Structural-Information Enhanced Inference for Large-Scale and High-Dimensional Data

大规模和高维推理过程的一个基本研究问题是如何将数据中的结构信息结合起来，以增强大规模计算、机器学习和统计推理。学习和利用这种结构对于更好地分析复杂数据集至关重要。该建议旨在将重要的数据结构和特征变量与响应变量之间的关联纳入设计大规模问题的有效实验方法和算法，并了解程序的理论特性。项目1提出了一种高维、低样本量的特征筛选方法，该方法考虑了特征间的相关结构。PI提出了一个推理框架，用于选择与响应变量相关的特征变量。在大规模同时推理的背景下，假设往往伴随着一定的结构先验信息。项目2提出了一个新的多重测试程序，它保持控制的错误发现率，同时结合先验信息。大规模的多测试任务往往表现出相关性，利用单个测试之间的相关性是统计学中一个重要但具有挑战性的问题。项目3提出了一个多重测试程序，允许一般的依赖结构和异构的依赖参数。这个建议旨在解决一些具有挑战性的研究问题，从生物，医学和科学研究的前沿，一个共同的主题是开发高维数据中的结构信息。将开发适用于大规模和高维数据的随机建模，计算算法，参数学习和统计推断的新工具，例如，脑功能磁共振成像数据和乳腺癌全基因组关联研究的数据集。这些发展的传播将促进新的知识发现，并加强跨学科合作。该研究还将通过当代最先进的数据挖掘和机器学习的多学科课程与教育实践相结合，并有利于本科生，研究生和代表性不足的少数民族的培训和学习。

A fundamental research issue for large-scale and high-dimensional inference procedures is how can we incorporate the structural information from the data to enhance large-scale computing, machine learning and statistical inference. Learning and exploiting such structure is crucial towards better analysis of complex datasets. This proposal aims to incorporate important structures of the data and association among feature variables and the response variable into devising efficient experimental approaches and algorithms for large scale problems and understanding theoretical properties of the procedures. Project 1 develops a feature screening approach in the high dimension, low sample size paradigm which takes into account the correlation structure among the features. The PI proposes a framework of inference for selecting feature variables relevant to the response variable. In the context of large-scale simultaneous inference, the hypotheses are often accompanied with certain structural prior information. Project 2 proposes a new multiple testing procedure, which maintains control of the false discovery rate while incorporating the prior information. Large-scale multiple testing tasks often exhibit dependence, and leveraging the dependence among individual tests is an important but challenging problem in statistics. Project 3 proposes a multiple testing procedure which allows general dependence structures and heterogeneous dependence parameters.This proposal aims to tackle some challenging research problems, arising from frontiers of biological, medical and scientific research, with a common theme of exploiting structural information in high-dimensional data. New tools for stochastic modeling, computational algorithms, parameter learning, and statistical inference applied to large-scale and high-dimensional data, for example, brain fMRI imaging data and datasets from genome-wide association studies on breast cancer, will be developed. Dissemination of these developments will enhance new knowledge discoveries, and strengthen interdisciplinary collaborations. The research will also be integrated with educational practice through multi-disciplinary courses on the contemporary state-of-the-art data mining and machine learning, and benefit the training and learning of undergraduate, graduate students and underrepresented minorities.