Empirical evaluation of scoring functions for Bayesian network model selection

Liu, Zhifa; Malone, Brandon; Yuan, Changhe

doi:10.1186/1471-2105-13-S15-S14

BMC Bioinformatics

Table 2 Summary of the effect of different α values on the performance of BDeu

From: Empirical evaluation of scoring functions for Bayesian network model selection

	α = 0.1				α= 0.5				α= 1
GoldNet	Min	Mean	Max	STD	Min	Mean	Max	STD	Min	Mean	Max	STD
Austra	0	2.44	14	4.38	0	2.11	14	4.32	0	1.94*	14	4.02
Breast	0	0.83	8	2.18	0	0.61	5	1.50	0	0.61	5	1.50
Car	0	1.44	5	2.28	0	0.89	5	1.91	0	0.89	5	1.91
Cleve	1	1.83	11	2.43	1	1.50	7	1.54	1	1.44*	7	1.46
Crx	3	5.72*	18	4.56	3	6.06	19	5.46	3	5.72	18	4.91
Diabetes	1	1.72	6	1.71	1	1.22*	4	0.73	1	1.28	4	0.75
Glass	1	1.83	7	2.01	1	1.00*	1	0.00	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
Hepatitis	3	3.72*	13	2.37	3	4.22	12	2.62	6	7.06	13	2.01
Iris	1	1.83	7	1.72	1	1.44	6	1.34	1	1.33*	4	0.97
Nursery	1	4.94	8	2.75	0	4.39	8	2.77	0	4.06	8	2.92
Vehicle	0	0.67	9	2.14	0	0.22	4	0.94	0	0.22*	4	0.94
Voting	0	1.61	23	5.38	0	1.39	22	5.17	0	1.28*	19	4.47
	α = 5				α = 10				α = 20
GoldNet	Min	Mean	Max	STD	Min	Mean	Max	STD	Min	Mean	Max	STD
Austra	0	3.61	18	5.81	1	13.94	21	3.81	14	15.39	25	3.11
Breast	0	0.22*	4	0.94	0	0.56	10	2.36	0	1.33	11	2.93
Car	0	0.28*	5	1.18	0	0.28	5	1.18	0	0.33	5	1.19
Cleve	4	6.61	13	2.85	9	12.56	19	2.18	20	21.56	25	1.10
Crx	5	13.72	21	5.49	13	16.83	20	1.86	18	20.17	29	2.90
Diabetes	3	3.22	6	0.73	5	5.33	10	1.19	9	9.11	11	0.47
Glass	7	7.89	8	0.32	12	14.67	15	0.84	18	19.83	20	0.51
Heart	1	1.00	1	0.00	1	1.44	2	0.51	2	2.22	4	0.55
Hepatitis	25	30.22	33	1.99	39	41.78	44	1.31	50	53.56	60	2.25
Iris	3	3.22	5	0.55	5	5.22	8	0.73	9	9.61	14	1.38
Nursery	0	3.17	8	2.64	0	2.50	8	2.48	0	2.39*	9	2.57
Vehicle	0	0.44	5	1.20	1	2.39	10	2.03	5	6.72	15	2.47
Voting	0	1.61	22	5.14	0	3.89	30	7.06	0	7.06	38	9.05
	α = 50				α = 80				α = 100
GoldNet	Min	Mean	Max	STD	Min	Mean	Max	STD	Min	Mean	Max	STD
Austra	16	19.67	33	4.35	18	22.50	42	5.99	19	24.17	42	5.86
Breast	2	7.44	14	3.35	7	11.67	16	3.36	7	13.72	20	3.72
Car	0	0.67	8	1.88	0	1.50	8	1.76	0	1.94	8	1.66
Cleve	26	27.50	34	1.95	27	29.72	41	3.27	28	30.50	42	3.49
Crx	19	25.39	37	4.41	24	29.28	40	4.08	27	31.78	44	4.35
Diabetes	13	14.89	16	1.13	14	16.33	18	1.37	14	15.67	18	1.50
Glass	18	18.11	20	0.47	18	21.61	26	2.06	20	24.44	26	2.04
Heart	4	4.11	5	0.32	4	4.61	5	0.50	4	4.94	5	0.24
Hepatitis	59	61.50	72	3.03	61	64.28	75	3.92	61	65.28	78	4.86
Iris	13	15.06	18	1.35	14	16.78	18	1.11	14	15.83	18	1.47
Nursery	0	2.11	11	2.78	0	2.33	10	2.81	0	2.61	11	3.13
Vehicle	14	18.44	30	3.88	19	23.50	36	4.08	22	27.44	39	4.15
Voting	6	22.28	43	9.78	16	30.00	52	8.60	23	34.50	56	8.21

This table shows SHD statistics about the networks learned using the sampled datasets for the BDeu scoring function for all of the α values that we analyzed. 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 α value. The α value with the lowest mean for each dataset is shown in bold and marked with "*".

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