A sparse partitioned-regression model for nonlinear system-environment interactions

This article focuses on the modeling of nonlinear interactions between the design and operational variables of a system and the multivariate outside environment in predicting the system’s performance. We propose a Sparse Partitioned-Regression (SPR) model that automatically searches for a partition of the environmental variables and fits a sparse regression within each subdivision of the partition, in order to fulfill an optimal criterion. Two optimal criteria are proposed, a penalized and a held-out criterion. We study the theoretical properties of SPR by deriving oracle inequalities to quantify the risks of the penalized and held-out criteria in both prediction and classification problems. An efficient recursive partition algorithm is developed for model estimation. Extensive simulation experiments are conducted to demonstrate the better performance of SPR compared with competing methods. Finally, we present an application of using building design and operational variables, outdoor environmental variables, and their interactions to predict energy consumption based on the Department of Energy’s Energy Plus data sets. SPR produces a high level of prediction accuracy. The result of the application also provides insights into the design, operation, and management of energy-efficient buildings.