The Powers of Precision: Structure-Informed Detection in Complex Systems -- From Customer Churn to Seizure Onset

TL;DR

This paper introduces a machine learning approach that leverages powers of covariance and precision matrices to detect emergent phenomena in complex systems, providing both accurate predictions and structural insights.

Contribution

The authors develop a novel method combining covariance power estimators with supervised learning for early detection and interpretability of critical events in complex systems.

Findings

Achieved competitive seizure detection results.

Effective churn prediction demonstrated.

Identified structural signatures with good interpretability.

Abstract

Emergent phenomena -- onset of epileptic seizures, sudden customer churn, or pandemic outbreaks -- often arise from hidden causal interactions in complex systems. We propose a machine learning method for their early detection that addresses a core challenge: unveiling and harnessing a system's latent causal structure despite the data-generating process being unknown and partially observed. The method learns an optimal feature representation from a one-parameter family of estimators -- powers of the empirical covariance or precision matrix -- offering a principled way to tune in to the underlying structure driving the emergence of critical events. A supervised learning module then classifies the learned representation. We prove structural consistency of the family and demonstrate the empirical soundness of our approach on seizure detection and churn prediction, attaining competitive results in both. Beyond prediction, and toward explainability, we ascertain that the optimal covariance power exhibits evidence of good identifiability while capturing structural signatures, thus reconciling predictive performance with interpretable statistical structure.