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结合数据中的结构信息来增强大规模计算、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。这一建议旨在将数据的重要结构以及特征变量和响应变量之间的关联纳入到设计大规模问题的有效实验方法和算法中，并理解过程的理论性质。项目1开发了一种高维、低样本量范例中的特征筛选方法，该方法考虑了特征之间的相关性结构。PI提出了用于选择与响应变量相关的特征变量的推理框架。在大规模同时推理的背景下，假设往往伴随着某些结构性的先验信息。项目2提出了一种新的多重测试程序，该程序在纳入先验信息的同时保持对错误发现率的控制。大规模的多个测试任务往往表现出相关性，而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提出了一种多重测试程序，允许一般的依赖结构和异质的依赖参数，该建议旨在解决一些具有挑战性的研究问题，这些问题来自生物、医学和科学研究的前沿，共同的主题是开发高维数据中的结构信息。将开发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。这些进展的传播将促进新的知识发现，并加强跨学科合作。这项研究还将通过关于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群体的培训和学习。

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.