ICML 2025

Causal Discovery from Conditionally Stationary Time Series
Carles Balsells-Rodas 1 Xavier Sumba 1 Tanmayee Narendra 2 Ruibo Tu 3
Gabriele Schweikert 2 Hedvig Kjellstr¨om 3 Yingzhen Li 1
Abstract
Causal discovery, i.e., inferring underlying causal
relationships from observational data, is highly
challenging for AI systems. In a time series mod-
eling context, traditional causal discovery meth-
ods mainly consider constrained scenarios with
fully observed variables and/or data from station-
ary time-series.
We develop a causal discov-
ery approach to handle a wide class of nonsta-
tionary time series that are conditionally station-
ary, where the nonstationary behaviour is mod-
eled as stationarity conditioned on a set of latent
state variables. Named State-Dependent Causal
Inference (SDCI), our approach is able to recover
the underlying causal dependencies, with prov-
able identifiablity for the state-dependent causal
structures. Empirical experiments on nonlinear
particle interaction data and gene regulatory net-
works demonstrate SDCI’s superior performance
over baseline causal discovery methods.
Im-
proved results over non-causal RNNs on mod-
eling NBA player movements demonstrate the
potential of our method and motivate the use of
causality-driven methods for forecasting.
1. Introduction
Deep learning has achieved profound success in vision and
language modelling (Brown et al., 2020; Nichol et al., 2022).
Still, it remains a grand challenge for deep neural networks
to perform causal discovery (Yi et al., 2020; Girdhar & Ra-
manan, 2020; Sauer & Geiger, 2021), which is critical for
interpretability, generalization, and robustness (Lake et al.,
2017; Sch¨olkopf et al., 2021). Theoretically, structure iden-
tifiability is key to ensure a unique correspondence between
observations and the underlying causal structures (Peters
1Imperial College London 2University of Dundee 3KTH Royal
Institute of Technology. Correspondence to: Carles Balsells-Rodas
<cb221@imperial.ac.u...