Ranking the Uniformity of Interval Pairs

We study the problem of finding the most uniform partition of a label distribution on an interval. This problem occurs, e.g., in discretization of continuous features, where evaluation heuristics need to find the location of the best place to split the current feature. The weighted average of empirical entropies of the interval label distributions is often used for this task. We observe that this rule is sub-optimal, because it prefers short intervals too much. Therefore, we proceed to study alternative approaches. A solution that is based on compression turns out to be the best in our empirical experiments. We also study how these alternative methods affect the performance of classification algorithms.