CAREER: Geometry and High-Dimensional Inference

职业：几何和高维推理米哈伊尔·贝尔金俄亥俄州立大学高维推理的机器学习技术正变得越来越重要，因为从磁共振成像、医学成像和生物数据到传感器网络以及更传统的语音和计算机视觉数据的许多来源变得可用并需要自动化处理。这个项目将解决围绕高维推理的流形和几何方法的理论和算法问题。智力优势：现代机器学习的三个基本挑战可以总结如下：数据的高维性。数据中复杂的非线性结构..从现代数据源获得的大量数据是未标记的，近年来出现了一种很有前途的研究方向，称为流形学习，它是一种使用某些几何思想来构造数据的紧凑低维表示并使用未标记数据进行学习的方法。这些算法现在已经成功地应用于从运动分割到马尔可夫决策过程的各种应用中，但我们对这些方法的理论理解还处于起步阶段。这个项目的主要重点是开发一个理论框架，用于分析利用高维数据的几何图形的算法。这样的框架将汇集计算机科学、统计学和数学的技术，以深入了解真实世界数据的性质。该框架将为针对现有问题设计更好的算法以及将现有方法扩展到新领域提供指导，如分析复杂的输出空间和时间相关数据。PI还计划研究这些思想在计算机视觉中的有用性。广泛影响：该项目旨在为一类新的推理算法建立理论基础，并设计新的高维推理算法并考虑其应用。对未标记数据及其在学习任务中的使用的严格理论理解可能会对算法设计和机器学习技术在实践中的应用产生重大影响。该项目将为研究生和本科生提供研究和教育机会，并让来自其他领域和行业的研究人员了解最新发展，并通过跨学科研讨会和机器学习school.http://www.cse.ohio-state.edu/~mbelkin/nsfcareerresearch鼓励合作

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