

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with latent processes endowed with a non-linear diffusion process prior are intractable problems. We build upon work within variational inference, approximating the posterior process as a linear diffusion process, and point out pathologies in the approach. We propose an alternative parameterization of the Gaussian variational process using a site-based exponential family description. This allows us to trade a slow inference algorithm with fixed-point iterations for a fast algorithm for convex optimization akin to natural gradient descent, which also provides a better objective for learning model parameters.
Original languageEnglish
Title of host publicationProceedings of the 27th International Conference on Artificial Intelligence and Statistics
PublisherJMLR
Pages1909-1917
Publication statusPublished - 2024
MoE publication typeA4 Conference publication
EventInternational Conference on Artificial Intelligence and Statistics - Valencia, Spain
Duration: 2 May 20244 May 2024
http://aistats.org/aistats2024/

Publication series

NameProceedings of Machine Learning Research
PublisherPMLR
Volume238
ISSN (Electronic)2640-3498

Conference

ConferenceInternational Conference on Artificial Intelligence and Statistics
Abbreviated titleAISTATS
Country/TerritorySpain
CityValencia
Period02/05/202404/05/2024
Internet address

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