An Integrated Toolkit for High-Dimensional Complex and Time Series Data Analysis

大脑结构如何随着年龄的增长而进化，基因活动如何受到转录因子的控制，这些基本问题可能会通过涉及高维数据集的研究得到解答。随着大量医学成像和基因组测序数据的收集，这些问题可以通过神经科学家和生物学家的专业知识与强大的数据分析工具相结合来研究，这些工具旨在解决数据中的微妙之处并揭示数据中隐藏的模式。该项目旨在为复杂生物系统的高通量估计开发一个可扩展、鲁棒且理论上合理的非参数和半参数解决方案的集成工具包。它解决了两个主要问题。第一个问题是考虑大量高维复杂结构数据，这些数据具有复杂的生成分布和相互关系，通常无法通过简单的线性系统捕获。这样的数据通常是有噪声的，并且包含大量的异常值。第二个问题考虑的是显示时空相关性和相对较弱信号的数据。假设独立和相同分布的数据可能导致错误的估计和预测，从而导致对生物系统的不准确解释。本项目旨在提供解决这两个问题的方法。本研究项目提出了有效分析生物系统的新方法，以统一的方式处理上述挑战。一个基本特征是大规模鲁棒非参数/半参数推理的概念。特别是，该项目旨在开发一个集成的方法工具包，这些方法：(1)易于扩展到具有大样本量的高维数据；(2)对数据建模假设和不同类型的数据污染具有鲁棒性；(3)建立在非参数或半参数意义上，其中相应的生成模型包含无限维组件，这些组件尽可能多地捕获数据信息或微妙之处。为了说明这一点，研究者打算构建、探索和应用高维广义回归模型、（广义）部分线性模型、形状约束回归模型和copula时间序列模型等，以揭示生物系统中隐藏的模式。正在开发的方法被设计为最优，即获得非参数极大极小或半参数下效率界。

Fundamental questions about how the brain's structure evolves with age and how gene activities are controlled by transcription factors may be answered by studies involving high-dimensional data sets. As massive amounts of medical imaging and genome sequencing data are now being collected, these questions can be investigated by combining neuroscientists' and biologists' expertise with powerful data analysis tools geared towards addressing the subtlety and uncovering hidden patterns in the data. This project aims to develop an integrated toolkit of scalable, robust, and theoretically sound nonparametric and semiparametric solutions for high-throughput estimation of complex biological systems. It addresses the resolution of two major problems. The first problem considers massive amounts of high-dimensional complex-structured data that possess complex generating distributions and interrelationships, which often cannot be captured by simple linear systems. Such data are usually noisy and contain numerous outliers. The second problem considers data exhibiting temporal and spatial correlations and a relatively weak signal. Assuming independent and identically distributed data could lead to erroneous estimation and prediction, giving rise to inaccurate interpretation of biological systems. This project aims to provide methods to solve both of these problems.This research project puts forward new methods for effective analysis of biological systems, handling the aforementioned challenges in a unified fashion. One essential feature is the concept of large-scale robust nonparametric/semiparametric inference. In particular, the project aims to develop an integrated toolkit of methods that are: (1) easily scalable to high-dimensional data with a large sample size; (2) robust to data modeling assumptions and different kinds of data contaminations; (3) built in a nonparametric or semiparametric sense, where the corresponding generative models contain infinite-dimensional components that capture the data information or subtlety as much as possible. To illustrate, the investigator intends to construct, explore, and apply high dimensional generalized regression models, (generalized) partially linear models, shape-constrained regression models, and copula time series models, among others, to unveil hidden patterns in biological systems. The methods under development are designed to be optimal, namely, attaining either a nonparametric minimax or a semiparametric lower efficiency bound.