CAREER: Geometry and High-Dimensional Inference

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CAREER: Geometry and High-Dimensional InferenceMikhail BelkinOhio State UniversityMachine learning techniques for high-dimensional inference are becoming progressively more important as many sources of abundant data ranging from MRI, medical imaging and biological data to sensor networks and to more traditional speech and computer vision data become avail- able and require automated processing. This project will address theoretical and algorithmic issues surrounding manifold and geometric methods for high- dimensional inference.Intellectual Merit: Three of the fundamental challenges for modern machine learning can be summarized as follows:. High dimensionality of the data.. Complex nonlinear structures in the data.. A large amount of data obtained from modern data sources is unlabeled.A promising line of research, known as Manifold Learning, emerged in recent years as a way to use certain geometric ideas to construct compact low- dimensional representation of the data and to use unlabeled data for learning. These algorithms have now been successfully used for a variety of applications from motion segmentation to Markov decision processes.However, our theoretical understanding of these methods is still in its infancy. The main focus of this project is to develop a theoretical framework for analysis of algorithms utilizing geometry of high-dimensional data. Such a framework will bring together techniques from computer science, statistics and mathematics to gain insight into properties of real-world data.This framework will provide guidelines for designing better algorithms for existing problems as well as extending existing methods to new domains, such as analysis complex output spaces and time dependent data. The PI also plans to investigate usefulness of these ideas in Computer Vision.Broader impacts: This project aims to build a theoretical foundation for a new class of inference algorithms as well as to design new algorithms for high- dimensional inference and to consider its application. A rigorous theoretical understanding of unlabeled data and its use in learning tasks is likely to have a significant impact in algorithms design and in applications of machine learning techniques in practice. This project will provide research and education opportunities for graduate and undergraduate students, and acquaint researchers from other areas and industry with recent developments and encourage collaborations through interdisciplinary workshops and a Machine Learning school.http://www.cse.ohio-state.edu/~mbelkin/nsfcareerresearch