Causal Discovery by Interventions via Integer Programming

TL;DR

This work presents an optimization-based framework for causal discovery via interventions by formulating interventional design as a binary integer program over a set of candidate interventions. The IP encodes Covariance (CC), Unordered Pair (UPC), and Ordered Pair (OPC) conditions to guarantee identifiability of the causal DAG on the observable variables $\mathcal{V}$, under standard causal assumptions and an independence oracle. It offers exact solutions with a modular structure that can incorporate costs, limits on the number of manipulated variables per intervention, and secondary objectives such as minimizing average or maximum intervention size. The approach recasts identifiability design as a Set-Covering Problem, enabling the use of well-established approximation methods while preserving the ability to obtain optimal intervention sets when computational budgets allow. Overall, the framework provides a flexible, principled tool for planning minimal, cost-aware interventional experiments to uncover causal structure in complex networks.

Abstract

Causal discovery is essential across various scientific fields to uncover causal structures within data. Traditional methods relying on observational data have limitations due to confounding variables. This paper presents an optimization-based approach using integer programming (IP) to design minimal intervention sets that ensure causal structure identifiability. Our method provides exact and modular solutions that can be adjusted to different experimental settings and constraints. We demonstrate its effectiveness through comparative analysis across different settings, demonstrating its applicability and robustness.

Figures (1)

• Figure 1: True DAG inference through interventions from solution 1