Career: Research and Education of Flexible Methods for Statistical Modeling and Prediction

近年来，统计学和其他相关领域（如机器学习和神经网络）开发了许多新的回归、分类和密度估计技术。其中一些方法在实践中非常成功，但它们的统计性质尚未完全了解。这阻碍了这些技术的进一步发展。该研究的目标是获得对这些技术的统计见解，并开发新的方法和改进的算法。研究的具体技术是支持向量机、随机树和连续和混合数据的对数密度函数方差分析模型。介绍了几种新技术。支持向量机在任意成本结构下的多类别分类将得到进一步发展。提出了一种将自适应最近邻估计与随机树相结合的新框架。利用稀疏网格方法，提出了对数密度泛函方差分析模型的反拟合算法，并将其应用于连续和混合数据的图形模型。这些新技术将通过理论调查和实证评估进行检验。研究者将开发一门研究生水平的课程，学习回归、分类和密度估计的灵活方法及其应用。部分建议的研究将被纳入课程材料。回归、分类和密度估计是统计学中的标准问题。传统方法通常采用强分布假设。随着今天巨大的计算能力，开发和实施更灵活的方法成为可能，并且在统计学和其他相关领域出现了大量新技术。其中许多都是计算密集型的，它们的统计特性还没有得到很好的理解。清楚地了解这些方法对于进一步发展和统计教育至关重要。本研究为当前研究兴趣的灵活统计方法提供了有价值的见解。研究中开发的技术为有效的数据分析提供了新的有用工具，并可应用于医学、社会、经济、环境和生物科学中的许多问题。当前统计教育的一个重要方面是教授灵活的统计方法，利用我们今天拥有的计算能力，并将其应用于不同的科学和工业领域。在建议的研究中开发的见解和新技术将被纳入研究生水平的课程，并有利于研究生的培养。

In recent years, many novel techniques for regression, classification, and density estimation have been developed, both in statistics and in other related areas such as machine learning and neural networks. Some of these methods have been very successful in practice, but their statistical properties are not fully understood. This hinders the further development of these techniques. The goal of the proposed research is to gain statistical insights into these techniques, and to develop new methodologies and improved algorithms. The specific techniques investigated are the support vector machine, the randomized trees, and the log density functional ANOVA model for continuous and mixed data. Several new techniques are introduced. The support vector machine for multi-category classification with arbitrary cost structures will be further developed. A new framework is proposed that connects the adaptive nearest neighbor estimation and the randomized trees. Through the use of the sparse grid method, a backfitting type algorithm is proposed for fitting the log density functional ANOVA model, with applications to graphical models for continuous and mixed data. These new techniques will be examined through theoretical investigation and empirical evaluation. The investigator will develop a graduate level course on flexible methods for regression, classification, and density estimation, and their applications. Part of the proposed research will be incorporated into the course material.Regression, classification, and density estimation are the standard problems in statistics. Traditional methods typically employ strong distributional assumptions. With the vast computing power of today, it becomes possible to develop and implement more flexible methods, and a host of new techniques emerged, both in statistics and other related areas. Many of these are computationally intensive, and their statistical properties have not been wellunderstood. A clear understanding of these methods is crucial for their further development and statistical education. The proposed research develops valuable insights into flexible statistical methods of current research interest. The techniques developed in the research provides new and useful tools to efficient data analysis, and can be applied to many problems in medical, social, economical, environmental and biological sciences. An important aspect of the current statistical education is the teaching of flexible statistical methods that take advantage of the computing power we have today, and their application in different scientific and industrial areas. The insights and new techniques developed in the proposed research will be incorporated into graduate level courses, and benefit the training of graduate students.