mlsanityData to 7 Oct 2026

Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes

arXiv 2402.18477 ↗First posted 28 Feb 2024cs.LG cs.AI stat.MLcited by 18

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Abstract (arXiv)

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.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 53 of its 121 references that are in the map. First posted on arXiv 28 Feb 2024.

Builds on

53 of 121 references.

References · 53

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38 more
  1. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
  2. 2021DiBS: Differentiable Bayesian Structure Learningcited by 105
  3. 2016A Primer on the Signature Method in Machine Learningcited by 100
  4. 2020A Measure-Theoretic Approach to Kernel Conditional Mean Embeddingscited by 86
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  6. 2020High-recall causal discovery for autocorrelated time series with latent confounderscited by 82
  7. 2017Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discoverycited by 76
  8. 2022Learning to Induce Causal Structurecited by 68
  9. 2021Granger Causality: A Review and Recent Advancescited by 62
  10. 2020The Signature Kernel is the solution of a Goursat PDEcited by 58
  11. 2018Signature moments to characterize laws of stochastic processescited by 54
  12. 2022Differentiable DAG Samplingcited by 46
  13. 2017Model-Powered Conditional Independence Testcited by 43
  14. 2021Neural graphical modelling in continuous-time: consistency guarantees and algorithmscited by 42
  15. 2023Scalable Causal Discovery with Score Matchingcited by 42
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  18. 2023Non-adversarial training of Neural SDEs with signature kernel scorescited by 36
  19. 2023A Survey on Causal Discovery Methods for I.I.D. and Time Series Datacited by 35
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  38. 2023Kernel-based independence tests for causal structure learning on functional datacited by 6

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Citing papers per year: 2024: 8; 2025: 5; 2026: 5.

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  1. 2024Theoretical Foundations of Deep Selective State-Space Modelscited by 73
  2. 2025Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Modelscited by 16
  3. 2024Lecture notes on rough paths and applications to machine learningcited by 13
  4. 2024Dynamic Structural Causal Modelscited by 13
  5. 2024Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshotscited by 10
  6. 2024Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signalscited by 9
  7. 2026Interventional Time Series Priors for Causal Foundation Modelscited by 6
  8. 2024Sparse Signature Coefficient Recovery via Kernelscited by 5
  9. 2025pySigLib -- Fast Signature-Based Computations on CPU and GPUcited by 5
  10. 2024SigDiffusions: Score-Based Diffusion Models for Time Series via Log-Signature Embeddingscited by 4
  11. 2025ParallelFlow: Parallelizing Linear Transformers via Flow Discretizationcited by 3
  12. 2025An Asymmetric Independence Model for Causal Discovery on Path Spacescited by 2
6 more
  1. 2026Causal-TS: A Python Library for Causal Discovery in High-Dimensional and Nonstationary Time Seriescited by 1
  2. 2024Log-PDE Methods for Rough Signature Kernelscited by 0
  3. 2025Novelty detection on path spacecited by 0
  4. 2026Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systemscited by 0
  5. 2026Faithful Embeddings of Irregular and Asynchronous Data for Online Log-NCDEscited by 0
  6. 2026Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shiftscited by 0