密度函数回归模型中的数据缩减方法

密度函数回归模型描述了响应变量密度函数与协变量之间的关系。相比于常用的条件均值、条件分位数回归模型，该模型更为灵活，能够提供更为丰富的信息。然而，密度函数回归模型在分析海量数据时，会面临由于数据样本量巨大带来的计算困难，无法有效地满足实际应用需求。数据缩减方法通过在原始观测数据中选取具有代表性的数据子集来进行统计建模，经常被用来降低模型计算复杂度。本项目将发展基于支撑点的数据缩减方法，解决密度函数回归模型在分析海量数据时的计算瓶颈。新方法将利用能量距离、连续排序得分以及Kullback-Leibler距离之间的联系，建立最优数据子集选择标准。理论方面，本项目将基于函数型方差分析模型及核函数偏差理论，对结构化模型进行分析，研究数据子集分布收敛性质和估计量误差收敛速率；实际应用方面，本项目拟将新方法应用到风能发电工程中涌现的实际问题中，为其提供高效的数据科学解决方案。

Density regression characterizes the conditional density of the response variable given the covariates, and provides much more information than the commonly used conditional mean or quantile regression. However, it is often computationally prohibitive and fails to deliver timely results when analyzing massive data sets. Data reduction aims at identifying representative data points from the original observations for downstream modeling to resolve the computational burden effectively. This project focuses on developing a novel data reduction approach with support points for density regression. The optimal selection rule will be based on the connections among energy distance, continuously ranked probabilistic score and the Kullback-Leibler distance. In theory, the project will study the structured model with functional ANOVA and kernel discrepancy methods, and establish the distributional convergence of the representative data set and the error convergence rate for the estimator. In application, the new method will be applied to solve real challenges in the wind energy industry. Efficient data analytics solutions will be developed.