Partial Effective Information Decomposition for Synergistic Causality

2026-05-04

AI Summary

Existing approaches lack a computable framework grounded in interventionist causality to identify synergistic causal relationships among multiple variables in complex systems. This work proposes the Partial Effective Information Decomposition (PEID) framework, which, for the first time within the interventionist causal paradigm, integrates maximum-entropy interventions with Partial Information Decomposition (PID) theory to rigorously decompose the influence of multiple source variables on a target variable into unique and synergistic components. The method adheres to PID axioms, supports the construction of causal graphs incorporating hyperedges and downward causation, and enables efficient analysis by combining information-theoretic principles with machine learning–based dynamical models. Applied to the KnowAir-V2 air quality forecasting task, PEID successfully uncovers interpretable synergistic causal structures among monitoring stations, demonstrating its effectiveness and novelty in multivariate causal inference for complex systems.

Abstract

Causality is a central topic in scientific inquiry, yet for complex systems, the identification and analysis of synergistic causation remain a challenging and fundamental problem. In the context of causal relations among multivariate variables, a decomposition framework grounded in interventionist causation is still lacking. To address this gap, this paper proposes Partial Effective Information Decomposition (PEID), a framework that decomposes the influence of multiple source variables on a target variable under maximum-entropy interventions into unique and synergistic information, thereby providing a unified and computable characterization of synergistic causal relations. Theoretically, in the three-variable case, the proposed framework is compatible with the major axioms of Partial Information Decomposition (PID). Empirically, under maximum-entropy interventions, correlations among input variables are removed, causing redundancy to vanish and thereby enabling PEID to compute synergistic relations. Furthermore, based on this framework, it is possible to define causal graphs containing hyperedges as well as downward causation, thus offering a unified toolkit for analyzing cross-scale and multivariate causal mechanisms in complex systems. Finally, applying the framework to a machine-learning-based air quality forecasting task on KnowAir-V2, we demonstrate that PEID can extract interpretable inter-station causal structures from a learned dynamical model. These results suggest that PEID provides a general interventionist information-theoretic tool for analyzing multivariate and synergistic causal mechanisms in complex systems.

Problem

• synergistic causality
• multivariate causal relations
• interventionist causation
• information decomposition
• complex systems

Innovation

• Partial Effective Information Decomposition
• synergistic causality
• maximum-entropy intervention
• causal hypergraph
• interventionist information theory