# Reconstructing regime-dependent causal relationships from observational time series

arXiv: https://arxiv.org/abs/2007.00267 · HTML: https://mlsanity.com/paper/2007.00267/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 28 of 28)

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- [Causal Discovery from Conditionally Stationary Time Series](https://mlsanity.com/paper/2110.06257/) (2021)
- [Discovering Mixtures of Structural Causal Models from Time Series Data](https://mlsanity.com/paper/2310.06312/) (2023)
- [On the Identifiability of Switching Dynamical Systems](https://mlsanity.com/paper/2305.15925/) (2023)
- [Causal Discovery from Time Series with Hybrids of Constraint-Based and Noise-Based Algorithms](https://mlsanity.com/paper/2306.08765/) (2023)
- [SpaceTime: Causal Discovery from Non-Stationary Time Series](https://mlsanity.com/paper/2501.10235/) (2025)
- [Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises](https://mlsanity.com/paper/2506.17065/) (2025)
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- [Causal Temporal Regime Structure Learning](https://mlsanity.com/paper/2311.01412/) (2023)
- [Causal Discovery-Driven Change Point Detection in Time Series](https://mlsanity.com/paper/2407.07290/) (2024)
- [Coarse-to-Fine Learning of Dynamic Causal Structures](https://mlsanity.com/paper/2602.22532/) (2026)
- [Identifying Nonstationary Causal Structures with High-Order Markov Switching Models](https://mlsanity.com/paper/2406.17698/) (2024)
- [Generating Hypotheses of Dynamic Causal Graphs in Neuroscience: Leveraging Generative Factor Models of Observed Time Series](https://mlsanity.com/paper/2505.20697/) (2025)
- [Transformer Is Inherently a Causal Learner](https://mlsanity.com/paper/2601.05647/) (2026)
- [End-to-End Identifiable and Consistent Recurrent Switching Dynamical Systems](https://mlsanity.com/paper/2605.06315/) (2026)
- [Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families](https://mlsanity.com/paper/2606.02231/) (2026)
- [Scalable Temporal Anomaly Causality Discovery in Large Systems: Achieving Computational Efficiency with Binary Anomaly Flag Data](https://mlsanity.com/paper/2412.11800/) (2024)
- [CausationEntropy: Pythonic Optimal Causation Entropy](https://mlsanity.com/paper/2601.13365/) (2026)
- [Latent-Space Causal Discovery from Indirect Neuroimaging Observations](https://mlsanity.com/paper/2602.09034/) (2026)
- [Deep Learning Surrogates for Emulating Stochastic Climate Tipping Dynamics](https://mlsanity.com/paper/2605.20580/) (2026)
- [Enhancing Regime Shift Detection Using Unstructured Data: A Study on the Treasury Market](https://mlsanity.com/paper/2605.30363/) (2026)
- [Modeling Covariate Transition for Efficient Estimation of Longitudinal Treatment Effects in Randomized Experiments](https://mlsanity.com/paper/2605.31443/) (2026)
- [Dynamic Structural Causal Modeling for Sleep](https://mlsanity.com/paper/2608.20285/) (2026)
- [Beyond Stationarity in Time Series: Discovering Causal Structures and Latent Regimes via Markov Blankets](https://mlsanity.com/paper/2609.05150/) (2026)
- [ITSY: Causal Discovery From Irregular Time-Series Data](https://mlsanity.com/paper/2609.23516/) (2026)

## Abstract (arXiv)

Inferring causal relations from observational time series data is a key problem across science and engineering whenever experimental interventions are infeasible or unethical. Increasing data availability over the past decades has spurred the development of a plethora of causal discovery methods, each addressing particular challenges of this difficult task. In this paper we focus on an important challenge that is at the core of time series causal discovery: regime-dependent causal relations. Often dynamical systems feature transitions depending on some, often persistent, unobserved background regime, and different regimes may exhibit different causal relations. Here, we assume a persistent and discrete regime variable leading to a finite number of regimes within which we may assume stationary causal relations. To detect regime-dependent causal relations, we combine the conditional independence-based PCMCI method with a regime learning optimisation approach. PCMCI allows for linear and nonlinear, high-dimensional time series causal discovery. Our method, Regime-PCMCI, is evaluated on a number of numerical experiments demonstrating that it can distinguish regimes with different causal directions, time lags, effects and sign of causal links, as well as changes in the variables' autocorrelation. Further, Regime-PCMCI is employed to observations of El Ni~no Southern Oscillation and Indian rainfall, demonstrating skill also in real-world datasets.