CBMS Conference: Topological Data Analysis: Topology, Geometry and Statistics, May 23-27, 2016; Austin, TX

该奖项将支持2016年春季在德克萨斯大学奥斯汀分校举行的为期5天的拓扑数据分析会议。拓扑数据分析(TDA)是最近兴起的一个活跃的新研究领域，引起了数学、统计学、计算机科学、机器学习和电气工程界的极大兴趣。TDA正被应用于图像分析、神经科学、网络分析、形态学、遗传学、癌症研究和其他问题。TDA的跨学科性质自然导致文献和活跃的研究人员分散在不同的领域。缺乏一个有凝聚力的学科之家，使得初级研究人员，特别是统计学专业的研究生，很难接触到这一领域。拟议的讲习班努力填补这一空白，侧重于关于拓扑数据分析的教程和概述讲座，并提供实际操作数据分析课程。会议将由杜克大学的Sayan Mukherjee教授担任首席讲师，并邀请另外五位演讲者。会议的目标是向研究生和初级研究人员介绍TDA，这是一个活跃的新领域，位于拓扑学、几何学和统计学的令人兴奋的交叉点上。这次会议还将成为促进研究合作和绘制未来可能的研究方向的机会。该计划将概述如何将几何和拓扑学用于统计推断。拟议的大纲开发了一个框架，用于如何将几何和拓扑用于统计推理中的一些常见任务，包括混合模型、建模表面和形状、谱聚类的扩展以及机器学习方面，如半监督学习。本课程将介绍一些应用和数据分析方面的知识，其中将使用一些常用的拓扑数据分析代码来模拟形状数据，特别是骨骼和器官的计算机断层扫描(CT)。该计划的应用方面将包括在数量遗传学、统计遗传学以及计算机视觉应用中开发的方法学的应用。该计划的另一个组成部分是关注几何学在统计中的作用。一些受邀的演讲者，如Rabi Bhattacharya教授和Susan Holmes教授将就这一主题发表演讲。

This award will support a 5-day conference in topological data analysis at the University of Texas at Austin in the spring of 2016. Topological data analysis (TDA) has recently emerged as an active new field of research, which has generated great interest across mathematics, statistics, computer science, machine learning, and electrical engineering communities. TDA is being applied to image analysis, neuroscience, networks analysis, morphology, genetics,cancer research and other problems. The interdisciplinary nature of TDA naturally leads to the literature and the active researchers being scattered across different fields. This lack of a cohesive disciplinary home makes it difficult for junior researchers and in particular graduate students from statistics to obtain exposure to the field. The proposed workshop strives to fill this gap by focusing on tutorial and overview talks on topological data analysis and providing hands-on data analysis sessions. The conference will feature Professor Sayan Mukherjee from Duke University as the principal lecturer, and five additional invited speakers. The goal of the conference is to introduce graduate students and junior researchers to TDA, an active new field, which lies at the exciting intersection of topology, geometry, and statistics. This conference will also serve as an opportunity to foster research collaborations and chart possible future directions for research.The program will provide an overview of how geometry and topology can be used for statistical inference. The proposed outline develops a framework for how geometry and topology is used for some common tasks in statistical inference including mixture models, modeling surfaces and shapes, extensions of spectral clustering, as well as machine learning aspects such as semisupervised learning. There will be some applied and data analysis aspects to the lecture where some common Topological Data Analysis codes will be used to model shape data, specifically computerized tomography (CT) scans of bones and organs. Applied aspects of the program will include applications of the methodology developed in quantitative genetics, statistical genetics, as well as computer vision applications. Another component of the program is focusing on the role of geometry in statistics. Some of the invited speakers such as Professors Rabi Bhattacharya and Susan Holmes will deliver lectures on this topics.