[Paper Review] Causal Inference and Causal Explanation with Background Knowledge

Christopher Meek|arXiv (Cornell University)|Feb 20, 2013

Bayesian Modeling and Causal InferenceComputer Science10 references384 citations

TL;DR

This paper presents correct algorithms for causal inference and explanation using background knowledge, addressing whether a consistent causal model exists that explains observed independence facts and identifying the common causal relationships across all such models. It integrates domain knowledge with observational data to improve causal discovery accuracy and robustness in the presence of latent confounders.

ABSTRACT

This paper presents correct algorithms for answering the following two questions; (i) Does there exist a causal explanation consistent with a set of background knowledge which explains all of the observed independence facts in a sample? (ii) Given that there is such a causal explanation what are the causal relationships common to every such causal explanation?

Motivation & Objective

• To develop algorithms that determine whether a causal model consistent with both observed independence facts and background knowledge exists.
• To identify the set of causal relationships that are common to all valid causal explanations under given background knowledge.
• To improve the reliability and accuracy of causal discovery by integrating domain-specific knowledge with statistical independence tests.
• To address limitations in standard causal discovery methods when latent confounders or incomplete data are present.

Proposed method

• The approach uses a constraint-based framework that combines conditional independence tests with background knowledge expressed as causal constraints.
• It formulates the problem as a logical consistency check over a set of conditional independence statements and background knowledge.
• The algorithm checks for the existence of a causal graph that satisfies all observed and background knowledge constraints.
• It employs a sound and complete procedure to enumerate all possible causal graphs consistent with the data and knowledge.
• The method uses a refinement process to eliminate graphs inconsistent with the background knowledge, narrowing down to a minimal set of explanations.
• It computes the intersection of all valid causal graphs to identify the common causal relationships across explanations.

Experimental results

Research questions

• RQ1 Does there exist a causal explanation consistent with both the observed data and the provided background knowledge?
• RQ2 What are the causal relationships that are common to every valid causal explanation under the given background knowledge?
• RQ3 How can background knowledge be formally integrated into causal discovery to improve the accuracy and robustness of inferred causal structures?
• RQ4 Can the method identify a unique set of causal relationships even when multiple valid causal graphs exist?
• RQ5 What are the conditions under which background knowledge enables the identification of a unique causal structure?

Key findings

• The paper presents a sound and complete algorithm for determining the existence of a causal model consistent with both observed independence facts and background knowledge.
• It provides a method to compute the intersection of all valid causal graphs, identifying the causal relationships that are common to every consistent explanation.
• The integration of background knowledge significantly reduces the set of possible causal models, increasing the confidence in inferred causal relationships.
• The approach is robust to latent confounders, as long as the background knowledge appropriately constrains their influence.
• The method ensures correctness by systematically checking logical consistency between the data-driven independence facts and the background knowledge.
• The algorithm is computationally feasible for practical applications and can be applied to real-world causal discovery problems with domain constraints.