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

预测建模是监督式机器学习中的一个基本问题。传统的预测建模方法通常为每个预测任务构建一个预测器。然而，在许多现实世界的问题中，需要同时为多个相互关联的任务构建预测器。例如，在实时麻醉决策中，麻醉药物会对麻醉患者的多个指标产生影响，如麻醉深度、血压、心率等。麻醉师在做出决定之前需要考虑所有这些不同的方面以及它们内在的依赖性。本项目的目标是对异构响应回归进行系统的研究，建立异构响应的多元回归模型，探索异构响应之间的关系。具体而言，该项目的异构响应回归框架基于定制的潜在因素模型，该模型捕获了低维空间中不同响应之间的关系。响应异质性将通过利用指数族分布和其他方法来捕获。模型参数可以通过正则化极大似然估计，通过最大-最小过程来学习。此外，还提出了一种基于乘法器交替方向法的分布式解决方案，提高了系统的可扩展性。该项目还将通过以下方式使框架更加灵活：(1)增加个性化的效应项以捕获样本/特征异质性并诱导任务依赖性；(2)利用功能模型来考虑时变预测因子并使预测具有时间敏感性。该项目将证明其方法在疾病风险预测和金融稳定建模方面的有效性。

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.