Learning Multiscale Non-stationary Causal Structures - Paper Abstract

Aug 2, 2026

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A solution for modeling causal relationships that evolve over time and operate at different time scales. The paper introduces the multiscale non-stationary directed acyclic graph (MN-DAG) for multivariate time series, combining spectral and causality theory to define a probabilistic generative model. It also proposes MN-CASTLE, a Bayesian learner using stochastic variational inference and local partial-correlation information across time resolutions, yielding realistic time-series properties and outperforming baselines on synthetic data.

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Pages39

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Abstract

1 Introduction

Learning Multiscale Non-stationary Causal Structures Gabriele D’Acunto [gabriele. dacunto@uniroma1.it](gabriele. dacunto@uniroma1.it) DIAG, Sapienza University of Rome Centai Institute, Turin, Italy Gianmarco De Francisci Morales [gdfm@acm. org](gdfm@acm. org) Centai Institute, Turin, Italy [Paolo Bajardi](Paolo Bajardi paolo. bajardi@centai. eu)[ paolo. bajardi@centai. eu](Paolo Bajardi paolo. bajardi@centai. eu) Centai Institute, Turin, Italy Francesco Bonchi [francesco. bonchi@centai. eu](francesco. bonchi@centai. eu) Centai Institute, Turin, Italy Reviewed on OpenReview: [https: // openreview. net/ forum? id= SQnPE63jtA](https: // openreview. net/ forum? id= SQnPE63jtA) Abstract This paper addresses a gap in the current state of the art by providing a solution for modeling causal relationships that evolve over time and occur at different time scales. Specifically, we introduce the multiscale non-stationary directed acyclic graph (MN-DAG), a framework for modeling multivariate time series data. Our contribution is twofold. Firstly, we exposea probabilistic generative model by leveraging results from spectral and causality theories. Our model allows sampling an MN-DAG according to user-specified priors on the timedependence and multiscale properties of the causal graph. Secondly, we devise a Bayesian method named Multiscale Non-stationary Causal Structure Learner (MN-CASTLE) that uses stochastic variational inference to estimate MN-DAGs. The method also exploits information from the local partial correlation between time series over different time resolutions. The data generated from an MN-DAG reproduces well-known features of time series in different domains, such as volatility clustering and serial correlation. Additionally, we show the superior performance of MN-CASTLE on synthetic data with different multiscale and non-stationary properties compared to baseline models. Finally, we apply MN-CASTLE to identify the drivers of the natural gas prices in the US market. Causal relationships have strengthened during the COVID-19 outbreak and the Russian invasion of Ukraine, a fact that baseline methods fail to capture. MN-CASTLE identifies the causal impact of critical economic drivers on natural gas prices, such as seasonal factors, economic uncertainty, oil prices, and gas storage deviations. 1 Introduction A causal graph describes causal relationships among the constituents of a given system, and represents a powerful tool to analyze such a system under interventions and distribution changes. In general, causal graphs are unknown. Fortunately, it is possible to leverage causal structure learning approaches to unveil and quantify the causal relationships among variables. While randomized experiments are the gold standard for testing causal hypotheses (especially in medicine and the social sciences), in many cases such interventional approaches are unfeasible or unethical. Hence, great effort has been devoted to the development of methods able to retrieve causal structures from observational data (Glymour et al. , 2019 ; Schölkopf et al. , 2021) . Regardless of the different causal structure learning methods, the most informative causal graph is a directed acyclic graph (DAG), where the nodes in V are the variables of the system, all possible edges eij ∈ E ⊆ V × V are directed and represent direct causal effects, and feedback loops among nodes are forbidden (acyclicity requirement) . A DAG can be associated with its functional representation, also known as structural equation model (SEM, Pearl 2009) . Here each node of the causal graph is written as a function of the values of a set of parents nodes and of an endogenous latent noise (see Appendix A) . In this work, we focus on the case in which such functions are linear and the latent noise is additive. Even though widely studied and applied, a linear SEM is not adequate to cope with causal relations that evolve over time and occur at different

FAQs

What problem does MN-DAG address in causal modeling?

It models causal relationships in multivariate time series that change over time and act at multiple time scales, overcoming limits of stationary single-timescale linear SEMs.

How does MN-CASTLE learn multiscale non-stationary causal structures?

MN-CASTLE is a Bayesian method that uses stochastic variational inference to estimate MN-DAGs and leverages local partial correlations between series across different time resolutions.

How is MN-DAG validated and where is it applied?

Synthetic experiments show it reproduces known time-series behaviors and improves over baselines. It is also applied to identify drivers of US natural gas prices during COVID-19 and the Russian invasion of Ukraine.

Aug 2, 2026

Upload by Maeve