Testing Causal Models with Hidden Variables in Polynomial Delay via Conditional Independencies

TL;DR

This paper introduces a polynomial delay algorithm for testing conditional independencies in causal models with hidden variables, enabling practical model validation against observational data.

Contribution

The paper presents the C-LMP property and a novel polynomial delay algorithm for listing relevant CIs in causal graphs with hidden variables, improving efficiency.

Findings

Algorithm operates with polynomial delay in listing CIs.

Effective testing of causal models with hidden variables demonstrated.

Practical applicability shown through experiments on real and synthetic data.

Abstract

Testing a hypothesized causal model against observational data is a key prerequisite for many causal inference tasks. A natural approach is to test whether the conditional independence relations (CIs) assumed in the model hold in the data. While a model can assume exponentially many CIs (with respect to the number of variables), testing all of them is both impractical and unnecessary. Causal graphs, which encode these CIs in polynomial space, give rise to local Markov properties that enable model testing with a significantly smaller subset of CIs. Model testing based on local properties requires an algorithm to list the relevant CIs. However, existing algorithms for realistic settings with hidden variables and non-parametric distributions can take exponential time to produce even a single CI constraint. In this paper, we introduce the c-component local Markov property (C-LMP) for causal graphs with hidden variables. Since C-LMP can still invoke an exponential number of CIs, we develop a polynomial delay algorithm to list these CIs in poly-time intervals. To our knowledge, this is the first algorithm that enables poly-delay testing of CIs in causal graphs with hidden variables against arbitrary data distributions. Experiments on real-world and synthetic data demonstrate the practicality of our algorithm.