A new philosophy for model selection and performance estimation of data-based approximate mappings

The MC-HARP algorithm uses a Monte Carlo strategy in conjunction with a hierarchical adaptive random partitioning scheme to develop data-based approximate mappings. An estimate of the variance of the Monte Carlo sample for every point in the domain (as opposed to only data points) is a natural artifact of the MC-HARP algorithm. We define global measures, computed from the approximation variance function, that are indicative of the performance of the approximation. We show how these performance indices can be used to select an MC-HARP model with optimal complexity when the data are polluted with noise. The proposed approach represents a philosophical departure from currently available sampling-based techniques for model selection and performance estimation and has distinct advantages when spatial relationships among the data are important.