[Paper Review] Causal Discovery from Heterogeneous/Nonstationary Data

Biwei Huang, Kun Zhang+5 more|arXiv (Cornell University)|Mar 5, 2019

Bayesian Modeling and Causal Inference76 citations

TL;DR

This paper proposes CD-NOD, a nonparametric constraint-based framework for causal discovery from heterogeneous or nonstationary data, leveraging distribution shifts to identify causal skeletons and directions without window segmentation. It enables estimation of low-dimensional representations of mechanism changes and reveals that data heterogeneity enhances causal structure identification even under confounding.

ABSTRACT

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.

Motivation & Objective

• To address the challenge of causal discovery in data where underlying mechanisms change across domains or over time due to distribution shifts.
• To develop a nonparametric method that identifies causal skeletons and orientations without relying on window segmentation or strong distributional assumptions.
• To estimate low-dimensional representations of the driving forces behind nonstationary causal mechanisms.
• To explore how data heterogeneity can improve causal structure identification, even in the presence of confounders.
• To establish a connection between nonstationarity and soft interventions in causal discovery.

Proposed method

• An enhanced constraint-based procedure detects variables with changing local mechanisms and recovers the causal skeleton across domains or time points.
• Causal orientations are determined by exploiting independent changes in data distributions, using information from distribution shifts implied by the causal model.
• A nonparametric approach estimates the low-dimensional representation of mechanism changes, capturing the driving force of nonstationarity.
• The method does not assume specific parametric forms for data distributions or causal mechanisms, ensuring broad applicability.
• It avoids window segmentation by modeling changes directly through distributional shifts across domains or time.
• The framework integrates insights from soft intervention theory, linking nonstationarity to intervention-like effects in causal discovery.

Experimental results

Research questions

• RQ1 How can causal structures be reliably recovered from heterogeneous or nonstationary data where mechanisms change across domains or time?
• RQ2 Can distribution shifts be leveraged to improve causal orientation detection without prior knowledge of change points?
• RQ3 What is an effective nonparametric method to estimate the low-dimensional representation of mechanism changes in causal models?
• RQ4 How does data heterogeneity affect causal structure identification, especially under confounding?
• RQ5 What is the theoretical connection between nonstationarity and soft interventions in causal discovery?

Key findings

• The proposed CD-NOD framework successfully identifies causal skeletons and orientations in heterogeneous and nonstationary data without requiring window segmentation.
• The method achieves improved causal structure identification by exploiting distribution shifts, even when confounders are present.
• Nonparametric estimation of mechanism change drivers enables effective low-dimensional representation of nonstationarity.
• Empirical results on synthetic, fMRI, and stock market data demonstrate the method’s robustness and efficacy across diverse data types.
• The study establishes a theoretical link between nonstationarity and soft interventions, enriching the conceptual framework of causal discovery.