Abstract:
Causality lies at the heart of scientific inquiry, serving as the fundamental basis for understanding the interactions among variables in physical systems. Despite its central role, current methods for causal inference face significant challenges due to the presence of nonlinear dependencies, stochastic and deterministic interactions, self-causation, mediator, confounder, and collider effects, and contamination from unobserved, exogenous factors, to name a few. While there are methods that can effectively address some of these challenges, no single approach has been successful in integrating all these aspects. Here, we tackle 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 based on available information from past observations. The formulation is non-intrusive and requires only pairs of past and future events, facilitating its application in both computational and experimental investigations, even when samples are scarce. We benchmark SURD against existing methods in scenarios that pose significant challenges in causal inference. These include synchronization in logistic maps, the Rössler-Lorenz system, the Lotka-Volterra prey-predator model, the Moran effect model, and energy cascade in turbulence, among others. Our findings demonstrate that SURD offers a more reliable quantification of causality compared to state-of-the-art methods for causal inference.
Bio:
Adrian Lozano Duran is an Associate Professor at GALCIT, Caltech, and a Visiting Associate Professor at MIT AeroAstro. He received his Ph.D. in Aerospace Engineering from the Technical University of Madrid in 2015. From 2016 to 2020, he was a Postdoctoral Research Fellow at Stanford University's Center for Turbulence Research. He served as an Assistant Professor at MIT from 2021 to 2024. His research focuses on computational fluid mechanics and the physics of turbulence, including causal inference, modeling, and control of turbulence using information theory. He is also interested in developing closure models for large-eddy simulations of aerospace applications using artificial intelligence.
Summary:
Focus: causal discovery in chaotic systems
Information theoretic
Causal inference
Application: decomposition of turbulent flow fields
Causality analysis pioneered by economics community
Goal: identify causal relationships among attributes of a system
Causal: which attributes influence the future evolution of the physical system
Causal analysis of high-dimensional chaotic systems
Physical insight
Causality-preserving reduced order models: small model captures the causal drivers encoded in the full system
Causality-driven control: indicate what needs to be changed to produce a given outcome
Casualty:
Causes should precede effect
Causality is different from correlation & correlation
Emergent macroscopic quantity
Challenges
Mediation: Q3->Q2->Q1
Confounder: Q3->Q2, Q3->Q1
One cause has multiple effects
The effects are correlated but not causally related to each other
Synnergistic collider: Q3->Q2, Q3->Q1
Combination of multiple causes produces novel effects
Redundant collider: Q3->Q1, Q2->Q1, Q3<->Q2
Multiple causes independently cause the same effect
Self-causation: Q1->Q1
Past values of variable cause future values
Noise
Exogenous/unobserved factors
Interventions are the best way to probe causality but it is challenging in practice
Impossible to intervene in the past
May be unethical (e.g. human studies)
Systems are often operating in their natural attractor and it is hard to push them out
Which interventions are meaningful for establishing causality?
Synergistic and redundant colliders force us to do many interventions to probe their structure
Observational methods can be applied much more generally
Model Forecasting
Statistical independence relations
Randomized experiments
Information-theoretic methods
Attractor reconstruction
Approach: SURD: Synnergistic, unique, redundant decomposition of causality
Causality is increase in information about the target variable (Shannon entropy)
Forward-in-time propagation of information
Goal: linearly decompose into causality components
Synnergistic: Join effect from multiple variables
Unique: causality from a var that cannot be obtained from other vars
Redundant: common to a group of vars
Leak: causality from unobserved vars
Method ensures these sources of causality add up to 1
Application: wind blowing over water, generating waves
To what extent does the wind drive the water and to what extent do the water waves affect the wind?
Data: experimental dataset of wind/water motion
SURD indicates that water does not drive the wind but there is a small redundancy between the two