Collaborative Causal Discovery with Atomic Interventions

TL;DR

This paper introduces a collaborative approach to causal discovery across multiple entities with independent causal graphs, leveraging clustering and atomic interventions to efficiently recover all graphs with fewer interventions than learning separately.

Contribution

It proposes algorithms for simultaneous causal graph recovery in a multi-entity setting using atomic interventions and clustering assumptions, reducing intervention complexity.

Findings

Algorithms recover all causal graphs with logarithmic interventions per entity.

Fewer interventions needed compared to learning each graph independently.

Provides a lower bound and discusses extensions of the collaborative setting.

Abstract

We introduce a new Collaborative Causal Discovery problem, through which we model a common scenario in which we have multiple independent entities each with their own causal graph, and the goal is to simultaneously learn all these causal graphs. We study this problem without the causal sufficiency assumption, using Maximal Ancestral Graphs (MAG) to model the causal graphs, and assuming that we have the ability to actively perform independent single vertex (or atomic) interventions on the entities. If the $M$ underlying (unknown) causal graphs of the entities satisfy a natural notion of clustering, we give algorithms that leverage this property and recovers all the causal graphs using roughly logarithmic in $M$ number of atomic interventions per entity. These are significantly fewer than $n$ atomic interventions per entity required to learn each causal graph separately, where $n$ is the number of observable nodes in the causal graph. We complement our results with a lower bound and discuss various extensions of our collaborative setting.