The previous chapter described a method of relaxing the constraints of storing only the homogeneous rules that are the best for at least one training example. As illustrated by the experimental results, this implementation does not improve the performance of BruteDL. As explained in the previous chapter, the causes of the unsatisfactory result are due to our implementation -- some of the best rules disappear in the output rule list while some new rules appear and are interleaved with the best rules. Since the best homogeneous rules provide rather good performance, it is reasonable to ask whether there exists a way to improve the learning system's performance by using only the best rules and some default strategy in place of the default rule. In other words, we are seeking a way to replace only the default rule with some better default strategy and all the other rules in the decision list remain the same as in the original BruteDL. The most straightforward way to accomplish this would be to store the homogeneous rules that are not the best for any training examples in the positions between the best rules and the default rule. When any future observations are not covered by any of the best rules, these homogeneous not-best rules will be used to match the observations before the default rule. Using this method, if the not-best homogeneous rules outperform the default rule, BruteDL's performance will be improved.
This modification can be easily made by first running BruteDL with only the best rules stored and then a second time with all homogeneous rules stored. The two output rule sets are compared and the rules in the ``all-rule-list'' that are not included in the original list are put between the best rules and the default rule according to their Laplace accuracies. For the example given in the previous chapter, the learned rules generated by the original BruteDL would be the same as shown in Figure 5 while those generated by the modified version (using the not-best homogeneous rules in place of the default rule) would be as displayed in Figure 7. In this list, rule 9 through 11 are not included in the original rule list -- they are homogeneous, but not the best for any training observation. Rule 1 and 7 in the original list shown in Figure 5 remain in the same place in Figure 7. The observations classified by the best rules are classified in the same way and the observations originally classified by the default rule may be covered by rules 9 through 11. This version, called BruteDL+, may provide a better result than both the original BruteDL and the storing-all-rules BruteDL described in the previous chapter in terms of the prediction accuracy.
Figure 7: The Decision List Output by the Modified BruteDL using the Non-best
Homogeneous Rules for the Example Given in Previous Chapter
Jing Lin
