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.

Background: Genetic profiling represents the future of neuro-oncology but suffers from inadequate biopsies in heterogeneous tumors like Glioblastoma (GBM). Contrast-enhanced MRI (CE-MRI) targets enhancing core (ENH) but yields adequate tumor in only ~60% of cases. Further, CE-MRI poorly localizes infiltrative tumor within surrounding non-enhancing parenchyma, or brain-around-tumor (BAT), despite the importance of characterizing this tumor segment, which universally recurs. In this study, we use multiple texture analysis and machine learning (ML) algorithms to analyze multi-parametric MRI, and produce new images indicating tumor-rich targets in GBM.

Methods: We recruited primary GBM patients undergoing image-guided biopsies and acquired pre-operative MRI: CE-MRI, Dynamic-Susceptibility-weighted-Contrast-enhanced-MRI, and Diffusion Tensor Imaging. Following image coregistration and region of interest placement at biopsy locations, we compared MRI metrics and regional texture with histologic diagnoses of high- vs low-tumor content (≥80% vs <80% tumor nuclei) for corresponding samples. In a training set, we used three texture analysis algorithms and three ML methods to identify MRI-texture features that optimized model accuracy to distinguish tumor content. We confirmed model accuracy in a separate validation set.

Results: We collected 82 biopsies from 18 GBMs throughout ENH and BAT. The MRI-based model achieved 85% cross-validated accuracy to diagnose high- vs low-tumor in the training set (60 biopsies, 11 patients). The model achieved 81.8% accuracy in the validation set (22 biopsies, 7 patients).

Conclusion: Multi-parametric MRI and texture analysis can help characterize and visualize GBM’s spatial histologic heterogeneity to identify regional tumor-rich biopsy targets.