[Paper Review] Causal Inference in the Presence of Latent Variables and Selection Bias

Peter Spirtes, Christopher Meek+1 more|arXiv (Cornell University)|Feb 20, 2013

Bayesian Modeling and Causal Inference21 references188 citations

TL;DR

This paper presents a reliable method for causal inference in the presence of latent variables and selection bias by leveraging conditional independence and dependence relations among observed variables. It establishes sufficient conditions to confidently infer causal paths or rule them out, even when unobserved confounders and selection effects are present, offering a robust framework for causal discovery under partial observability.

ABSTRACT

We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional independence and dependence relations between measured variables, even when latent variables and selection bias may be present, there are sufficient conditions for reliably concluding that there is a causal path from one variable to another, and sufficient conditions for reliably concluding when no such causal path exists.

Motivation & Objective

• To develop a reliable procedure for causal discovery when both latent confounders and selection bias may affect observed data.
• To identify sufficient conditions for concluding the existence or non-existence of causal paths between variables despite unobserved factors.
• To extend causal discovery methods beyond the assumption of no unmeasured confounders or selection bias.
• To provide a formal framework that maintains validity and informativeness under partial observability and latent structure.
• To ensure that conclusions about causality are both informative and reliable even when the data-generating process includes hidden variables and selection effects.

Proposed method

• The method relies on analyzing conditional independence and dependence relations among observed variables to infer causal structure.
• It uses a sound and complete algorithmic framework based on the faithfulness assumption and conditional independence testing.
• The approach incorporates adjustments for selection bias by modeling how selection mechanisms affect observed conditional independence relations.
• It extends the PC algorithm and similar constraint-based methods to handle latent variables and selection bias simultaneously.
• The method identifies v-structures and orientation rules that remain valid under latent confounding and selection bias.
• It applies a set of graphical criteria to determine when a causal path from X to Y can be reliably inferred or ruled out.

Experimental results

Research questions

• RQ1 Under what conditions can we reliably infer a causal path from one observed variable to another when latent confounders are present?
• RQ2 How can selection bias be formally accounted for in causal discovery algorithms to avoid spurious causal conclusions?
• RQ3 What criteria allow us to distinguish between genuine causal paths and spurious associations due to unobserved confounders or selection effects?
• RQ4 Can we maintain the reliability and informativeness of causal inference when both latent variables and selection bias affect the data?
• RQ5 What graphical and conditional independence constraints are sufficient to conclude the absence of a causal path between two variables in the presence of hidden confounding?

Key findings

• The paper establishes sufficient conditions for reliably concluding that a causal path exists from one variable to another, even when latent variables and selection bias are present.
• It provides sufficient conditions for reliably concluding that no causal path exists between two variables under the same conditions.
• The method maintains reliability and informativeness in causal discovery when unobserved confounders and selection bias affect the data-generating process.
• The framework allows for the identification of causal structures using only observed conditional independence and dependence relations, without requiring full knowledge of latent variables.
• The approach generalizes existing constraint-based methods by incorporating selection bias and latent confounding into the causal discovery process.
• The results demonstrate that causal inference remains possible and informative even under complex data limitations involving hidden variables and selection effects.