Distributed Dynamic Invariant Causal Prediction in Environmental Time Series

Ziruo Hao; Tao Yang; Xiaofeng Wu; Bo Hu

cs.LGMar 3, 2026

Distributed Dynamic Invariant Causal Prediction in Environmental Time Series

Authors: Ziruo Hao, Tao Yang, Xiaofeng Wu, Bo Hu

Abstract

The extraction of invariant causal relationships from time series data with environmental attributes is critical for robust decision-making in domains such as climate science and environmental monitoring. However, existing methods either emphasize dynamic causal analysis without leveraging environmental contexts or focus on static invariant causal inference, leaving a gap in distributed temporal settings. In this paper, we propose Distributed Dynamic Invariant Causal Prediction in Time-series (DisDy-ICPT), a novel framework that learns dynamic causal relationships over time while mitigating spatial confounding variables without requiring data communication. We theoretically prove that DisDy-ICPT recovers stable causal predictors within a bounded number of communication rounds under standard sampling assumptions. Empirical evaluations on synthetic benchmarks and environment-segmented real-world datasets show that DisDy-ICPT achieves superior predictive stability and accuracy compared to baseline methods A and B. Our approach offers promising applications in carbon monitoring and weather forecasting. Future work will extend DisDy-ICPT to online learning scenarios.

Figures & tables

Method	Distributed System	Time Dynamics	Client Heterogeneity
CD‑NOD [ 1 ]	$\times$ Centralized	$\checkmark$ Temporal shifts	$\checkmark$ Environmental shifts
SpaceTime [ 4 ]	$\times$ Centralized	$\checkmark$ Temporal shifts	$\checkmark$ Environmental shifts
CDANs [ 5 ]	$\times$ Centralized	$\checkmark$ Dynamic lag/contemporaneous	$\times$
DyCAST [ 2 ]	$\times$ Centralized	$\checkmark$ Dynamic contemporaneous DAGs	$\times$
FedCDH [ 3 ]	$\checkmark$ Federated	$\times$ Static structure	$\checkmark$ Non-i.i.d clients
FedCDI [ 6 ]	$\checkmark$ Federated (interventional)	$\times$	$\checkmark$ Client-specific mechanisms

TABLE I: Summary Table of Related Approaches

Causal Inference

Causal inference studies how interventions and counterfactuals reveal cause-and-effect relationships beyond observed associations.

See all 316 papers

From Causal Discovery to Dynamic Causal Inference in Neural Time Series
Mar 21, 2026Dmitry Zaytsev, Valentina Kuskova, Michael CoppedgeCausal Inference Time-Series Causal Discovery
Lucy Family Institute for Data & Society, University of Notre Dame, Notre Dame, Indiana, USA · Political Science, University of Notre Dame, Notre Dame, Indiana, USA
Coarse-to-Fine Learning of Dynamic Causal Structures
Feb 26, 2026Dezhi Yang, Qiaoyu Tan, Carlotta Domeniconi +3Time-Series Causal Discovery Causal Structure Learning
School of Software Shandong University Jinan, China · Department of Computer Science New York University Shanghai, China · Department of Computer Science George Mason University VA, USA +1
DCD: Decomposition-based Causal Discovery from Autocorrelated and Non-Stationary Temporal Data
Feb 1, 2026Muhammad Hasan Ferdous, Ian Stockwell, Md Osman GaniTime-Series Causal Discovery Causal Discovery
Causal AI Lab, Department of Information Systems, University of Maryland, Baltimore County, Baltimore, MD, USA

Mar 21, 2026J/K move · Enter open · S save

From Causal Discovery to Dynamic Causal Inference in Neural Time Series

Dmitry Zaytsev, Valentina Kuskova, Michael Coppedge

Lucy Family Institute for Data & Society, University of Notre Dame, Notre Dame, Indiana, USA · Political Science, University of Notre Dame, Notre Dame, Indiana, USA

Causal Inference Time-Series Causal Discovery Causal Structure Learning Autoregressive Modeling

Open paper AskPDF arXiv

Time-varying causal models provide a powerful framework for studying dynamic scientific systems, yet most existing approaches assume that the underlying causal network is known a priori - an assumption rarely satisfied in real-world domains where causal structure is uncertain, evolving, or only indirectly observable. This limits the applicability of dynamic causal inference in many scientific settings. We propose Dynamic Causal Network Autoregression (DCNAR), a two-stage neural causal modeling framework that integrates data-driven causal discovery with time-varying causal inference. In the first stage, a neural autoregressive causal discovery model learns a sparse directed causal network from multivariate time series. In the second stage, this learned structure is used as a structural prior for a time-varying neural network autoregression, enabling dynamic estimation of causal influence without requiring pre-specified network structure. We evaluate the scientific validity of DCNAR using behavioral diagnostics that assess causal necessity, temporal stability, and sensitivity to structural change, rather than predictive accuracy alone. Experiments on multi-country panel time-series data demonstrate that learned causal networks yield more stable and behaviorally meaningful dynamic causal inferences than coefficient-based or structure-free alternatives, even when forecasting performance is comparable. These results position DCNAR as a general framework for using AI as a scientific instrument for dynamic causal reasoning under structural uncertainty.

Abstract

Causal Inference

Explore similar work

From Causal Discovery to Dynamic Causal Inference in Neural Time Series

Coarse-to-Fine Learning of Dynamic Causal Structures

DCD: Decomposition-based Causal Discovery from Autocorrelated and Non-Stationary Temporal Data