Grammar-Guided Evolutionary Construction of Bayesian Networks - Foundations on Natural and Artificial Computation - page 66

Tabl e 1 . Descriptive statistical results for 20 executions of EvoBANE with grammars
G 16 4 3 3 , G 16333 , G 16133 and a genetic algorithm for the “Vote” dataset

Std.
Deviation

95% Confidence Interval for Mean

N Mean Std. Error Minimum Maximum

Lower Bound Upper Bound

G 16 4 3 3 20 95.8966 .2209 .0494 95.7931 96.0000 95.5172 96.2069

G 16 3 3 3 20 95.9828 .2313 .0517 95.8745 96.0910 95.5172 96.2069

Fitness
training

G 16 1 3 3 20 96.1207 .6216 .1390 95.8298 96.4116 95.5172 98.6207

GA 20 92.7586 .0000 .0000 92.7586 92.7586 92.7586 92.7586

Total 80 95.1897 1.4557 .1627 94.8657 95.5136 92.7586 98.6207

G 16 4 3 3 20 96.7586 .5526 .1236 96.5000 97.0173 95.8621 97.2414

G 16 3 3 3 20 96.5517 .5003 .1119 96.3176 96.7859 95.8621 97.2414

Fitness
testing

G 16 1 3 3 20 96.3448 .9253 .2069 95.9118 96.7779 93.1034 97.2414

GA

20 95.8621 .0000 .0000 95.8621 95.8621 95.8621 95.8621

Total

80 96.3793 .6720 .0751 96.2298 96.5289 93.1034 97.2414

Tabl e 2 . Results of the ANOVA test for the “Vote” dataset

Sum of Squares df Mean Square F Sig.

Between Groups .511 2 .256 1.569 .217

Fitness
training

Within Groups 9.287 57 .163

9.798 59

Total

Between Groups 1.712 2 .856 1.819 .171

Fitness
testing

Within Groups 26.825 57 .471

28.537 59

Total

values are equal in the training and test sets) cannot be rejected with a signif-
icance of the value F

equal to 0.217 in training and 0.171 in the
testing. Even though the null hypotheses cannot be rejected, the significance
values indicate that there is a high probability of finding differences between the
means. Tukey's HSD test has been used to show where the differences between
the three approaches lie.
Table 3 contains the results of Tukey's HSD test. It shows that the means
of the first two approaches are closer to each other than to the third approach
in both the training and testing phases. Insofar as the lowest fitness during the
testing phase belongs to the third approach, we infer that the simplification of
the search space by the grammar G 16 1 3 3 leads to slight drop in the accuracy of
the BNs generated by EvoBANE.
The second dataset is called “Postoperative”, and its classification task is to
determine where patients in a postoperative recovery area should be sent to
next: intensive care unit, hospital floor or home. Eight feature variables should
be used for classification purposes. The CFG generator was set to generate the
grammars G 8444 , G 8344 and G 8144 . Table 4 shows the descriptive statistics of
these three EvoBANE approaches and the GA. All the EvoBANE approaches
again achieve better results than the GA in both the training and the testing
phases.
Table 5 details the results of the ANOVA test performed on the three EvoBANE
approaches. In this dataset, the equality of the means (null hypothesis) cannot be
rejected in the testing phase with a significance of the value F

( df =2 / 57)

equal to
0.886. This suggests that all three EvoBANE approaches achieve the same results.

( df =2 / 57)