Pattern-Aided Regression Modeling and Prediction Model Analysis

This paper first introduces pattern aided regression (PXR) models, a new type of regression models designed to represent accurate and interpretable prediction models. This was motivated by two observations: (1) Regression modeling applications often involve complex diverse predictor-response relationships, which occur when the optimal regression models (of given regression model type) fitting two or more distinct logical groups of data are highly different. (2) State-of-the-art regression methods are often unable to adequately model such relationships. This paper defines PXR models using several patterns and local regression models, which respectively serve as logical and behavioral characterizations of distinct predictor-response relationships. The paper also introduces a contrast pattern aided regression (CPXR) method, to build accurate PXR models. In experiments, the PXR models built by CPXR are very accurate in general, often outperforming state-of-the-art regression methods by big margins. Usually using (a) around seven simple patterns and (b) linear local regression models, those PXR models are easy to interpret; in fact, their complexity is just a bit higher than that of (piecewise) linear regression models and is significantly lower than that of traditional ensemble based regression models. CPXR is especially effective for high-dimensional data. The paper also discusses how to use CPXR methodology for analyzing prediction models and correcting their prediction errors.