Partial Effective Information Decomposition for Synergistic Causality

Causality remains a cornerstone of scientific inquiry, but analyzing synergistic causation in multivariate systems has been a persistent challenge. In a new paper submitted to arXiv, researchers Mingzhe Yang, Shuo Wang, and Jiang Zhang introduce Partial Effective Information Decomposition (PEID), a framework grounded in interventionist causation. PEID decomposes the influence of multiple source variables on a target variable under maximum-entropy interventions into unique and synergistic information. Theoretically, for three-variable cases, PEID aligns with the major axioms of Partial Information Decomposition (PID), providing a unified computable characterization of synergistic causal relations. By removing correlations among input variables through maximum-entropy interventions, redundancy vanishes, allowing PEID to isolate synergistic effects. This opens the door to defining causal graphs that include hyperedges and downward causation, making it a versatile tool for cross-scale analysis in complex systems.

Empirically, the researchers applied PEID to a machine-learning-based air quality forecasting task using the KnowAir-V2 dataset. The framework successfully extracted interpretable inter-station causal structures from a learned dynamical model, demonstrating its practical utility. This application shows how PEID can reveal hidden multivariate causal mechanisms in real-world data, such as how pollutant levels at one monitoring station synergistically influence predictions at another. By providing a general interventionist information-theoretic toolkit, PEID advances the analysis of causal mechanisms in both natural and engineered systems, with potential implications for fields ranging from climate science to neuroscience and AI interpretability.