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SIGNATURE KERNEL CONDITIONAL INDEPENDENCE TESTS IN CAUSAL DISCOVERY FOR STOCHASTIC PROCESSES

Manten, Georg ; Casolo, Cecilia ; Ferrucci, Emilio ; Mogensen, Søren Wengel LU ; Salvi, Cristopher and Kilbertus, Niki (2025) 13th International Conference on Learning Representations, ICLR 2025 In 13th International Conference on Learning Representations, ICLR 2025 p.62970-63006
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 modeled 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 conditional independence (CI) constraints on coordinate processes over selected intervals that are Markov with respect to the acyclic dependence graph (allowing self-loops) induced by a general SDE model. We then provide a sound and complete causal discovery algorithm, capable of handling both fully and partially observed data, and uniquely... (More)

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 modeled 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 conditional independence (CI) constraints on coordinate processes over selected intervals that are Markov with respect to the acyclic dependence graph (allowing self-loops) induced by a general SDE model. We then provide a sound and complete causal discovery algorithm, capable of handling both fully and partially observed data, and uniquely recovering the underlying or induced ancestral graph by exploiting time directionality assuming a CI oracle. Finally, to make our algorithm practically usable, we also propose a flexible, consistent signature kernel-based CI test to infer these constraints from data. We extensively benchmark the CI test in isolation and as part of our causal discovery algorithms, outperforming existing approaches in SDE models and beyond.

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author
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organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
13th International Conference on Learning Representations, ICLR 2025
series title
13th International Conference on Learning Representations, ICLR 2025
pages
37 pages
publisher
International Conference on Learning Representations, ICLR
conference name
13th International Conference on Learning Representations, ICLR 2025
conference location
Singapore, Singapore
conference dates
2025-04-24 - 2025-04-28
external identifiers
  • scopus:105010254918
ISBN
9798331320850
language
English
LU publication?
yes
id
7c9cb1f3-d156-4c50-9895-82709a103387
date added to LUP
2026-01-20 16:21:24
date last changed
2026-01-20 16:22:38
@inproceedings{7c9cb1f3-d156-4c50-9895-82709a103387,
  abstract     = {{<p>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 modeled 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 conditional independence (CI) constraints on coordinate processes over selected intervals that are Markov with respect to the acyclic dependence graph (allowing self-loops) induced by a general SDE model. We then provide a sound and complete causal discovery algorithm, capable of handling both fully and partially observed data, and uniquely recovering the underlying or induced ancestral graph by exploiting time directionality assuming a CI oracle. Finally, to make our algorithm practically usable, we also propose a flexible, consistent signature kernel-based CI test to infer these constraints from data. We extensively benchmark the CI test in isolation and as part of our causal discovery algorithms, outperforming existing approaches in SDE models and beyond.</p>}},
  author       = {{Manten, Georg and Casolo, Cecilia and Ferrucci, Emilio and Mogensen, Søren Wengel and Salvi, Cristopher and Kilbertus, Niki}},
  booktitle    = {{13th International Conference on Learning Representations, ICLR 2025}},
  isbn         = {{9798331320850}},
  language     = {{eng}},
  pages        = {{62970--63006}},
  publisher    = {{International Conference on Learning Representations, ICLR}},
  series       = {{13th International Conference on Learning Representations, ICLR 2025}},
  title        = {{SIGNATURE KERNEL CONDITIONAL INDEPENDENCE TESTS IN CAUSAL DISCOVERY FOR STOCHASTIC PROCESSES}},
  year         = {{2025}},
}