Improving Accuracy of Permutation DAG Search using Best Order Score Search

TL;DR

The paper introduces BOSS, a new permutation-based DAG search algorithm that achieves high accuracy on larger and denser graphs by using a weaker assumption and a novel permutation traversal method, outperforming existing methods.

Contribution

BOSS offers a novel permutation traversal and weaker assumptions, enabling accurate DAG search on larger, denser graphs than previous algorithms like SP and GSP.

Findings

BOSS achieves near-perfect accuracy on models with up to 60 variables.

BOSS can handle up to 300 variables with sparse models on a laptop.

Performance improvements are consistent across linear, Gaussian, and mixed data types.

Abstract

The Sparsest Permutation (SP) algorithm is accurate but limited to about 9 variables in practice; the Greedy Sparest Permutation (GSP) algorithm is faster but less weak theoretically. A compromise can be given, the Best Order Score Search, which gives results as accurate as SP but for much larger and denser graphs. BOSS (Best Order Score Search) is more accurate for two reason: (a) It assumes the "brute faithfuness" assumption, which is weaker than faithfulness, and (b) it uses a different traversal of permutations than the depth first traversal used by GSP, obtained by taking each variable in turn and moving it to the position in the permutation that optimizes the model score. Results are given comparing BOSS to several related papers in the literature in terms of performance, for linear, Gaussian data. In all cases, with the proper parameter settings, accuracy of BOSS is lifted considerably with respect to competing approaches. In configurations tested, models with 60 variables are feasible with large samples out to about an average degree of 12 in reasonable time, with near-perfect accuracy, and sparse models with an average degree of 4 are feasible out to about 300 variables on a laptop, again with near-perfect accuracy. Mixed continuous discrete and all-discrete datasets were also tested. The mixed data analysis showed advantage for BOSS over GES more apparent at higher depths with the same score; the discrete data analysis showed a very small advantage for BOSS over GES with the same score, perhaps not enough to prefer it.