Graphical Approaches to Modeling High-Dimensional Data

本研究涉及高维数据学习与表示的理论和应用研究。术语高维是指变量的个数或未知数？通常比手头可获得的观测数量多得多。一个关键的挑战是能够在样本和计算要求在维度数量上进行有利的缩放的情况下表示和学习这种现象。该项目通过图形方法来解决这些挑战，利用了许多大数据集中固有的图形结构。本研究考虑通过概率图形模型来建模高维数据，也称为马尔可夫随机场。该建议的一个重要研究方向是在图形模型的框架下开发新的学习和推理算法。这一建议的另一个重要主题是开发高效的可伸缩模型，用于表示传统的图形模型框架之外的高维数据。这项研究为所开发的方法建立了坚实的理论保证，并将其应用于真实数据不同领域，包括遗传和金融数据，以及来自大型在线社交网络(如Facebook和Twitter)的数据。

This research involves theoretical and applied research on learning and representation of high-dimensional data. The term high dimensionality refers to the property that the number of variablesor ?unknowns? is typically much larger than the number of observations available at hand. A keychallenge is being able to represent and learn such phenomena with sample and computationalrequirements scaling favorably in the number of dimensions. This project addresses these challengesthrough a graphical approach by exploiting the inherent graphical structure present in many largedata-sets.This research considers modeling high-dimensional data through probabilistic graphical models,also known as Markov random fields. An important research thrust of this proposal is to developnovel algorithms for learning and inference under the framework of graphical models. Anotherimportant thrust of this proposal is to develop efficient scalable models for representing high-dimensional data beyond the traditional framework of graphical models. This research establishesstrong theoretical guarantees for the developed methods, as well as applies them to real data invarious domains, including genetic and financial data, and data from large online social networkssuch as Facebook and Twitter.