# An Asymmetric Independence Model for Causal Discovery on Path Spaces

arXiv: https://arxiv.org/abs/2503.09859 · HTML: https://mlsanity.com/paper/2503.09859/

## 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.

## Builds on (most cited first, 13 of 13)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders](https://mlsanity.com/paper/1807.03024/) (2018)
- [Markov Properties for Graphical Models with Cycles and Latent Variables](https://mlsanity.com/paper/1710.08775/) (2017)
- [Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles](https://mlsanity.com/paper/2005.00610/) (2020)
- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [Conditional Independence Testing in Hilbert Spaces with Applications to Functional Data Analysis](https://mlsanity.com/paper/2101.07108/) (2021)
- [Nonparametric Conditional Local Independence Testing](https://mlsanity.com/paper/2203.13559/) (2022)
- [Kernel-based independence tests for causal structure learning on functional data](https://mlsanity.com/paper/2311.08743/) (2023)
- [A Constraint Propagation Approach to Probabilistic Reasoning](https://mlsanity.com/paper/1304.3422/) (2013)

## Built on by (most cited first, 2 of 2)

- [Learning Causal Structure of Time Series using Best Order Score Search](https://mlsanity.com/paper/2603.05370/) (2026)
- [Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts](https://mlsanity.com/paper/2606.28228/) (2026)

## 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.