Table 3.

A comparison of the performance of four scoring functions in recovering the true underlying Bayesian network structures

	AIC				MDL				fNML				BDeu
GoldNet	Min	Mean	Max	STD	Min	Mean	Max	STD	Min	Mean	Max	STD	Min	Mean	Max	STD
Austra	3	10.72	21	5.02	0	1.50*	13	3.49	11	12.44	31	4.78	0	1.94	14	4.02
Breast	0	1.28	6	1.64	0	0.61	5	1.50	0	0.39	4	1.14	0	0.22*	4	0.94
Car	0	1.00	7	1.91	0	1.67	5	2.43	5	5.94	6	0.24	0	0.28*	5	1.18
Cleve	2	10.44	22	3.94	0	0.44*	5	1.34	0	0.94	12	2.82	1	1.44	7	1.46
Crx	9	15.28	24	4.20	3	4.67*	18	3.79	13	14.44	34	4.94	3	5.72	18	4.56
Diabetes	0	2.00	5	1.41	0	0.22*	3	0.73	0	0.22*	3	0.73	1	1.22	4	0.73
Glass	0	0.00*	0	0.00	0	0.00*	0	0.00	0	0.06	1	0.24	1	1.00	1	0.00
Heart	0	0.00*	0	0.00	0	0.00*	0	0.00	0	0.00*	0	0.00	0	0.00*	0	0.00
Hepatitis	17	21.83	31	4.13	0	0.44*	6	1.46	0	2.94	24	5.95	3	3.72	13	2.37
Iris	0	1.78	5	1.80	0	0.33	3	0.97	0	0.17*	3	0.71	1	1.33	4	0.97
Nursery	0	3.61*	12	3.99	0	4.94	8	3.28	8	9.22	16	2.18	0	4.39	8	2.77
Vehicle	0	0.72	4	1.07	0	1.11	16	3.77	0	0.39	7	1.65	0	0.22*	4	0.94
Voting	8	14.61	32	6.15	0	1.11*	16	3.77	0	2.50	31	7.42	0	1.28	19	4.47

This table shows SHD statistics about the networks learned using the sampled datasets for all scoring functions that we analyzed. For BDeu, we used the value of α that gave the lowest mean SHD. GoldNet gives the name of the network. We have used abbreviated names from Table 1, but the order of the datasets is the same in both tables. Min, Mean, Max and STD give the particular statistic for SHD for all sample sizes for the given network and scoring function. The scoring function with the lowest mean for each dataset is shown in bold.