Spectral Ranking of Causal Influence in Complex Systems

TL;DR

This paper presents a spectral ranking method combining transfer entropy and eigenvector centrality to identify influential parameters in complex, high-dimensional systems with nonlinear dynamics, demonstrated on semiconductor lithography data.

Contribution

The paper introduces a novel spectral ranking algorithm that effectively detects true causal influences in complex systems with redundant information transfer networks.

Findings

Robust identification of influential sources in complex systems.

Effective handling of redundant edges in information transfer networks.

Validation on semiconductor lithography system data.

Abstract

Like natural complex systems such as the Earth's climate or a living cell, semiconductor lithography systems are characterized by nonlinear dynamics across more than a dozen orders of magnitude in space and time. Thousands of sensors measure relevant process variables at appropriate sampling rates, to provide time series as primary sources for system diagnostics. However, high-dimensionality, non-linearity and non-stationarity of data remain a major challenge to effectively diagnose rare or new system issues by merely using model-based approaches. To reduce the causal search space, we validate an algorithm that applies transfer entropy to obtain a weighted directed graph from a system's multivariate time series and graph eigenvector centrality to identify the system's most influential parameters. The results suggest that this approach robustly identifies the true influential sources in a complex system, even when its information transfer network includes redundant edges.