III: Small: Collaborative Research: Comprehensive Heterogeneous Response Regression from Complex Data

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Predictive modeling is one fundamental problem in supervised machine learning. Traditional predictive modeling approaches typically built one predictor for each prediction task. However, in many real world problems, one needs to build predictors for multiple inter-correlated tasks simultaneously. For example, in real-time anesthesia decision making, the anesthesia drugs will have impact on multiple indicators of an anesthesia patient, such as anesthesia depth, blood pressures, heart rates, etc. The anesthesiologist needs to consider all those different aspects as well as their intrinsic dependence before s/he can make the decision. The goal of this project is to conduct systematic research on heterogeneous response regression, which builds multiple regression models for heterogeneous responses as well as exploring the relationship among them.Specifically, the project's heterogeneous response regression framework is based on a tailored latent factor model that captures the relationship among different responses in a low-dimensional space. The response heterogeneity will be captured by utilizing the exponential family distributions and beyond. The model parameters can be learned through regularized maximum likelihood estimation via a majorization-minimization procedure. Moreover, a distributed solution based on the alternating direction method of multipliers can be derived to enhance the scalability. The project will also make the framework more flexible by (1) adding individualized effect terms to capture sample/feature heterogeneity and induce task dependency; and (2) leveraging a functional model to account for time-varying predictors and to make the prediction time-sensitive. The project will demonstrate the effectiveness of its method in disease risk prediction and financial stability modeling.