Structure-Regularized Partition-Regression Models for Nonlinear System-Environment Interactions

Under different environmental conditions, the relationship between the design and operational variables of a system and the system’s performance is likely to vary and is difficult to be described by a single model. The environmental variables (e.g., temperature, humidity) are not controllable while the variables of the system (e.g. heating, cooling) are mostly controllable. This phenomenon has been widely seen in the areas of building energy management, mobile communication networks, and wind energy. To account for the complicated interaction between a system and the multivariate environment under which it operates, a Sparse Partitioned-Regression (SPR) model is proposed, which automatically searches for a partition of the environmental variables and fits a sparse regression within each subdivision of the partition. SPR is an innovative approach that integrates recursive partitioning and high-dimensional regression model fitting within a single framework. Moreover, theoretical studies of SPR are explicitly conducted to derive the oracle inequalities for the SPR estimators which could provide a bound for the difference between the risk of SPR estimators and Bayes’ risk. These theoretical studies show that the performance of SPR estimator is almost (up to numerical constants) as good as of an ideal estimator that can be theoretically achieved but is not available in practice. Finally, a Tree-Based Structure-Regularized Regression (TBSR) approach is proposed by considering the fact that the model performance can be improved by a joint estimation on different subdivisions in certain scenarios. It leverages the idea that models for different subdivisions may share some similarities and can borrow strength from each other. The proposed approaches are applied to two real datasets in the domain of building energy. (1) SPR is used in an application of adopting building design and operational variables, outdoor environmental variables, and their interactions to predict energy consumption based on the Department of Energy’s EnergyPlus data sets. SPR produces a high level of prediction accuracy and provides insights into the design, operation, and management of energy-efficient buildings. (2) TBSR is used in an application of predicting future temperature condition which could help to decide whether to activate or not the Heating, Ventilation, and Air Conditioning (HVAC) systems in an energy-efficient manner.