

![0_image_0.png](0_image_0.png)

results, we outperform CN2-POE on both accuracy and size. Finally, on "Vote0", note that WIDC with optimistic pruning is slightly outperformed by CN2-POE by 2.51%, but the DC obtained is fifteen times smaller than the decision list of CN2-POE. If we dwell on the results of C4.5, similar conclusions can be brought: on 12 out of 13 datasets on which we ran C4.5, W IDC(p) finds smaller formulas, and still beats C4.5's accuracy on 9 of them.

A quantitative comparison of lpc against the number of nodes of the DTs shows that on 4 datasets out of the 13 (Pole, Shuttle, TicTacToe, Australian), the DCs are more than 6 times smaller, while they only incur a loss in accuracy for 2 of them, and limited to 1.8%. For this latter problem (TicTacToe), a glimpse at Table 1 shows that the DCs, with less than 7 rules on average, keeps comparatively most of the information contained in DTs having more than a hundred leaves.  On many problems where mining issues are crucial, such a size reduction would be well worth the (comparatively slight) loss in accuracy, because we keep a significant part of the information on very small classifiers, thus likely to be interpretable.

## 6.2 Interpretability Issues

In the XD6 domain, each example has 10 binary variables. The tenth is irrelevant in the strongest sense (John, Kohavi, & Pfleger, 1994). The target concept f is a 3-DNF (a