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

本研究主要围绕高维数据的学习和表示进行理论和应用研究。术语高维性是指变量或未知数的数量通常远大于手头可用的观测值的数量的属性。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需求的规模有利的维数。该项目通过图形方法来解决这些挑战，通过利用许多大型数据集中存在的固有图形结构。该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。这项研究建立了强有力的理论保证开发的方法，以及将它们应用到真实的数据在各个领域，包括遗传和金融数据，以及数据从大型在线社交网络，如Facebook和Twitter。

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.