Efficient multisplitting on numerical data

Numerical data poses a problem to symbolic learning methods, since numerical value ranges inherently need to be partitioned into intervals for representation and handling. An evaluation function is used to approximate the goodness of different partition candidates. Most existing methods for multisplitting on numerical attributes are based on heuristics, because of the apparent efficiency advantages. We characterize a class of well-behaved cumulative evaluation functions for which efficient discovery of the optimal multisplit is possible by dynamic programming. A single pass through the data suffices to evaluate multisplits of all arities. This class contains many important attribute evaluation functions familiar from symbolic machine learning research. Our empirical experiments convey that there is no significant differences in efficiency between the method that produces optimal partitions and those that are based on heuristics. Moreover, we demonstrate that optimal multisplitting can be beneficial in decision tree learning in contrast to using the much applied binarization of numerical attributes or heuristical multisplitting.