CAREER: Modeling Dependencies via Graphs: Scalable Inference Methods for Massive Datasets

本研究主要针对高维数据的学习和表示进行理论和应用研究。术语高维是指变量或未知数的数量通常比手头可用观测的数量多得多的特性。一个关键的挑战是能够用样本和计算要求在维度数量上有利地缩放来表示和学习这种现象。该项目通过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来建模高维数据，也称为马尔可夫随机场。该方案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强有力的理论保障，并将其应用于各个领域的真实数据，包括遗传和金融数据，以及来自Facebook和Twitter等大型在线社交网络的数据。

This research centers on theoretical and applied research on learning and representation of high-dimensional data. The term high dimensionality refers to the property that the number of variables or unknowns is typically much larger than the number of observations available at hand. A key challenge is being able to represent and learn such phenomena with sample and computational requirements scaling favorably in the number of dimensions. This project addresses these challenges through a graphical approach by exploiting the inherent graphical structure present in many large data-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 develop novel algorithms for learning and inference under the framework of graphical models. Another important thrust of this proposal is to develop efficient scalable models for representing high-dimensional data beyond the traditional framework of graphical models. This research establishes strong theoretical guarantees for the developed methods, as well as applies them to real data in various domains, including genetic and financial data, and data from large online social networks such as Facebook and Twitter.