An Asymmetric Independence Model for Causal Discovery on Path Spaces

MCML Authors

Georg Manten

→ Group Niki Kilbertus
 Ethics in Systems Design and Machine Learning

Cecilia Casolo

→ Group Niki Kilbertus
 Ethics in Systems Design and Machine Learning

Niki Kilbertus

Prof. Dr.

Principal Investigator

Ethics in Systems Design and Machine Learning

Abstract

We develop the theory linking 'E-separation' in directed mixed graphs (DMGs) with conditional independence relations among coordinate processes in stochastic differential equations (SDEs), where causal relationships are determined by 'which variables enter the governing equation of which other variables'. We prove a global Markov property for cyclic SDEs, which naturally extends to partially observed cyclic SDEs, because our asymmetric independence model is closed under marginalization. We then characterize the class of graphs that encode the same set of independence relations, yielding a result analogous to the seminal 'same skeleton and v-structures' result for directed acyclic graphs (DAGs). In the fully observed case, we show that each such equivalence class of graphs has a greatest element as a parsimonious representation and develop algorithms to identify this greatest element from data. We conjecture that a greatest element also exists under partial observations, which we verify computationally for graphs with up to four nodes.

inproceedings

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CLeaR 2025

4th Conference on Causal Learning and Reasoning. Lausanne, Switzerland, May 07-09, 2025.

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Authors

G. Manten • C. Casolo • S. W. Mogensen • N. Kilbertus

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Links

URL

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Research Area

 A3 | Computational Models