Causal Feature Learning via Generalized Rayleigh Quotients

Extracting causally meaningful features from time-series data is fundamental for robust machine learning under distribution shifts. In process monitoring, existing methods struggle to maintain detection performance when operating conditions change. Current approaches capture either temporal causal relationships or cross-environment invariance, but not both simultaneously. We propose Causal Feature Learning (CFL), a unified framework that jointly optimizes for temporal relevance and environment mean invariance. CFL formulates feature extraction as a generalized Rayleigh-quotient problem, maximizing correlation with target variables while penalizing sensitivity to environment-dependent mean shifts. Theoretical analysis establishes conditions under which CFL identifies a mean-invariant predictive subspace. Experiments on the Tennessee Eastman Process demonstrate that CFL achieves 93.69\% average fault detection rate, outperforming 15 baseline methods and validating the benefit of jointly capturing both aspects of causality.

Industrial processes such as chemical plants generate vast sensor data, and detecting faults early is essential for safety and efficiency. Existing detection methods often fail when operating conditions shift, because they rely on statistical correlations rather than true cause-and-effect structure. We argue that genuinely causal features have two complementary properties. One is temporal predictiveness, meaning past readings carry information about current process states. The other is invariance, meaning the relationships stay stable across different operating conditions. Most existing methods capture one property but not both. Our framework, called Causal Feature Learning, jointly enforces both through a single mathematical optimization that finds data projections informative about target variables and stable across operating environments. We provide theoretical guarantees and evaluate on the standard Tennessee Eastman benchmark with 21 fault types. The method achieves 93.7 percent average detection rate, outperforming 15 alternative approaches, with the largest gains on difficult faults involving subtle process changes.