# Dynamic Structural Causal Models

arXiv: https://arxiv.org/abs/2406.01161 · HTML: https://mlsanity.com/paper/2406.01161/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 45 references that are in the map.
- First posted on arXiv 3 Jun 2024.

## Builds on (most cited first, 12 of 12)

- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [From Deterministic ODEs to Dynamic Structural Causal Models](https://mlsanity.com/paper/1608.08028/) (2016)
- [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)
- [Causal Modeling of Dynamical Systems](https://mlsanity.com/paper/1803.08784/) (2018)
- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Bias](https://mlsanity.com/paper/1901.00433/) (2019)
- [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)
- [Conditional independences and causal relations implied by sets of equations](https://mlsanity.com/paper/2007.07183/) (2020)
- [Graphical criteria for the identification of marginal causal effects in continuous-time survival and event-history analyses](https://mlsanity.com/paper/2202.02311/) (2022)

## Built on by (most cited first, 14 of 14)

- [TabPFN-3: Technical Report](https://mlsanity.com/paper/2605.13986/) (2026)
- [Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots](https://mlsanity.com/paper/2410.22729/) (2024)
- [CausalDynamics: A large-scale benchmark for structural discovery of dynamical causal models](https://mlsanity.com/paper/2505.16620/) (2025)
- [Interventional Time Series Priors for Causal Foundation Models](https://mlsanity.com/paper/2603.11090/) (2026)
- [Emergence of psychopathological computations in large language models](https://mlsanity.com/paper/2504.08016/) (2025)
- [Towards Continuous-time Causal Foundation Models](https://mlsanity.com/paper/2605.28880/) (2026)
- [Deep Koopman operator framework for causal discovery in nonlinear dynamical systems](https://mlsanity.com/paper/2505.14828/) (2025)
- [Causal Representation Meets Stochastic Modeling under Generic Geometry](https://mlsanity.com/paper/2602.05033/) (2026)
- [Causal Process Models: Reframing Dynamic Causal Graph Discovery as a Reinforcement Learning Problem](https://mlsanity.com/paper/2507.13920/) (2025)
- [A Causal DAG Prior for Synthetic Time-Series Classification Datasets](https://mlsanity.com/paper/2606.21776/) (2026)
- [Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Models](https://mlsanity.com/paper/2606.04822/) (2026)
- [Temporal Causal Prior-Data Fitted Networks for Panel Data with Learned Reliability Signals](https://mlsanity.com/paper/2606.20889/) (2026)
- [Beyond Directed Acyclic Graphs: Causal Zeros and Causal Differential Equations](https://mlsanity.com/paper/2607.22910/) (2026)
- [One Intervention per Component is Enough: Towards Identifiability in Linear Stochastic Dynamics from Steady State](https://mlsanity.com/paper/2609.19955/) (2026)

## Abstract (arXiv)

We study a specific type of SCM, called a Dynamic Structural Causal Model (DSCM), whose endogenous variables represent functions of time, which is possibly cyclic and allows for latent confounding. As a motivating use-case, we show that certain systems of Stochastic Differential Equations (SDEs) can be appropriately represented with DSCMs. An immediate consequence of this construction is a graphical Markov property for systems of SDEs. We define a time-splitting operation, allowing us to analyse the concept of local independence (a notion of continuous-time Granger (non-)causality). We also define a subsampling operation, which returns a discrete-time DSCM, and which can be used for mathematical analysis of subsampled time-series. We give suggestions how DSCMs can be used for identification of the causal effect of time-dependent interventions, and how existing constraint-based causal discovery algorithms can be applied to time-series data.