Fast Proxy Experiment Design for Causal Effect Identification

TL;DR

This paper introduces efficient algorithms for designing proxy experiments to identify causal effects at lower costs, improving over previous NP-hard problem solutions with extensive simulation validation.

Contribution

It reformulates the optimal proxy experiment design problem, enabling more efficient solutions and addressing related adjustment set design for causal effect identification.

Findings

Proposed reformulations lead to significantly faster algorithms.

Extensive simulations demonstrate improved efficiency.

New methods successfully identify causal effects with lower-cost proxy experiments.

Abstract

Identifying causal effects is a key problem of interest across many disciplines. The two long-standing approaches to estimate causal effects are observational and experimental (randomized) studies. Observational studies can suffer from unmeasured confounding, which may render the causal effects unidentifiable. On the other hand, direct experiments on the target variable may be too costly or even infeasible to conduct. A middle ground between these two approaches is to estimate the causal effect of interest through proxy experiments, which are conducted on variables with a lower cost to intervene on compared to the main target. Akbari et al. [2022] studied this setting and demonstrated that the problem of designing the optimal (minimum-cost) experiment for causal effect identification is NP-complete and provided a naive algorithm that may require solving exponentially many NP-hard problems as a sub-routine in the worst case. In this work, we provide a few reformulations of the problem that allow for designing significantly more efficient algorithms to solve it as witnessed by our extensive simulations. Additionally, we study the closely-related problem of designing experiments that enable us to identify a given effect through valid adjustments sets.