iCReN identifies both instantaneous and lagged causal relations in time series by exploiting nonstationarity
Related research and updates
Synopsis
Addressing the challenge of jointly modeling instantaneous within-interval causal effects and lagged cross-interval causal effects while accounting for nonstationarity in time-series causal representation learning, this work establishes sufficient conditions for identifying latent states and their instantaneous and lagged causal structures using an observed auxiliary variable such as time or a condition label, and proposes iCReN, a contrastive-learning framework with discrete or continuous auxiliary variables that learns latent representations and estimates both causal structures, with experiments showing accurate recovery of latent states and both structures on synthetic data and utility of the learned representations for downstream forecasting on real-world data.
Figure 1: Generative model with d z = 2 d_{z}=2 and L = 1 L=1 . Gray dash-dotted, solid black, red, blue, and dashed black arrows denote conditioning of the transition-noise distributions on the auxiliary variable, transition-noise inputs to the structural functions, instantaneous causal relations, lagged causal relations, and the observation mapping, respectively.
arXivInterpretation
The paper establishes sufficient conditions for identifying latent states and their instantaneous and lagged causal structures in nonstationary time series, with identification holding up to component permutation and component-wise invertible transformations. Prior methods tend to address either lagged or instantaneous relations and rarely incorporate nonstationarity jointly; this work places both relation types and nonstationarity within a single identification framework, using an observed auxiliary variable such as time or a condition label tied to changes in transition-noise distributions. The identification result is presented as a set of sufficient conditions, i.e., a provable identifiability statement rather than an empirical inference alone.
The paper proposes iCReN, a framework that uses contrastive learning with discrete or continuous auxiliary variables to learn latent representations and estimate their instantaneous and lagged causal structures. The framework turns the identification conditions into an operational contrastive-learning objective and supports both discrete and continuous auxiliary variables, covering different sources of nonstationarity such as time indices and condition labels. The method design corresponds to its identification theory and is evaluated on both synthetic and real-world data.
Experiments show accurate recovery of latent states and of both instantaneous and lagged causal structures on synthetic data, and utility of the learned representations for downstream forecasting on real-world data. The results cover both representation recovery and structure recovery, and further test the usability of the representations in a downstream forecasting task rather than stopping at structure-recovery metrics. Evidence comes from synthetic and real-world experiments; at the abstract level it reports recovery accuracy and downstream forecasting utility without specific values, sample sizes, or comparison settings.
Perspective
The work targets research settings that identify latent states and their causal structures from observed time series, and applies when an observed auxiliary variable such as time or a condition label associated with changes in transition-noise distributions is available, supporting both discrete and continuous auxiliary variables. Its identification conclusions hold up to component permutation and component-wise invertible transformations, so the learned representations are not uniquely determined in the original coordinates. The method is used on synthetic data to verify recovery of latent states and both causal structures, and on real-world data to test the utility of the learned representations for downstream forecasting, so its direct scope is nonstationary time-series modeling and forecasting tasks.
The abstract does not give the specific synthetic data generation setup, the names and sizes of real-world datasets, evaluation metric values, or comparison baselines, so the relative magnitude of recovery accuracy and forecasting gains remains to be confirmed in the main text. The identification conditions rely on an association between the auxiliary variable and changes in transition-noise distributions; how the framework behaves when such auxiliary variables are unavailable or the change signal is weak remains an open question. Whether instantaneous and lagged structures can be reliably distinguished on real data also needs further experimental detail in the main text.