Structured Inference Networks for Nonlinear State Space Models

TL;DR

This paper presents a unified, scalable algorithm for learning both linear and nonlinear state space models, including deep neural network variants, using structured variational inference with recurrent neural networks.

Contribution

It introduces a novel algorithm that jointly learns generative models and inference networks for complex state space models, enhancing scalability and performance.

Findings

Higher held-out likelihood with structured posterior approximation

Effective on both synthetic and real-world datasets

Supports deep neural network emission and transition models

Abstract

Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified algorithm to efficiently learn a broad class of linear and non-linear state space models, including variants where the emission and transition distributions are modeled by deep neural networks. Our learning algorithm simultaneously learns a compiled inference network and the generative model, leveraging a structured variational approximation parameterized by recurrent neural networks to mimic the posterior distribution. We apply the learning algorithm to both synthetic and real-world datasets, demonstrating its scalability and versatility. We find that using the structured approximation to the posterior results in models with significantly higher held-out likelihood.