CIF: Medium: Collaborative Research: Learning in High Dimensions: From Theory to Data and Back

统计建模是分析现代数据集的基石，而使用观测数据来学习底层统计模型是大多数数据分析任务的关键部分。然而，随着数据利用的成功，其复杂性也大大增加，表现为复杂的模型、众多的参数和高维特征。这项研究项目从理论和实践两个方面研究了学习此类高维模型的问题，并使用前沿应用中的实际数据集进行了研究。有效地学习高维模型，无论是在计算方面还是在数据使用方面，都是一个重要的挑战。这项研究刻画了几个关键分布学习问题的样本和计算复杂性的基本限制，以及达到这些限制的相关最优学习算法。学习问题是重要任务的基础，如聚类、假设的多重检验和信息度量估计。开发的新算法和新方法在三个具体应用的真实数据上进行了评估和应用：1)高通量转录数据的去噪；2)个性化医学的组学数据分析；3)生态种群研究。虽然这些应用本身是有用的，但在语音识别、主题建模、字符识别、神经科学等领域也将有许多其他潜在的应用。

Statistical-modeling is the cornerstone of analyzing modern data sets, and using observed data to learn the underlying statistical model is a crucial part of most data analysis tasks. However, with the success of data utilization came a vast increase in its complexity as expressed in complex models, numerous parameters, and high dimensional features. This research project studies problems in learning such high-dimensional models, both in theory and in practice with actual datasets in cutting-edge applications. Learning high-dimensional models efficiently, both in terms of computation and in terms of the use of the data, is an important challenge. The research characterizes the fundamental limits on the sample and computational complexity of several key distribution learning problems, as well as the associated optimal learning algorithms that achieve the limits. The learning problems underpin important tasks such as clustering, multiple testing of hypothesis and information measure estimation. The new algorithms and new methodologies developed are evaluated and applied on real data from three specific applications: 1) denoising of high throughput transcriptomic data; 2) analysis of omics data for personalized medicine; 3) ecological population studies. While these applications are useful on their own right, there will also be many other potential applications in fields such as speech recognition, topic modeling, character recognition, neuroscience, etc.