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

预测建模是有监督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，在许多真实的世界的问题，一个需要建立多个相互关联的任务同时预测。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，麻醉医生需要考虑所有这些不同方面以及它们的内在依赖性，然后才能做出决定。本项目的目标是对异质响应回归进行系统的研究，为异质响应建立多元回归模型，并探索它们之间的关系。具体来说，本项目的异质响应回归框架是基于一个定制的潜在因素模型，该模型在低维空间中捕捉不同响应之间的关系。将通过使用指数族分布及更高分布捕获响应异质性。模型参数可以通过优化最小化过程通过正则化最大似然估计来学习。此外，一个分布式的解决方案的基础上交替方向的乘法器可以得到增强的可扩展性。该项目还将通过以下方式使框架更加灵活：（1）添加个性化的效应项，以捕获样本/特征异质性并诱导任务依赖性;（2）利用函数模型来解释随时间变化的预测因子，并使预测对时间敏感。该项目将展示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.