Georg Manten and Cecilia Casolo

Abstract

Inferring the causal structure underlying stochastic dynamical systems from observational data holds great promise in domains ranging from science and health to finance. Such processes can often be accurately modelled via stochastic differential equations (SDEs), which naturally imply causal relationships via `which variables enter the differential of which other variables'. In this paper, we develop a kernel-based test of conditional independence (CI) on `path-space'---solutions to SDEs---by leveraging recent advances in signature kernels. We demonstrate strictly superior performance of our proposed CI test compared to existing approaches on path-space. Then, we develop constraint-based causal discovery algorithms for acyclic stochastic dynamical systems (allowing for loops) that leverage temporal information to recover the entire directed graph. Assuming faithfulness and a CI oracle, our algorithm is sound and complete. We empirically verify that our developed CI test in conjunction with the causal discovery algorithm reliably outperforms baselines across a range of settings. 

Our speakers

Georg is a PhD student in Niki Kilbertus group at the Technical University of Munich, working on causal discovery and identifiability in dynamical systems. He received a MSc in Mathematics and a MSc in Theoretical Physics from the University of Heidelberg, during which he worked on Algebraic Geometry and Topological Quantum Field Theories

Cecilia is a PhD student in Niki Kilbertus group at the Technical University of Munich and Helmholtz, working on the intersection of causality and dynamical systems. She received her MSc in Applied Mathematics from Technical University of Delft. During her studies, she had the opportunity to pursue her thesis at ETH on Causal Fairness of Machine Learning, under the supervision of Marloes Maathuis and Geurt Jongbloed.

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