The Sparse Regression Cube: A Reliable Modeling Technique for Open Cyber-Physical Systems

Understanding the end-to-end behavior of complex systems where computing technology interacts with physical world properties is a core challenge in cyber-physical computing. This paper develops a hierarchical modeling methodology for open cyber-physical systems that combines techniques in estimation theory with those in data mining to reliably capture complex system behavior at different levels of abstraction. Our technique is also novel in the sense that it provides a measure of confidence in predictions. An application to green transportation is discussed, where the goal is to reduce vehicular fuel consumption and carbon footprint. First-principle models of cyber-physical systems can be very complex and include a large number of parameters, whereas empirical regression models are often unreliable when a high number of parameters is involved. Our new modeling technique, called the Sparse Regression Cube, simultaneously (i) partitions sparse, high-dimensional measurements into subspaces within which reliable linear regression models apply and (ii) determines the best reliable model for each partition, quantifying uncertainty in output prediction. Evaluation results show that the framework significantly improves modeling accuracy compared to previous approaches and correctly quantifies prediction error, while maintaining high efficiency and scalability.