A New Paradigm for Multiple Correlated Outputs Given Dissimilarity and Other Information From Multiple Sources

该奖项是根据2009年《美国复苏和再投资法案》(Public Law 111-5)资助的。本研究的目标是开发新的/改进的方法，用于当训练集具有复杂的连续和离散属性变量，并包括但不限于超长属性向量时，建立统计模型和估计风险因素，其中只有一小部分相互作用的变量被认为是相关的，但尚不清楚哪些是相关的。此外，可以知道足够多的训练集成员对之间的噪声关系或相异信息，以及多个相关的伯努利结果。在此背景下，目标是对属性和相异信息与多个伯努利结果之间的关系以及它们的相关性和条件关系进行建模。特别是，这项工作将涉及开发具有不同输入数据和惩罚函数的多重相关伯努利案例的调整程序、在这种复杂设置中的变量选择问题以及开发新的/改进的计算工具来处理具有复杂优化标准的大数据集。随着海量数据的可用和高速计算，现代统计建模和数据挖掘工具正在做令人印象深刻的事情来提取从天文学到动物学的几乎所有科学领域的信息，更不用说营销、政府、国防、卫生和经济方面的问题了。在许多感兴趣的领域中的数据集包含与各种结果的风险有关的深度嵌入的信息，给定复杂的输入或观察。然而，在许多努力领域中产生的巨大、复杂的数据集正开始超过可用于分析它们的工具。提出了一种新的发展范式，它建立在以往结果的基础上，以处理复杂的异质数据结构的能力为核心，理解复杂的多变量输入信息和复杂的多变量相关响应之间的关系。拟议的工作完成并传播后，将为将复杂输入结构中的观测数据与复杂的多相关结果相关联的新的/改进的统计模型建立/数据挖掘提供一套重要和有用的工具。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The objective of this research is to develop novel/improved methods for statistical model building and risk factor estimation when the training set has complex continuous and discrete attribute variables and including, but not limited to extremely long attribute vectors of which only a small set of interacting variables are believed to be relevant, but it is not known which. In addition, noisy relationship or dissimilarity information may be known between sufficiently many pairs of training set members, along with multiple correlated Bernoulli outcomes. In this context the objective is to model relations between the attribute and dissimilarity information and the multiple Bernoulli outcomes, as well as their correlations and conditional relationships. In particular the work will be concerned with issues related to developing tuning procedures for the multiple correlated Bernoulli case with heterogenous input data and penalty functionals, variable selection problems in this complex setup and the development of novel/improved computational tools to handle large data sets with complex optimization criteria.With the availability of huge amounts of data and high speed computing, modern statistical model building and data mining tools are doing impressive things to extract information in just about every scientific field from Astronomy to Zoology, not to mention problems in marketing, government, defense, health and the economy. Data sets in many areas of interest contain deeply embedded information relating to the risks of various outcomes, given complex inputs or observables.However the generation of huge, complex data sets in many fields of endeavor is beginning to outstrip the tools available for analyzing them. A new paradigm is proposed for development, which builds on previous results and which has as core the ability to deal with complex heterogenous data structures, to understand relationships between complex multivariate input information and complex multivariate correlated responses.The proposed work, when completed and disseminated, will provide a set of important and useful tools for new/improved statistical model building/data mining relating observational data in complex input structures to complex multiple correlated outcomes.