Consistent Estimation for Partition-Wise Regression and Classification Models

Rex C. Y. Cheung, Alexander Aue, Thomas C. M. Lee

Abstract: Partition-wise models offer a flexible approach for modeling complex and multidimensional data and are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with a simple submodel. The success of this approach highly depends on the quality of the partition, as too large a region could lead to a nonsimple submodel, while too small a region could inflate estimation variance. This paper proposes an automatic procedure for choosing the partition (i.e., the number of regions and the boundaries between regions) as well as the submodels for the regions. It is shown that under the assumption of the existence of a true partition, as well as a set of known significant predictors, the proposed partition estimator is statistically consistent. Features of the proposed methodology are highlighted for both regression and classification problems on synthetic and real data.