Greedy Relaxations of the Sparsest Permutation Algorithm

TL;DR

The paper introduces GRaSP, a permutation-based causal discovery algorithm that outperforms existing methods in dense graphs with many variables, under weaker assumptions than faithfulness.

Contribution

It develops a new class of algorithms, GRaSP, that extend permutation-based causal search with greedy relaxations, achieving efficiency and consistency under weaker assumptions.

Findings

GRaSP outperforms state-of-the-art causal search algorithms in simulations.

It is efficient and accurate for dense graphs with over 100 variables.

GRaSP operates under weaker assumptions than faithfulness.

Abstract

There has been an increasing interest in methods that exploit permutation reasoning to search for directed acyclic causal models, including the "Ordering Search" of Teyssier and Kohler and GSP of Solus, Wang and Uhler. We extend the methods of the latter by a permutation-based operation, tuck, and develop a class of algorithms, namely GRaSP, that are efficient and pointwise consistent under increasingly weaker assumptions than faithfulness. The most relaxed form of GRaSP outperforms many state-of-the-art causal search algorithms in simulation, allowing efficient and accurate search even for dense graphs and graphs with more than 100 variables.