# Distributed Dynamic Invariant Causal Prediction in Environmental Time Series

arXiv: https://arxiv.org/abs/2603.02902 · HTML: https://mlsanity.com/paper/2603.02902/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Invariant Causal Prediction for Sequential Data](https://mlsanity.com/paper/1706.08058/) (2017)
- [Federated Causal Discovery from Heterogeneous Data](https://mlsanity.com/paper/2402.13241/) (2024)
- [A review of spatial causal inference methods for environmental and epidemiological applications](https://mlsanity.com/paper/2007.02714/) (2020)
- [Causal Discovery from Conditionally Stationary Time Series](https://mlsanity.com/paper/2110.06257/) (2021)
- [Federated Causality Learning with Explainable Adaptive Optimization](https://mlsanity.com/paper/2312.05540/) (2023)
- [CDANs: Temporal Causal Discovery from Autocorrelated and Non-Stationary Time Series Data](https://mlsanity.com/paper/2302.03246/) (2023)
- [Time Series Causal Link Estimation under Hidden Confounding using Knockoff Interventions](https://mlsanity.com/paper/2209.11497/) (2022)
- [Differentiable Invariant Causal Discovery](https://mlsanity.com/paper/2205.15638/) (2022)
- [Granger Causality using Neural Networks](https://mlsanity.com/paper/2208.03703/) (2022)
- [Federated Causal Discovery From Interventions](https://mlsanity.com/paper/2211.03846/) (2022)
- [Federated Causal Inference in Healthcare: Methods, Challenges, and Applications](https://mlsanity.com/paper/2505.02238/) (2025)

## Abstract (arXiv)

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.