Online Variational Filtering and Parameter Learning
This addresses the problem of scalable online inference for sequential data in machine learning, offering an incremental improvement over existing batch variational techniques.
The paper tackles online state estimation and parameter learning in state-space models by introducing a variational method that operates entirely online, avoiding revisitation of historic observations and maintaining constant update costs. It demonstrates performance on high-dimensional SSMs and sequential Variational Auto-Encoders, though no concrete numbers are provided.
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.