Collaborative Research: Statistical Learning and Object Oriented Data Analysis

这项研究是在统计学习和面向对象的数据分析(OODA)相关领域进行的。这些领域的重大挑战由一组研究人员解决，他们带来了不同但互补的技能集来探索。统计学习被广泛认为是一个非常活跃的跨学科研究领域，介于统计学、计算机科学和最优化之间。利用最新的优化工具，本研究提供了一套新的统计学习方法，包括正则化的新惩罚，大边缘分类器的进一步理论和数值发展，以及硬边缘分类器的非参数概率校正。此外，还为“高维-低样本量”(HDLSS)数据开发了新的可视化和分析工具。这种发展是极其重要的，因为HDLSS已经成为许多不同领域中遇到的数据的共同特征，例如医学成像和基因表达的微阵列分析，但它超出了经典统计多变量分析的领域。Ooda是对功能数据分析(FDA)最近非常富有成效的领域的概括。在FDA中，曲线是数据点，曲线族中的变化是分析的重点。Ooda将这一概念扩展到数据点是更复杂对象的群体，如图像、形状表示，甚至树形结构对象。该研究为FDA提供了一套新的工具，包括指数族泛函主成分分析、稳健泛函主成分分析、曲线判别、曲线时间序列的预测和动态更新。拟议的研究还将推进光滑流形和树形对象数据的Ooda。该研究的主要应用领域是卫生、医药和民用基础设施。这项研究是由癌症研究、医学成像、呼叫中心管理和网络流量建模推动的，并将对其产生有益影响。然而，开发的统计方法将在远远超出推动这项研究的领域发挥作用，例如人口学/流行病学、金融经济学和时空建模。该团队由久负盛名的资深研究人员和年轻的初级研究人员组成。在几个层面上提供强有力的指导是该项目的重要组成部分。首先，在这些令人兴奋的新研究领域，对研究生进行了强有力的培训，目标是为他们提供开始自己研究生涯所需的背景和技能。其次，有更有经验的研究团队成员对初级研究人员进行强有力的指导。除了在研究项目上密切合作外，初级研究人员还将通过与资深成员一起共同监督，学习为博士生提供建议的技能。该团队继续通过合作工作、学术报告和期刊出版物快速广泛地传播研究成果。创建网页是为了使用户能够快速访问新方法的用户友好和可访问的软件实施以及技术报告和相关参考资料。

This research is in the related areas of Statistical Learning and Object Oriented Data Analysis (OODA). There are major challenges in these areas that are addressed by a team of researchers, who bring different but complementary skill sets to explore. Statistical Learning is widely recognized as a very active area of interdisciplinary research, which lives between statistics, computer science, and optimization. With state-of-art optimization tools, this research offers a set of new approaches for statistical learning, including new penalties for regularization, further developments of large margin classifiers both theoretically and numerically, as well as nonparametric-based probability calibration for hard margin classifiers. In addition, new visualization and analytical tools for ``High Dimension-Low Sample Size'' (HDLSS) data are developed. Such development is extremely important since HDLSS has become a common feature of data encountered in many divergent fields such as medical imaging and micro-array analysis for gene expression but is outside of the domain of classical statistical multivariate analysis. OODA is a generalization of the recently very productive area of Functional Data Analysis (FDA). In FDA, curves are data points and variation in a family of curves is the focus of analysis. OODA extends this notion to populations where the data points are more complex objects, such as images, shape representations, and even tree-structured objects. The proposed research offers a set of new tools for FDA, including exponential family functional principal components analysis (PCA), robust functional PCA, curve discrimination, and forecasting and dynamic updating of time series of curves. Proposed research will also advance OODA for data on smooth manifolds and tree-structured objects.The main application area of the research is in health and medicine and civil infrastructure. The research is motivated by and will have beneficial impacts on cancer research, medical imaging, call center management, and network traffic modeling. However, the developed statistical methods will be useful in fields far beyond those motivating this research, such as demography/epidemiology, financial economics and spatial-temporal modeling. The team consists of a good mix of well established senior researchers and young junior researchers. Strong mentoring at several levels is an important component of this project. First, there is strong training of graduate students, in these exciting new research areas, with the goal of giving them the background, and skills needed to start their own research careers. Second, there is strong mentoring of the junior researchers, by the more experienced members of the research team. In addition to working closely together on research projects, the junior researchers will learn the skills of advising PhD students, through joint supervision together with the more senior members. The team continues to disseminate the research results quickly and broadly through collaborative work, academic presentations, and journal publications. Web pages are created to enable quick access to user-friendly and accessible software implementations of new methods as well as technical reports and relevant references.