Scalable Computation of Causal Bounds

TL;DR

This paper introduces a scalable method for computing bounds on causal queries in complex graphs with unobserved confounders, significantly improving efficiency and enabling analysis of larger problems.

Contribution

It presents a pruning technique for linear programs that compute causal bounds, extends this to fractional LPs, and offers a heuristic for large-scale problems, advancing causal inference methods.

Findings

Pruning LPs enables computation of bounds in larger causal graphs.

The method achieves significant runtime improvements over existing techniques.

The heuristic produces high-quality bounds for very large problems.

Abstract

We consider the problem of computing bounds for causal queries on causal graphs with unobserved confounders and discrete valued observed variables, where identifiability does not hold. Existing non-parametric approaches for computing such bounds use linear programming (LP) formulations that quickly become intractable for existing solvers because the size of the LP grows exponentially in the number of edges in the causal graph. We show that this LP can be significantly pruned, allowing us to compute bounds for significantly larger causal inference problems compared to existing techniques. This pruning procedure allows us to compute bounds in closed form for a special class of problems, including a well-studied family of problems where multiple confounded treatments influence an outcome. We extend our pruning methodology to fractional LPs which compute bounds for causal queries which incorporate additional observations about the unit. We show that our methods provide significant runtime improvement compared to benchmarks in experiments and extend our results to the finite data setting. For causal inference without additional observations, we propose an efficient greedy heuristic that produces high quality bounds, and scales to problems that are several orders of magnitude larger than those for which the pruned LP can be solved.