Interventional Causal Structure Discovery over Graphical Models with Convergence and Optimality Guarantees

TL;DR

This paper introduces Bloom, a novel mathematical framework for causal structure discovery that integrates observational and interventional data, offering convergence guarantees and a distributed version to enhance privacy and efficiency.

Contribution

The paper develops a bilevel polynomial optimization framework that unifies observational and interventional data for causal discovery, with proven convergence and optimality, and extends it to a distributed setting.

Findings

Bloom outperforms existing algorithms on synthetic datasets.

The distributed version reduces communication and privacy risks.

The framework provides theoretical guarantees for convergence and optimality.

Abstract

Learning causal structure from sampled data is a fundamental problem with applications in various fields, including healthcare, machine learning and artificial intelligence. Traditional methods predominantly rely on observational data, but there exist limits regarding the identifiability of causal structures with only observational data. Interventional data, on the other hand, helps establish a cause-and-effect relationship by breaking the influence of confounding variables. It remains to date under-explored to develop a mathematical framework that seamlessly integrates both observational and interventional data in causal structure learning. Furthermore, existing studies often focus on centralized approaches, necessitating the transfer of entire datasets to a single server, which lead to considerable communication overhead and heightened risks to privacy. To tackle these challenges, we develop a bilevel polynomial optimization (Bloom) framework. Bloom not only provides a powerful mathematical modeling framework, underpinned by theoretical support, for causal structure discovery from both interventional and observational data, but also aspires to an efficient causal discovery algorithm with convergence and optimality guarantees. We further extend Bloom to a distributed setting to reduce the communication overhead and mitigate data privacy risks. It is seen through experiments on both synthetic and real-world datasets that Bloom markedly surpasses other leading learning algorithms.