Continuous Forecasting via Neural Eigen Decomposition

TL;DR

The paper introduces NESDE, a neural eigen decomposition method for continuous, robust forecasting of stochastic processes, especially effective in high-noise, limited-data medical applications, with decoupled control and measurement modeling.

Contribution

The paper presents NESDE, a novel spectral-based neural differential equation approach that enhances robustness, control-measurement decoupling, and continuous prediction in noisy, real-world scenarios.

Findings

Robust forecasting in high-noise medical data

Decoupled control and measurement modeling

Closed-form continuous predictions

Abstract

Neural differential equations predict the derivative of a stochastic process. This allows irregular forecasting with arbitrary time-steps. However, the expressive temporal flexibility often comes with a high sensitivity to noise. In addition, current methods model measurements and control together, limiting generalization to different control policies. These properties severely limit applicability to medical treatment problems, which require reliable forecasting given high noise, limited data and changing treatment policies. We introduce the Neural Eigen-SDE algorithm (NESDE), which relies on piecewise linear dynamics modeling with spectral representation. NESDE provides control over the expressiveness level; decoupling of control from measurements; and closed-form continuous prediction in inference. NESDE is demonstrated to provide robust forecasting in both synthetic and real high-noise medical problems. Finally, we use the learned dynamics models to publish simulated medical gym environments.