Locally Linear Continual Learning for Time Series based on VC-Theoretical Generalization Bounds

TL;DR

This paper introduces SyMPLER, an explainable, adaptive time series forecasting model for nonstationary environments that uses VC-theoretical bounds to automatically add local models, balancing accuracy and interpretability.

Contribution

SyMPLER is a novel explainable model that employs statistical learning theory to automatically determine when to add local models, avoiding explicit data clustering.

Findings

Achieves comparable performance to black-box models.

Maintains human-interpretable structure.

Effectively adapts to nonstationary data.

Abstract

Most machine learning methods assume fixed probability distributions, limiting their applicability in nonstationary real-world scenarios. While continual learning methods address this issue, current approaches often rely on black-box models or require extensive user intervention for interpretability. We propose SyMPLER (Systems Modeling through Piecewise Linear Evolving Regression), an explainable model for time series forecasting in nonstationary environments based on dynamic piecewise-linear approximations. Unlike other locally linear models, SyMPLER uses generalization bounds from Statistical Learning Theory to automatically determine when to add new local models based on prediction errors, eliminating the need for explicit clustering of the data. Experiments show that SyMPLER can achieve comparable performance to both black-box and existing explainable models while maintaining a human-interpretable structure that reveals insights about the system's behavior. In this sense, our approach conciliates accuracy and interpretability, offering a transparent and adaptive solution for forecasting nonstationary time series.