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. Author manuscript; available in PMC: 2014 Oct 3.
Published in final edited form as: J Mach Learn Res. 2013 Feb;14:499–566.

Table 13.

Results showing the number of distinct Markov boundaries or variable sets (N) extracted by each method, their average size in terms of the number of variables (S) and average classification performance (AUC) in each of 13 real data sets. The row labeled “All variables” shows performance of the entire set of variables available in each data set.

Method Infant_ Mortality Ohsumed ACPJ_ Etiology Lymphoma Gisette
N S AUC N S AUC N S AUC N S AUC N S AUC
All variables 1 86 0.821 1 14,373 0.857 1 28,228 0.938 1 7,399 0.659 1 5,000 0.997
TIE* max-k = 3, α =0.05 41 4 0.825 2,497 37 0.776 5,330 18 0.908 4,533 16 0.635 227 54 0.990
KIAMB Number of runs = 5000, α = 0.05, K = 0.7 67 4 0.753 250 7 0.651 1,354 9 0.884 88 3 0.562 5,000 8 0.871
Number of runs = 5000, α = 0.05, K = 0.8 39 4 0.752 133 7 0.650 830 9 0.883 50 3 0.561 5,000 8 0.871
Number of runs = 5000, α = 0.05, K = 0.9 17 4 0.752 58 7 0.648 414 9 0.884 23 3 0.561 5,000 8 0.871
EGS-NCMIGS l = 7, δ = 0.015 6 4 0.809 6 4 0.584 6 3 0.743 7 3 0.591 7 3 0.913
l = 7, K = 10 3 10 0.874 1 10 0.691 3 10 0.780 5 10 0.615 7 10 0.952
l = 7, K = 50 1 50 0.821 1 50 0.828 3 35 0.842 3 50 0.662 5 50 0.986
l = 5000, δ = 0.015 84 4 0.806 4,999 4 0.564 4,999 4 0.770 4,992 3 0.574 4,999 5 0.920
l = 5000, K = 10 77 10 0.862 4,991 10 0.693 4,991 10 0.785 4,981 10 0.600 4,994 10 0.953
l = 5000, K = 50 39 50 0.822 4,951 50 0.830 4,981 31 0.843 4,947 50 0.653 4,957 50 0.987
EGS-CMIM l = 7, K = 10 2 10 0.865 1 10 0.696 2 10 0.915 6 10 0.577 7 10 0.956
l = 7, K = 50 1 50 0.829 1 50 0.843 1 32 0.917 4 50 0.608 5 50 0.987
l = 5000, K = 10 77 10 0.863 4,991 10 0.687 4,991 10 0.842 4,970 10 0.581 4,992 10 0.963
l = 5000, K = 50 38 50 0.827 4,951 50 0.841 4,982 31 0.857 4,942 50 0.613 4,957 50 0.987
EGSG Number of Markov boundaries = 30, t = 5 30 12 0.634 30 70 0.653 30 84 0.840 30 58 0.600 30 35 0.959
Number of Markov boundaries = 30, t = 10 30 12 0.568 30 70 0.634 30 84 0.835 30 58 0.616 30 35 0.946
Number of Markov boundaries = 30, t = 15 30 12 0.552 30 70 0.602 30 84 0.792 30 58 0.607 30 35 0.936
Number of Markov boundaries = 5,000, t = 5 991 12 0.631 5,000 70 0.649 5,000 84 0.837 5,000 58 0.604 5,000 35 0.961
Number of Markov boundaries = 5,000, t = 10 3,576 12 0.587 5,000 70 0.624 5,000 84 0.822 5,000 58 0.617 5,000 35 0.950
Number of Markov boundaries = 5,000, t = 15 4,272 12 0.556 5,000 70 0.606 5,000 84 0.780 5,000 58 0.609 5,000 35 0.941
Resampling+RFE without statistical comparison 4,230 17 0.825 4,942 3,889 0.846 5,000 2,441 0.924 4,919 1,293 0.634 4,948 697 0.997
with statistical comparison (α = 0.05) 3,222 9 0.814 5,000 914 0.836 5,000 308 0.864 4,962 45 0.587 5,000 134 0.995
Resampling+UAF without statistical comparison 4,868 26 0.859 2,533 10,722 0.855 4,963 3,883 0.929 4,215 2,546 0.647 5,000 1,673 0.999
with statistical comparison (α = 0.05) 3,141 15 0.777 4,925 7,690 0.864 5,000 1,600 0.918 4,895 195 0.600 5,000 1,088 0.998
IR-HITON-PC max-k = 3, α = 0.05 1 5 0.857 2 40 0.778 4 22 0.875 12 10 0.593 3 64 0.990
IR-SPLR without statistical comparison 1 8 0.835 1 176 0.829 4 123 0.885 16 456 0.577 1 466 0.996
with statistical comparison (α = 0.05) 1 2 0.828 3 122 0.728 5 26 0.844 139 47 0.572 1 261 0.996