  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.
