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