A recursive partitioning tool for interval prediction

Abstract

The traditional approach to regression trees involves partitioning the space of predictor variables into subsets that optimise a function of the response variable(s), and then predicting future response values by a single-valued summary statistic in each subset. Our belief is that a prediction interval is of greater practical use than a predictive value, and that the criterion for the partitioning should be based on such intervals rather than on single values. We define four potential criteria in the case of a single response variable, discuss computational aspects of producing the partition, evaluate the criteria on both real and simulated data, and draw some tentative conclusions about their relative efficacies. The methodology is extended to the case of multiple response variables, and its viability is demonstrated by application to some further real data. The possibility of fitting distributions to within-subsets data is discussed, and some potential extensions are briefly outlined.

Knowledge discovery in data streams with regression tree methods

“…More recently, thanks to the development of models and techniques for nonnormal and/or nonlinear data, there has been an increasing interest in assessing the predictive accuracy through more informative measures such as interval prediction or evaluation of the whole predictive density 7,47,48. Some remarkable examples in this direction are Gooijer and Gannoun,49 Olive,32,48 and Hawkins 50.…”

“…Moreover, smaller trees, i.e., those that do not have too many splits, are easy to interpret. In many applications, the ease of interpretation is just as important as predictive accuracy 6,7…”