By Joe Suzuki, Maomi Ueno
This quantity constitutes the refereed complaints of the second one overseas Workshop on complex Methodologies for Bayesian Networks, AMBN 2015, held in Yokohama, Japan, in November 2015.
The 18 revised complete papers and six invited abstracts awarded have been rigorously reviewed and chosen from a variety of submissions. within the foreign Workshop on complicated Methodologies for Bayesian Networks (AMBN), the researchers discover methodologies for reinforcing the effectiveness of graphical versions together with modeling, reasoning, version choice, logic-probability family members, and causality. The exploration of methodologies is complemented discussions of sensible concerns for using graphical types in actual international settings, overlaying matters like scalability, incremental studying, parallelization, and so on.
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Extra info for Advanced Methodologies for Bayesian Networks: Second International Workshop, AMBN 2015, Yokohama, Japan, November 16-18, 2015. Proceedings
However, only the method with αijk = 1/2 converges to zero error for a uniform distribution. From Fig. 6, for a small network, performances with de Campos’s method and MI are more adversely aﬀected than those with the other methods because they have no strong consistency. 3 Experimentally Obtained Result with the Alarm Network To evaluate a large network, we ﬁrst used the Alarm network because it is widely known as a benchmark structure for the evaluation of learning Bayesian networks. The Alarm network includes 37 variables and 46 edges.
If it is greater (smaller) than the critical value, then the null is rejected (cannot be rejected) (Agresti 2002; Spirtes et al. 2000). f=(|X|−1)(|Y |−1) , 2 = Xst (7) x∈X,y∈Y where Oxy (Exy ) is the number of records (expected to be if the null was correct) for which X = x, Y = y, and |X| and |Y | are the corresponding cardinalities. If the null is correct, P (x, y) = P (x) · P (y), ∀x ∈ X, y ∈ Y . We expect that Exy /N = (Ex /N ) · (Ey /N ), ∀x ∈ X, y ∈ Y and Exy = Ex · Ey /N for Ex and Ey , which are the numbers of records in which X = x and Y = y, respectively, and 2 is greater than a critical value where N is the total number of records.
Besides, algorithm showing good performance in the ﬁrst experiment may performs terrible and require much more samples to achieve certain KL divergence. For example, QMAP can learn notably low KL divergence parameters with small data set. 2), extremely large number of samples (more than 100) are needed by QMAP algorithm. Learning Bayesian Network Parameters from Small Data Set 43 Fig. 8. 3 Time Consumption Analysis To show the time consumption of each algorithm, we continue the experiments and calculate the average running time of algorithm.