Variational Gaussian Process Diffusion Processes

• URL: http://arxiv.org/abs/2306.02066v3
• Date: Tue, 27 Feb 2024 16:18:27 GMT
• Title: Variational Gaussian Process Diffusion Processes
• Authors: Prakhar Verma, Vincent Adam, Arno Solin
• Abstract summary: Diffusion processes are a class of differential equations (SDEs) providing a rich family of expressive models. 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.
• Score: 17.716059928867345
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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