Reframed GES with a Neural Conditional Dependence Measure

TL;DR

This paper introduces a reframed GES algorithm guided by a neural conditional dependence measure, enabling consistent nonparametric causal discovery and demonstrating improved performance over kernel-based methods.

Contribution

It proposes a flexible, nonparametric GES framework using a neural measure of conditional dependence, with theoretical guarantees and practical effectiveness.

Findings

Reframed GES is consistent in nonparametric causal discovery.

Neural conditional dependence measure outperforms kernel-based measures.

Method demonstrates strong empirical results in causal structure learning.

Abstract

In a nonparametric setting, the causal structure is often identifiable only up to Markov equivalence, and for the purpose of causal inference, it is useful to learn a graphical representation of the Markov equivalence class (MEC). In this paper, we revisit the Greedy Equivalence Search (GES) algorithm, which is widely cited as a score-based algorithm for learning the MEC of the underlying causal structure. We observe that in order to make the GES algorithm consistent in a nonparametric setting, it is not necessary to design a scoring metric that evaluates graphs. Instead, it suffices to plug in a consistent estimator of a measure of conditional dependence to guide the search. We therefore present a reframing of the GES algorithm, which is more flexible than the standard score-based version and readily lends itself to the nonparametric setting with a general measure of conditional dependence. In addition, we propose a neural conditional dependence (NCD) measure, which utilizes the expressive power of deep neural networks to characterize conditional independence in a nonparametric manner. We establish the optimality of the reframed GES algorithm under standard assumptions and the consistency of using our NCD estimator to decide conditional independence. Together these results justify the proposed approach. Experimental results demonstrate the effectiveness of our method in causal discovery, as well as the advantages of using our NCD measure over kernel-based measures.