Collaborative Research: Smoothing Spline Semiparametric Density Models

合作研究：平滑样条半参数密度模型

• 批准号: 1507620
• 负责人: Yuedong Wang
• 金额: $ 22.81万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2019-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1507620&HistoricalAwards=false
• 关键词: Collaborative; Research; Smoothing; Spline; Semiparametric

A probability density function of multiple variables describes the likelihood of different values the variables can jointly take, therefore, contains full information regarding the distribution of individual variables and their interactions. Given observed data of the random variables, density estimation is at the heart of Statistics and machine learning, where the classical problems such as regression, variable selection, clustering, and dimension reduction, can all be cast into a density estimation problem. Advanced density estimation methods are therefore essential for the extraction of as much information as possible from the data. There has been lack of systematic research in flexible density estimation with high dimensional data or complex data such as clustered data. The overall goal of this project is to develop a smoothing spline based systematic framework that allows for flexible density model building for complex and high dimensional data. As such data arise from a wide range of applications, the results of this proposed research are useful for researchers from a wide range of fields. In particular, the proposed methods will be applied to analyze data in health and medicine, speech, environmental change, food and computer sciences, in collaboration with researchers in these areas. High-performance computing tools will be developed as a result of this research and made publicly available.This project adopts a semi-parametric approach that combines advantages of parametric and nonparametric methods. Flexible and general semi-parametric density and conditional density models for independent and clustered data will be developed and studied. Regularization methods for adaptive density estimation, variable selection in high dimensional conditional density estimation and interaction selection in semi-parametric graphical models will be developed. Nonparametric components will be modeled using reproducing kernel Hilbert spaces which can deal with different density models on different domains with different penalties in a unified fashion. The semiparametric density models considered in this project contain most existing semiparametric density models as special cases as well as many new interesting models. Many methods in this project for adaptive estimation, model/variable selection, model diagnostics and inference are new. These novel methodologies constitute advances in density estimation.

因此，多个变量的概率密度函数描述了变量可以共同获取的不同值的可能性，因此包含有关单个变量及其相互作用的分布的完整信息。给定观察到的随机变量的数据，密度估计是统计和机器学习的核心，其中经典问题，例如回归，可变选择，聚类和降低尺寸，都可以将其放入密度估计问题中。 因此，高级密度估计方法对于从数据中提取尽可能多的信息至关重要。具有高维数据或复杂数据（例如群集数据）的柔性密度估计缺乏系统的研究。该项目的总体目标是开发基于平滑样条的系统框架，该框架允许为复杂和高维数据构建灵活的密度模型。由于这些数据来自广泛的应用，因此这项拟议的研究的结果对来自各个领域的研究人员很有用。特别是，该方法将用于分析健康和医学，言语，环境变化，食品和计算机科学方面的数据，并与这些领域的研究人员合作。这项研究将开发高性能计算工具，并公开可用。该项目采用了一种结合参数和非参数方法优势的半参数方法。将开发和研究用于独立和群集数据的柔性和一般半参数密度和条件密度模型。用于自适应密度估计的正则化方法，将开发出高维条件密度估计中的可变选择和半参数图形模型中的相互作用选择。非参数组件将使用复制的内核希尔伯特空间进行建模，该空间可以在不同的域上处理不同的密度模型，并以统一的方式处理不同的惩罚。该项目中考虑的半参数密度模型包含大多数现有的半参数密度模型作为特殊情况以及许多新的有趣模型。该项目中的许多方法用于自适应估计，模型/变量选择，模型诊断和推理是新的。这些新颖的方法构成了密度估计的进步。