Scalable Intervention Target Estimation in Linear Models

TL;DR

This paper introduces a scalable algorithm for estimating intervention targets in linear causal models using differences in precision matrices, improving efficiency and accuracy over existing methods.

Contribution

It presents a novel, scalable method to identify intervention sites in linear SEMs by analyzing precision matrix differences, with proven consistency and improved sample complexity.

Findings

Algorithm accurately identifies intervention targets in simulations.

Method outperforms existing approaches in scalability and sample efficiency.

Code and implementation are publicly available for reproducibility.

Abstract

This paper considers the problem of estimating the unknown intervention targets in a causal directed acyclic graph from observational and interventional data. The focus is on soft interventions in linear structural equation models (SEMs). Current approaches to causal structure learning either work with known intervention targets or use hypothesis testing to discover the unknown intervention targets even for linear SEMs. This severely limits their scalability and sample complexity. This paper proposes a scalable and efficient algorithm that consistently identifies all intervention targets. The pivotal idea is to estimate the intervention sites from the difference between the precision matrices associated with the observational and interventional datasets. It involves repeatedly estimating such sites in different subsets of variables. The proposed algorithm can be used to also update a given observational Markov equivalence class into the interventional Markov equivalence class. Consistency, Markov equivalency, and sample complexity are established analytically. Finally, simulation results on both real and synthetic data demonstrate the gains of the proposed approach for scalable causal structure recovery. Implementation of the algorithm and the code to reproduce the simulation results are available at \url{https://github.com/bvarici/intervention-estimation}.