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

最近的技术进步在不同的科学领域产生了前所未有的大小和复杂性的数据。为了分析如此复杂的数据，首席调查员(PI)的目标是开发新的统计方法。国际和平研究所建议研究四个相互关联的研究课题。首先，PI专注于大间隔分类，并提出了新的大间隔分类器来提供竞争分类和条件类概率估计。他还建议解决这样的问题，即对于特定的分类任务，软分类器还是硬分类器是首选的，以及如何结合估计的条件类概率来改进具有分类响应的数据的降维。其次，PI提出了最小角度回归的扩展，以处理广义线性模型，更一般地，处理严格凸优化问题。新的解路径由常微分方程组分段给出，稍加修改即可得到相应的套索正则解路径。第三，考虑了具有稀疏和不规则函数预测器的数据。提出了一种新的基于响应的累积切片降维方法，并提出了一种扩展大间隔分类器分析此类数据的可行方案。第四，PI侧重于半参数多指标回归。通过注意到海森算子自动滤除线性分量的影响，PI提供了一种直接估计方案来估计多个指数所跨越的空间。与已有方法不同的是，新方法在估计多个指标所占空间时不需要估计非参数链路，具有广泛的应用前景。例如，新的大间隔分类器可用于分析具有分类响应的基因组数据，如癌症类型；新的基于常微分方程的求解路径算法可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；在分析衰老的纵向数据时，新提出的稀疏和不规则功能数据的统计方法将是有用的。为了方便建议的新方法的使用，PI将在R或MatLab中实施这些方法，并将新软件与相应的研究报告一起提供给公众。这项拟议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.