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

University Of Texas At Austin, Austin TX

Investigators

Abstract

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.