Online variational filtering and parameter learning

Conference item

We present a variational method for online state estimation and parameter learning in state-space models (SSMs), a ubiquitous class of latent variable models for sequential data. As per standard batch variational techniques, we use stochastic gradients to simultaneously optimize a lower bound on the log evidence with respect to both model parameters and a variational approximation of the states' posterior distribution. However, unlike existing approaches, our method is able to operate in an entirely online manner, such that historic observations do not require revisitation after being incorporated and the cost of updates at each time step remains constant, despite the growing dimensionality of the joint posterior distribution of the states. This is achieved by utilizing backward decompositions of this joint posterior distribution and of its variational approximation, combined with Bellman-type recursions for the evidence lower bound and its gradients. We demonstrate the performance of this methodology across several examples, including high-dimensional SSMs and sequential Variational Auto-Encoders.

Authors: Campbell, A; Shi, Y; Rainforth, T; Doucet, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Curran Associates
• Host title: Advances in Neural Information Processing Systems 34 (NeurIPS 2021)
• Volume: 34
• Pages: 18633-18645
• Publication date: 2022-05-31
• Acceptance date: 2021-10-04
• Event title: 35th Conference on Neural Information Processing Systems (NeurIPS 2021)
• Event location: Virtual event
• Event website: https://nips.cc/Conferences/2021/
• Event start date: 2021-12-06
• Event end date: 2021-12-14
• ISSN: 1049-5258
• ISBN: 9781713845393
• Language: English
• Keywords: FFR