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Identifying Nonstationary Causal Structures with High-Order Markov Switching Models

Carles Balsells-Rodas, Yixin Wang, Pedro A. M. Mediano, Yingzhen Li

TL;DR

This work addresses nonstationary time-series causal discovery by introducing regime-dependent graphs captured through high-order Markov Switching Models (MSMs). It proves identifiability for both non-parametric and parametric Gaussian MSMs, enabling recovery of regime-specific causal structures up to permutation, and proposes an EM-based estimation framework with neural-network parameterizations for transitions. Through synthetic experiments and analysis of ECoG brain data, the approach demonstrates scalability and reveals richer dynamics under different regimes, particularly in Awake versus Anaesthetised states. The paper thus provides a principled, scalable avenue for identifying causal structure in nonstationary time series, with significant implications for neuroscience and other domains dealing with regime shifts.

Abstract

Causal discovery in time series is a rapidly evolving field with a wide variety of applications in other areas such as climate science and neuroscience. Traditional approaches assume a stationary causal graph, which can be adapted to nonstationary time series with time-dependent effects or heterogeneous noise. In this work we address nonstationarity via regime-dependent causal structures. We first establish identifiability for high-order Markov Switching Models, which provide the foundations for identifiable regime-dependent causal discovery. Our empirical studies demonstrate the scalability of our proposed approach for high-order regime-dependent structure estimation, and we illustrate its applicability on brain activity data.

Identifying Nonstationary Causal Structures with High-Order Markov Switching Models

TL;DR

This work addresses nonstationary time-series causal discovery by introducing regime-dependent graphs captured through high-order Markov Switching Models (MSMs). It proves identifiability for both non-parametric and parametric Gaussian MSMs, enabling recovery of regime-specific causal structures up to permutation, and proposes an EM-based estimation framework with neural-network parameterizations for transitions. Through synthetic experiments and analysis of ECoG brain data, the approach demonstrates scalability and reveals richer dynamics under different regimes, particularly in Awake versus Anaesthetised states. The paper thus provides a principled, scalable avenue for identifying causal structure in nonstationary time series, with significant implications for neuroscience and other domains dealing with regime shifts.

Abstract

Causal discovery in time series is a rapidly evolving field with a wide variety of applications in other areas such as climate science and neuroscience. Traditional approaches assume a stationary causal graph, which can be adapted to nonstationary time series with time-dependent effects or heterogeneous noise. In this work we address nonstationarity via regime-dependent causal structures. We first establish identifiability for high-order Markov Switching Models, which provide the foundations for identifiable regime-dependent causal discovery. Our empirical studies demonstrate the scalability of our proposed approach for high-order regime-dependent structure estimation, and we illustrate its applicability on brain activity data.
Paper Structure (37 sections, 15 theorems, 57 equations, 2 figures, 1 table)

This paper contains 37 sections, 15 theorems, 57 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Causal Discovery in Time Series
  4. Markov Switching Models
  5. Identifiability Analysis
  6. High-Order MSMs
  7. Non-parametric identifiability.
  8. Regime-dependent Causal Discovery
  9. Estimation
  10. Experiments
  11. Synthetic Data
  12. Regime-dependent causal structure estimation
  13. Assumption violations
  14. Brain Activity Data
  15. Conclusions
  16. ...and 22 more sections

Key Result

Theorem 3.2

Consider the Markov switching model family with order $M$ defined in Equation (eq:msm_finite_mixture) under non-linear Gaussian families $\mathcal{M}(\mathcal{I}_{\mathcal{A}}^M, \mathcal{G}_{\mathcal{B}}^M)$. Assume: Then the Markov switching model family is identifiable as defined in def:identifiability.

Figures (2)

  • Figure 1: Synthetic experiments on high-order MSMs: averaged $F_1$ score on (a) low and (b) high sparsity settings; (c) averaged $L_2$ distance using different model assumptions.
  • Figure 2: (a) Test log-likelihood of ECoG data using different lags. (b) Posterior distribution of an ECoG epoch on Awake and Anaesthetised conditions using $K=5$ states and $M=2$ lags.

Theorems & Definitions (30)

  • Definition 3.1
  • Theorem 3.2
  • Definition 3.3
  • Corollary 3.4
  • Definition A.1
  • Definition A.2
  • Proposition A.3
  • Proposition B.1
  • Theorem B.2
  • proof
  • ...and 20 more