Note on Equivalence Between Recurrent Neural Network Time Series Models and Variational Bayesian Models

TL;DR

This paper reveals an equivalence between RNN training and variational Bayesian methods for time series, proposing an extension with multiple particles to better model uncertainty and multimodality.

Contribution

It establishes a theoretical link between RNNs and variational Bayesian models and introduces a multi-particle RNN extension for enhanced uncertainty representation.

Findings

RNN training objective is equivalent to a variational Bayesian objective.

Multi-particle RNN effectively captures uncertainty and multimodality.

Theoretical insights may inspire new RNN and Bayesian model extensions.

Abstract

We observe that the standard log likelihood training objective for a Recurrent Neural Network (RNN) model of time series data is equivalent to a variational Bayesian training objective, given the proper choice of generative and inference models. This perspective may motivate extensions to both RNNs and variational Bayesian models. We propose one such extension, where multiple particles are used for the hidden state of an RNN, allowing a natural representation of uncertainty or multimodality.