# Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes

arXiv: https://arxiv.org/abs/1903.01672 · HTML: https://mlsanity.com/paper/1903.01672/

## Key facts

- Cited by 166 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2019.

## Built on by (most cited first, 30 of 166)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
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- [TEMPO: Prompt-based Generative Pre-trained Transformer for Time Series Forecasting](https://mlsanity.com/paper/2310.04948/) (2023)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [Causal Machine Learning for Healthcare and Precision Medicine](https://mlsanity.com/paper/2205.11402/) (2022)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [ZIN: When and How to Learn Invariance Without Environment Partition?](https://mlsanity.com/paper/2203.05818/) (2022)
- [Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis](https://mlsanity.com/paper/2206.02013/) (2022)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [AdaRL: What, Where, and How to Adapt in Transfer Reinforcement Learning](https://mlsanity.com/paper/2107.02729/) (2021)
- [A Survey on Causal Reinforcement Learning](https://mlsanity.com/paper/2302.05209/) (2023)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Nonlinear Invariant Risk Minimization: A Causal Approach](https://mlsanity.com/paper/2102.12353/) (2021)
- [Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data](https://mlsanity.com/paper/2203.15756/) (2022)
- [Towards Robust and Adaptive Motion Forecasting: A Causal Representation Perspective](https://mlsanity.com/paper/2111.14820/) (2021)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [Why did the distribution change?](https://mlsanity.com/paper/2102.13384/) (2021)
- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [A Survey on Causal Discovery Methods for I.I.D. and Time Series Data](https://mlsanity.com/paper/2303.15027/) (2023)
- [Identifying Weight-Variant Latent Causal Models](https://mlsanity.com/paper/2208.14153/) (2022)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [Action-Sufficient State Representation Learning for Control with Structural Constraints](https://mlsanity.com/paper/2110.05721/) (2021)
- [Factored Adaptation for Non-Stationary Reinforcement Learning](https://mlsanity.com/paper/2203.16582/) (2022)
- [Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noise](https://mlsanity.com/paper/2210.14706/) (2022)
- [TS-Reasoner: Domain-Oriented Time Series Inference Agents for Reasoning and Automated Analysis](https://mlsanity.com/paper/2410.04047/) (2024)
- [DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets](https://mlsanity.com/paper/2302.04178/) (2023)
- [BaCaDI: Bayesian Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2206.01665/) (2022)
- [Data Generating Process to Evaluate Causal Discovery Techniques for Time Series Data](https://mlsanity.com/paper/2104.08043/) (2021)

## Abstract (arXiv)

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper, we develop a framework for causal discovery from such data, called Constraint-based causal Discovery from heterogeneous/NOnstationary Data (CD-NOD), to find causal skeleton and directions and estimate the properties of mechanism changes. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a method to determine causal orientations by making use of independent changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. After learning the causal structure, next, we investigate how to efficiently estimate the "driving force" of the nonstationarity of a causal mechanism. That is, we aim to extract from data a low-dimensional representation of changes. The proposed methods are nonparametric, with no hard restrictions on data distributions and causal mechanisms, and do not rely on window segmentation. Furthermore, we find that data heterogeneity benefits causal structure identification even with particular types of confounders. Finally, we show the connection between heterogeneity/nonstationarity and soft intervention in causal discovery. Experimental results on various synthetic and real-world data sets (task-fMRI and stock market data) are presented to demonstrate the efficacy of the proposed methods.