Results

Table 3 shows the accuracy of recommendations for dependency networks and Bayesian networks across the various protocols and three datasets. For a comparison, we also measured the accuracy of recommendation lists produced by a Bayesian network with no arcs (baseline model). This model recommends items based on their overall popularity, $p(x_i=1)$. A score in boldface corresponds to a statistically significant winner. We use ANOVA (e.g., McClave and Dietrich, 1988) with $\alpha=0.1$ to test for statistical significance. When the difference between two scores in the same column exceed the value of RD (required difference), the difference is significant. As in the case of density estimation, we see from the table that Bayesian networks are more accurate than dependency networks, but only slightly so. In particular, the ratio of (cfaccuracy(BN) - cfaccuracy(DN)) to (cfaccuracy(BN) - cfaccuracy(Baseline)) averages $4 \pm 5$ percent across the datasets and protocols. As before, the differences are probably due to the fact that dependency networks are less statistically efficient than Bayesian networks. Tables 4 and 5 compare the two methods with the remaining criteria. Here, dependency networks are a clear winner. They are significantly faster at prediction--sometimes by almost an order of magnitude--and require substantially less time and memory to learn. Overall, Bayesian networks are slightly more accurate but much less attractive from a computational perspective.

Table 3: CF accuracy for the MS.COM, Nielsen, and MSNBC datasets. Higher scores indicate better performance. Statistically significant winners are shown in boldface.

	MS.COM
Algorithm	Given2	Given5	Given10	AllBut1
BN	53.18	52.48	51.64	66.54
DN	52.68	52.54	51.48	66.60
RD	0.30	0.73	1.62	0.34
Baseline	43.37	39.34	39.32	49.77

	Nielsen
Algorithm	Given2	Given5	Given10	AllBut1
BN	24.99	30.03	33.84	45.55
DN	24.20	29.71	33.80	44.30
RD	0.32	0.40	0.65	0.72
Baseline	12.65	12.72	12.92	13.59

	MSNBC
Algorithm	Given2	Given5	Given10	AllBut1
BN	40.34	34.20	30.39	49.58
DN	38.84	32.53	30.03	48.05
RD	0.35	0.77	1.54	0.39
Baseline	28.73	20.58	14.93	32.94

Table 4: Number of predictions per second for the MS.COM, Nielsen, and MSNBC datasets.

	MS.COM
Algorithm	Given2	Given5	Given10	AllBut1
BN	3.94	3.84	3.29	3.93
DN	23.29	19.91	10.20	23.48

	Nielsen
Algorithm	Given2	Given5	Given10	AllBut1
BN	22.84	21.86	20.83	23.53
DN	36.17	36.72	34.21	37.41

	MSNBC
Algorithm	Given2	Given5	Given10	AllBut1
BN	7.21	6.96	6.09	7.07
DN	11.88	11.03	8.52	11.80

Table 5: Computational resources for model learning.

	MS.COM
Algorithm	Memory (Meg)	Learn Time (sec)
BN	42.4	144.65
DN	5.3	98.31

	Nielsen
Algorithm	Memory (Meg)	Learn Time (sec)
BN	3.3	7.66
DN	2.1	6.47

	MSNBC
Algorithm	Memory (Meg)	Learn Time (sec)
BN	43.0	105.76
DN	3.7	96.89