Graphical Approaches to Modeling High-Dimensional Data

本研究涉及高维数据学习和表示的理论和应用研究。术语高维性是指变量的数量或？未知数？通常远大于手头可用的观测数量。一个关键的挑战是能够表示和学习这样的现象与样本和计算要求缩放有利的数量的维度。本项目通过图形化的方法，利用许多大型数据集中固有的图形结构来解决这些挑战。本研究考虑通过概率图形模型（也称为马尔可夫随机场）对高维数据进行建模。该方案的一个重要研究方向是在图模型的框架下开发新的学习和推理算法。这个建议的另一个重要的推动力是开发高效的可扩展模型，用于表示超越传统的图形模型框架的高维数据。这项研究为所开发的方法建立了强有力的理论保证，并将其应用于各个领域的真实的数据，包括遗传和财务数据，以及来自Facebook和Twitter等大型在线社交网络的数据。

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.