[Paper Review] Identifying Direct Causes using Intervened Target Variable

Kang Du, Yu Xiang+1 more|arXiv (Cornell University)|Jul 15, 2023

Bayesian Modeling and Causal InferenceComputer Science3 citations

TL;DR

This paper proposes a novel method for identifying direct causal parents of a target variable in linear structural causal models when the target is intervened upon, using an invariant matching property (IMP) framework. By leveraging interventional data where only the target variable is manipulated, the method identifies causal parents through a voting procedure over invariant matching properties, demonstrating robust performance on synthetic and real-world datasets, including flow cytometry and COVID-19 case prediction, even under violated invariance assumptions.

ABSTRACT

Identifying the direct causes or causal parents of a target variable is crucial for scientific discovery. Focusing on linear models, the invariant prediction framework was built upon the invariance principle, namely, the conditional distribution of the target variable given its causal parents is invariant across multiple environments or experimental conditions. However, their identifiability results for causal parents can be restrictive with respect to the underlying graph structure and the experimental conditions for generating interventional data. Motivated by a recent alternative formulation of invariance, called the invariant matching property, we establish identifiability results under relatively mild assumptions, which leads to a simple yet effective procedure for identifying causal parents. We demonstrate the performance of the proposed method over various synthetic and real datasets.

Motivation & Objective

• To address the limitation of existing invariant causal prediction (ICP) methods, which fail when the target variable is intervened upon.
• To establish identifiability of causal parents under milder assumptions than prior work, particularly when only the target variable is intervened.
• To develop a simple yet effective voting procedure for estimating causal parents in finite-sample settings using the invariant matching property (IMP).
• To validate the method on both synthetic data with known structures and real-world datasets where causal structures are unknown or violated.
• To demonstrate that IMP-based methods can outperform ICP and LiNGAM in settings where invariance assumptions are violated due to interventions on the target

Proposed method

• Proposes a new identifiability framework based on the invariant matching property (IMP), which holds when the conditional distribution of the target given its parents remains invariant across environments despite interventions on the target.
• Introduces a voting procedure that aggregates IMPs across multiple environments to estimate the set of causal parents, with each feature receiving a vote if it satisfies the IMP condition in a given environment.
• Uses linear minimum mean squared error (LMMSE) estimators to define the IMP condition, ensuring computational efficiency and robustness to noise.
• Applies the method to both synthetic data and real datasets (flow cytometry and COVID-19), comparing results with ICP and LiNGAM.
• Employs a significance test to assess whether a feature set satisfies the IMP condition, with a focus on identifying features that are consistently selected across environments.
• Validates the method under conditions where the standard invariance principle (ICP) fails due to interventions on the target variable

Experimental results

Research questions

• RQ1 Can causal parents of a target variable be identified when the target is intervened upon, under milder assumptions than those required by the standard invariance principle?
• RQ2 Does the invariant matching property (IMP) remain a valid form of invariance when only the target variable is intervened, and can it be used for causal discovery?
• RQ3 How does the proposed voting procedure compare to ICP and LiNGAM in identifying causal parents under intervention on the target variable?
• RQ4 Can the IMP-based method identify meaningful causal features in real-world datasets with unknown or complex causal structures, such as the flow cytometry and COVID-19 datasets?
• RQ5 To what extent do the assumptions of the IMP method hold in practice, and how robust is the method when these assumptions are violated?

Key findings

• In the flow cytometry dataset, the proposed method correctly identified Raf as the causal parent of MEK 1/2, which is consistent with known biological interactions, and Raf received the highest number of votes (46% at n=200).
• ICP failed to identify any causal parents in the flow cytometry dataset due to interventions on the target variable, while the proposed IMP-based method successfully detected the true parent.
• In the COVID-19 dataset, the feature 'virus pressure' (index 10) received significantly more votes than other features, and it is biologically plausible as a key predictor of local case counts due to spatial correlation.
• LiNGAM identified the target variable as isolated from all others, likely due to its reliance on non-Gaussianity and continuous variable assumptions, which may not hold in this setting.
• ICP rejected the null hypothesis of invariance at the 0.05 significance level, indicating that the standard invariance principle does not hold when the target is intervened upon.
• IMP${}_{ ext{inv}}$ failed to identify any IMPs in the COVID dataset at the 0.05 level, suggesting that the invariance condition (4) is violated, likely due to nonlinearities or hidden confounders