Published Paper: Reconstructing regime-dependent causal relationships from observational time series

MPE Reading Student Elena Saggioro’s paper has been published open access in

Chaos: An Interdisciplinary Journal of Nonlinear Science.

You can read the paper here

A full list of Authors:  Elena Saggioro, Jana de Wiljes, Marlene Kretschmer, and Jakob Runge


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 few 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 [based on a condition-selection step (PC) followed by the momentary conditional independence (MCI) test] with a regime learning optimization approach. PCMCI allows for causal discovery from high-dimensional and highly correlated time series. Our method, Regime-PCMCI, is evaluated on a number of numerical experiments demonstrating that it can distinguish regimes with different causal directions, time lags, and sign of causal links, as well as changes in the variables’ autocorrelation. Furthermore, Regime-PCMCI is employed to observations of El Niño Southern Oscillation and Indian rainfall, demonstrating skill also in real-world datasets.


E Saggiori Fig2

Key to Figure:

Example case Sign X 1 X 2 . (a) The ground-truth regime- assigning process, {γ }re f (top), the Regime-PCMCI reconstructed process, {γ}reco. (middle) and the difference between the two, ∆γ (bottom). (b) The ground-truth networks for each regime (top), the Regime-PCMCI reconstructed networks (middle) and the difference between the two (bottom). The links are labelled with the associated linear coefficient Φkj (i, τ ) and the lag τ . The sign of the coefficient is highlighted by the color (red for positive, blue for negative).