Decomposing causality into its synergistic, unique, and redundant components

Creators: Martínez-Sánchez, Álvaro¹; Arranz, Gonzalo¹; Lozano-Durán, Adrián^{1, 2}

1. Massachusetts Institute of Technology
2. California Institute of Technology

Abstract

Causality lies at the heart of scientific inquiry, serving as the fundamental basis for understanding interactions among variables in physical systems. Despite its central role, current methods for causal inference face significant challenges due to nonlinear dependencies, stochastic interactions, self-causation, collider effects, and influences from exogenous factors, among others. While existing methods can effectively address some of these challenges, no single approach has successfully integrated all these aspects. Here, we address these challenges with SURD: Synergistic-Unique-Redundant Decomposition of causality. SURD quantifies causality as the increments of redundant, unique, and synergistic information gained about future events from past observations. The formulation is non-intrusive and applicable to both computational and experimental investigations, even when samples are scarce. We benchmark SURD in scenarios that pose significant challenges for causal inference and demonstrate that it offers a more reliable quantification of causality compared to previous methods.

Copyright and License (English)

Open Access. This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

Acknowledgement (English)

The authors acknowledge the MIT SuperCloud and Lincoln Laboratory Supercomputing Center for providing HPC resources that have contributed to the research results reported within this paper. The authors would like to thank Yuenong Ling for his contributions to this work and Mathieu Le Provost for his assistance with the implementation of the transport map method.

Funding (English)

This work was supported by the National Science Foundation under Grant No. 2140775 and MISTI Global Seed Funds and UPM. Á.M.-S. received the support of a fellowship from the ”la Caixa” Foundation (ID 100010434). The fellowship code is LCF/BQ/EU22/11930094. G.A. was partially supported by the Predictive Science Academic Alliance Program (PSAAP; grant DE-NA0003993) managed by the NNSA (National Nuclear Security Administration) Office of Advanced Simulation and Computing and the STTR N68335-21-C-0270 with Cascade Technologies, Inc. and the Naval Air Systems Command.

Contributions (English)

The authors would like to thank Yuenong Ling for his contributions to this work and Mathieu Le Provost for his assistance with the implementation of the transport map method.

Á.M.-S.: Methodology, Software, Validation, Investigation, Data Curation, Writing—Original Draft, Writing—Review & Editing, Visualization. G. A.: Methodology, Software, Investigation, Writing—Review & Editing. A.L.-D.: Ideation, Methodology, Writing—Review & Editing, Supervision, Resources, Funding acquisition.

Data Availability (English)

The data generated in this study as well as the analysis and simulation code have been deposited in a Zenodo database under identifier https://doi.org/10.5281/zenodo.13750918.

Code Availability (English)

The codes¹²⁹ developed for this work are available at: https://github.com/Computational-Turbulence-Group/SURD.

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