Improving the Noise Estimation of Latent Neural Stochastic Differential Equations

TL;DR

This paper addresses the underestimation of noise in latent neural SDEs by introducing an explicit noise regularization, significantly improving their ability to model stochastic dynamics in time series data.

Contribution

The authors propose a simple yet effective noise regularization technique to enhance noise estimation in latent neural SDEs, improving their modeling of stochastic processes.

Findings

Enhanced noise estimation accuracy in latent neural SDEs

Improved modeling of stochastic bistable dynamics

Demonstrated effectiveness on conceptual model system

Abstract

Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in such data, limiting their ability to capture stochastic dynamics accurately. We investigate this underestimation in detail and propose a straightforward solution: by including an explicit additional noise regularization in the loss function, we are able to learn a model that accurately captures the diffusion component of the data. We demonstrate our results on a conceptual model system that highlights the improved latent neural SDE's capability to model stochastic bistable dynamics.