Extremely Greedy Equivalence Search

TL;DR

This paper introduces XGES, an improved version of GES for causal discovery that reduces local optima issues and is significantly faster, with better accuracy demonstrated on simulated datasets.

Contribution

XGES proposes a new heuristic for greedy causal discovery that enhances search efficiency and accuracy while maintaining theoretical guarantees.

Findings

XGES outperforms GES in recovering true graphs.

XGES is approximately 10 times faster than GES.

XGES effectively reduces local optima in dense graphs.

Abstract

The goal of causal discovery is to learn a directed acyclic graph from data. One of the most well-known methods for this problem is Greedy Equivalence Search (GES). GES searches for the graph by incrementally and greedily adding or removing edges to maximize a model selection criterion. It has strong theoretical guarantees on infinite data but can fail in practice on finite data. In this paper, we first identify some of the causes of GES's failure, finding that it can get blocked in local optima, especially in denser graphs. We then propose eXtremely Greedy Equivalent Search (XGES), which involves a new heuristic to improve the search strategy of GES while retaining its theoretical guarantees. In particular, XGES favors deleting edges early in the search over inserting edges, which reduces the possibility of the search ending in local optima. A further contribution of this work is an efficient algorithmic formulation of XGES (and GES). We benchmark XGES on simulated datasets with known ground truth. We find that XGES consistently outperforms GES in recovering the correct graphs, and it is 10 times faster. XGES implementations in Python and C++ are available at https://github.com/ANazaret/XGES.