An Asymmetric Independence Model for Causal Discovery on Path Spaces
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 13 of its 37 references that are in the map. First posted on arXiv 12 Mar 2025.
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13 of 37 references.
References · 13
- 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
- 2017Detecting causal associations in large nonlinear time series datasetscited by 244
- 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 211
- 2013Causal Inference in the Presence of Latent Variables and Selection Biascited by 166
- 2020Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasetscited by 137
- 2018Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounderscited by 35
- 2017Markov Properties for Graphical Models with Cycles and Latent Variablescited by 32
- 2020Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cyclescited by 31
- 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
- 2021Conditional Independence Testing in Hilbert Spaces with Applications to Functional Data Analysiscited by 12
- 2022Nonparametric Conditional Local Independence Testingcited by 7
- 2023Kernel-based independence tests for causal structure learning on functional datacited by 6
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Citing papers per year: 2026: 2.
2 papers.