# Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes

arXiv: https://arxiv.org/abs/2402.18477 · HTML: https://mlsanity.com/paper/2402.18477/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 121 references that are in the map.
- First posted on arXiv 28 Feb 2024.

## Builds on (most cited first, 30 of 53)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [High-recall causal discovery for autocorrelated time series with latent confounders](https://mlsanity.com/paper/2007.01884/) (2020)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Learning to Induce Causal Structure](https://mlsanity.com/paper/2204.04875/) (2022)
- [Granger Causality: A Review and Recent Advances](https://mlsanity.com/paper/2105.02675/) (2021)
- [The Signature Kernel is the solution of a Goursat PDE](https://mlsanity.com/paper/2006.14794/) (2020)
- [Signature moments to characterize laws of stochastic processes](https://mlsanity.com/paper/1810.10971/) (2018)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [Scalable Causal Discovery with Score Matching](https://mlsanity.com/paper/2304.03382/) (2023)
- [Model-Powered Conditional Independence Test](https://mlsanity.com/paper/1709.06138/) (2017)
- [Neural graphical modelling in continuous-time: consistency guarantees and algorithms](https://mlsanity.com/paper/2105.02522/) (2021)
- [From Ordinary Differential Equations to Structural Causal Models: the deterministic case](https://mlsanity.com/paper/1408.2063/) (2014)
- [Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions](https://mlsanity.com/paper/1604.05251/) (2016)
- [Non-adversarial training of Neural SDEs with signature kernel scores](https://mlsanity.com/paper/2305.16274/) (2023)

## Built on by (most cited first, 18 of 18)

- [Theoretical Foundations of Deep Selective State-Space Models](https://mlsanity.com/paper/2402.19047/) (2024)
- [Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Models](https://mlsanity.com/paper/2505.17761/) (2025)
- [Lecture notes on rough paths and applications to machine learning](https://mlsanity.com/paper/2404.06583/) (2024)
- [Dynamic Structural Causal Models](https://mlsanity.com/paper/2406.01161/) (2024)
- [Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots](https://mlsanity.com/paper/2410.22729/) (2024)
- [Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signals](https://mlsanity.com/paper/2405.13587/) (2024)
- [Interventional Time Series Priors for Causal Foundation Models](https://mlsanity.com/paper/2603.11090/) (2026)
- [Sparse Signature Coefficient Recovery via Kernels](https://mlsanity.com/paper/2412.08579/) (2024)
- [pySigLib -- Fast Signature-Based Computations on CPU and GPU](https://mlsanity.com/paper/2509.10613/) (2025)
- [SigDiffusions: Score-Based Diffusion Models for Time Series via Log-Signature Embeddings](https://mlsanity.com/paper/2406.10354/) (2024)
- [ParallelFlow: Parallelizing Linear Transformers via Flow Discretization](https://mlsanity.com/paper/2504.00492/) (2025)
- [An Asymmetric Independence Model for Causal Discovery on Path Spaces](https://mlsanity.com/paper/2503.09859/) (2025)
- [Causal-TS: A Python Library for Causal Discovery in High-Dimensional and Nonstationary Time Series](https://mlsanity.com/paper/2607.24673/) (2026)
- [Log-PDE Methods for Rough Signature Kernels](https://mlsanity.com/paper/2404.02926/) (2024)
- [Novelty detection on path space](https://mlsanity.com/paper/2512.03243/) (2025)
- [Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems](https://mlsanity.com/paper/2603.08311/) (2026)
- [Faithful Embeddings of Irregular and Asynchronous Data for Online Log-NCDEs](https://mlsanity.com/paper/2605.30213/) (2026)
- [Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts](https://mlsanity.com/paper/2606.28228/) (2026)

## 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.