High Dimensional Models for Multivariate Time Series Analysis

用于多元时间序列分析的高维模型

基本信息

批准号：
EP/I005250/1
负责人：
Sofia Olhede
金额：
$ 126.15万
依托单位：
University College London
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2010
资助国家：
英国
起止时间：
2010 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FI005250%2F1
关键词：
Dimensional Models Multivariate Time Series

项目摘要

This fellowship will focus on developing methods for high dimensional time series analysis. Methodology for high dimensional data is one of the most important current research topics in statistics and signal processing, where massive data sets have inspired the development of a new statistical paradigm based on sparsity. Such developments have mainly concerned deterministic structure immersed in noise, while this program will model the signal of interest as stochastic. The advantage of modeling an observed signal stochastically as a time series is that one can deduce properties of a population of series, important for the correct understanding of uncertainty or variability in structure.Traditional time series methods are restricted to stationary processes, whose structure is homogeneous in time. The project will instead develop theory and methodology for classes of nonstationary processes, that can experience changes in their generating mechanism over the time course of observation. Such processes are important as they allow us to model the evolution of an observable quantity, and also enable us to quantify this evolution explicitly. Nonstationary processes are observed in a number of applications such as geoscience (remote sensing and satellite observations), oceanography (drifter and float measurements), neuroscience (functional MRI and EEG) and ecology (species abundance) to mention but a few areas. In such applications single processes are rarely of interest, and so we shall develop methods for the analysis of multiple (or equivalently multivariate) signals, to quantify the evolving interdependencies of observed processes.The difficulty in analyzing nonstationary signals is their high degree of overparameterization, that is much exacerbated if inferences are to be made of multiple series. At first glance reliable estimation in such problems seems impossible, as a consequence of the extreme overparameterization. Assumptions on sparsity have recently been used to enable estimation in related overparameterized problems. Such methods need careful extension and substantial innovation to cover the case of multivariate and stochastic signals, that we propose to address via this project. Key to developing such methods is introducing new sparse classes of nonstationary processes, building on recent developments in statistics for high dimensional data. Sparse models despite a nominal degree of high complexity are described by some unknown but simpler structure of smaller complexity. Sparse models will be constructed to contain previously incompatible nonstationary processes, thus enabling us to treat series that lacked a natural analysis framework.This proposal therefore aims to a) introduce new classes of nonstationary processes for single signals using sparsity, b) extend these classes to rich families of multivariate processes for scenarios where either the group structure of the processes is known or has to be learned, c) develop a theoretical understanding of the estimability of such classes of processes and d) develop general estimation methods as well as application specific methodology.We expect this work to impact statistics much beyond time series. New forms of sparsity and methods will also be relevant to related problems in mathematics, machine learning and signal processing, especially in terms of defining new forms of signal group sparsity. The work will also have more than a methodological impact as the development of these methods will allow us to analyze multiple series that previously could not be analyzed, and we intend to develop application specific methods with our collaborators.

该奖学金将着重于开发用于高维时间序列分析的方法。高维数据的方法是统计和信号处理中最重要的研究主题之一，其中大量数据集启发了基于稀疏性的新统计范式的发展。此类发展主要涉及沉浸在噪声中的确定性结构，而该程序将把感兴趣的信号模拟为随机性。以随机为时间序列对观察到的信号进行建模的优势在于，人们可以推断出系列人群的性质，对于正确理解结构中的不确定性或变异性很重要。传统时间序列方法仅限于固定过程，其结构在时间上是同质的。相反，该项目将开发非组织过程类别的理论和方法，这些过程可以在观察过程中体验其生成机制的变化。这样的过程很重要，因为它们使我们能够对可观察数量的演变进行建模，并使我们能够明确量化这一进化。在许多应用中观察到非平稳过程，例如地球科学（遥感和卫星观测），海洋学（漂流者和浮点测量值），神经科学（功能性MRI和EEG）以及生态学（物种丰度），以提及一些领域。在此类应用中，单个过程很少引起人们的兴趣，因此我们将开发用于分析多个（或等效多元）信号的方法，以量化观察过程的不断发展的相互依赖性。分析非机构信号的困难是其高度参数化的高度，如果是高度的，那么这是多种多次的系列。乍看之下，由于极端的过度参数化，这种问题的可靠估计似乎是不可能的。关于稀疏性的假设最近已用于实现相关过度参数问题的估计。这种方法需要仔细扩展和实质性创新，以涵盖我们建议通过该项目解决的多元和随机信号的情况。开发此类方法的关键是引入新的稀疏类别的非机构过程，这是基于高维数据的统计数据的最新发展。稀疏模型尽管标称的高复杂性程度是通过一些未知但更简单的复杂性结构来描述的。 Sparse models will be constructed to contain previously incompatible nonstationary processes, thus enabling us to treat series that lacked a natural analysis framework.This proposal therefore aims to a) introduce new classes of nonstationary processes for single signals using sparsity, b) extend these classes to rich families of multivariate processes for scenarios where either the group structure of the processes is known or has to be learned, c) develop a theoretical understanding of the estimability of such流程类别和d）开发一般估计方法以及特定的方法。我们希望这项工作会影响统计数据超出时间序列。新形式的稀疏性和方法也将与数学，机器学习和信号处理中的相关问题有关，尤其是在定义新形式的信号组稀疏性方面。这项工作还将不仅具有方法论上的影响，因为这些方法的开发将使我们能够分析以前无法分析的多个系列，我们打算与我们的合作者开发特定的应用方法。