CAREER: New Statistical Methods for Classification and Analysis of High Dimensional and Functional Data

最近的技术进步产生了不同科学领域前所未有的规模和复杂性的数据。为了分析这些复杂的数据，主要研究者（PI）的目标是开发新的统计方法。PI建议研究四个相互关联的研究主题。首先，PI专注于大间隔分类，并提出新的大间隔分类器来提供竞争性分类和条件类概率估计。他还建议解决软分类器或硬分类器是否适合特定分类任务的问题，以及如何将估计的条件类概率用于改进具有分类响应的数据的降维。其次，PI提出了一个扩展的最小角度回归处理广义线性模型，更一般地说，一个严格的凸优化问题。新的解路径是由常微分方程组分段给出的，并且可以稍微修改以得到相应的LASSO正则化解路径。第三，考虑具有稀疏和不规则函数预测的数据。新的响应为基础的降维方法，提出了这样的数据，使用累积切片和一个可行的计划也提出了扩展的大间隔分类器来分析这样的数据。第四，PI侧重于半参数多指标回归。通过注意到Hessian算子自动过滤掉线性分量的影响，PI提供了一个直接的估计方案来估计多个指数所跨越的空间。与现有方法不同的是，新方法在估计多个指标所覆盖的空间时不需要估计非参数环节，所提出的统计方法学创新在各个领域都有广泛的应用。例如，所提出的新的大边缘分类器可以应用于分析具有分类响应的基因组数据，例如癌症类型;新的基于常微分方程的解路径算法可以用于分析生存或二进制基因组数据以识别重要的预测因子;在分析老化的纵向数据时，新提出的稀疏和不规则功能数据的统计方法将是有用的。为了便于使用拟议的新方法，PI将在R或Matlab中实现它们，并将新软件与相应的研究报告一起沿着向公众提供。这项研究的成功将有助于改善公众健康。

Recent technology advances have generated data of unprecedented size and complexity across different scientific fields. To analyze such complex data, the principal investigator (PI) aims to develop new statistical methodologies. The PI proposes to study four interrelated research topics. First, the PI focuses on large-margin classification and proposes new large-margin classifiers to deliver competitive classification and conditional class probability estimation. He also proposes to address the question of whether a soft or hard classifier is preferred for a particular classification task and how to incorporate estimated conditional class probability to improve dimension reduction for data with a categorical response. Second, the PI proposes an extension of the least angle regression to deal with generalized linear models and, more generally, a strictly convex optimization problem. The new solution path is piecewise given by systems of ordinary differential equations and can be slightly modified to get the corresponding LASSO regularized solution path. Third, data with a sparse and irregular functional predictor are considered. New response-based dimensional reduction methods are proposed for such data using cumulative slicing and a viable scheme is also proposed to extend large-margin classifiers to analyze such data. Fourth, the PI focuses on the semi-parametric multi-index regression. By noticing that the Hessian operator filters out the effect of the linear component automatically, the PI provides a direct estimation scheme to estimate the space spanned by the multiple indices. The new scheme differs from existing methods in that it does not require estimating the nonparametric link while estimating the space spanned by the multiple indices as in other existing approaches.The proposed statistical methodology innovations are widely applicable in various fields. For example, the proposed new large-margin classifiers can be applied to analyze genomic data with a categorical response such as cancer type; new ordinary differential equation based solution path algorithms can used to analyze survival or binary genomic data to identify important predictors; while analyzing longitudinal data of aging, the new proposed statistical methods for sparse and irregular functional data will be useful. In order to facilitate the use of the proposed new methods, the PI will implement them in R or Matlab and make new software available to the public along with the corresponding research reports. The success of the proposed research will help to improve public health.