Sequential Density Estimation via Nonlinear Continuous Weighted Finite Automata

TL;DR

This paper introduces nonlinear continuous weighted finite automata (NCWFAs) combined with RNADE for improved density estimation over sequences of continuous variables, outperforming traditional models like Gaussian HMMs.

Contribution

The paper proposes a novel nonlinear extension to continuous WFAs and integrates RNADE, enhancing expressiveness and density estimation capabilities for sequence data.

Findings

NCWFAs are more expressive than Gaussian HMMs.

RNADE-NCWFA outperforms baseline methods in synthetic density estimation tasks.

The model effectively estimates densities for sequences longer than training data.

Abstract

Weighted finite automata (WFAs) have been widely applied in many fields. One of the classic problems for WFAs is probability distribution estimation over sequences of discrete symbols. Although WFAs have been extended to deal with continuous input data, namely continuous WFAs (CWFAs), it is still unclear how to approximate density functions over sequences of continuous random variables using WFA-based models, due to the limitation on the expressiveness of the model as well as the tractability of approximating density functions via CWFAs. In this paper, we propose a nonlinear extension to the CWFA model to first improve its expressiveness, we refer to it as the nonlinear continuous WFAs (NCWFAs). Then we leverage the so-called RNADE method, which is a well-known density estimator based on neural networks, and propose the RNADE-NCWFA model. The RNADE-NCWFA model computes a density function by design. We show that this model is strictly more expressive than the Gaussian HMM model, which CWFA cannot approximate. Empirically, we conduct a synthetic experiment using Gaussian HMM generated data. We focus on evaluating the model's ability to estimate densities for sequences of varying lengths (longer length than the training data). We observe that our model performs the best among the compared baseline methods.