EPSRC Project Summary: New Methods for Network Time Series Analysis

EPSRC 项目摘要：网络时间序列分析的新方法

• 批准号: 2283002
• 金额: --
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2283002
• 关键词: EPSRC; Project; Summary; New; Methods

The rapidly increasing availability of multivariate time series data with explicit or implicit network structure have resulted in a heightened interest in network time series models for the purposes of forecasting or network structure inference. Such models have been used to forecast time series across a diverse array of research areas, from epidemiology to meteorology to social media networks. For example, the wind speed in a given area may depend on both past observations in the same location and those of its geographic neighbours, with varying lags and effect sizes. An accurate wind speed model may be a useful tool for deciding on the locations of new wind turbines, when it is not cost effective to collect the data at all candidate locations for long periods of time. The recently-developed generalised network autoregressive (GNAR) model provides both a flexible and highly parsimonious approach to the modelling of such data, by allowing dependence of the modelled series on an autoregressive component and neighbours across multiple covariate networks. My research aims to extend the GNAR modelling framework and develop new methods pertaining to network time series analysis in several areas. One extension would involve the development of novel algorithms for GNAR network structure inference in the absence of any network priors, allowing the treatment of all multivariate time series data sets as network time series. This would build on existing research for structural inference of Bayesian networks. Secondly, the GNAR model structure may be extended to incorporate node-specific exogenous time series regressors, which should lead to better forecasts and useful inferences when informative explanatory variables are available. Thirdly, my research will attempt to generalise network time series models to tensor-valued time series. For example, in the area of epidemiology, this would allow the parsimonious modelling of network time series where each location (or node in the network) possesses multiple time series representing case numbers, meteorological conditions and other factors relevant to disease transmission.Finally, I will examine the applications of deep learning to big network time series data sets, by using an initial network lifting preprocessing step to detrend and spatially decorrelate the data set. Of particular interest are extensions of `hybrid' deep learning architectures, such as the recently-developed Gaussian Process Long Short Term Memory (GP-LSTM) model. GP-LSTM uses a recurrent neural network to embed the kernel matrix of a Gaussian process and perform inference in a highly scalable fashion. As well as achieving state-of-the-art performance in time series forecasting tasks, the GP-LSTM allows for the straightforward estimation of the uncertainty in predictions of traditionally `opaque' neural networks. Furthermore, to my knowledge, the use of a network lifting scheme for feeding data into such deep learning models has not yet been examined in the machine learning literature.It is my hope that research in these areas will present novel contributions to the field of network time series analysis, that is to provide methodological tools to forecast multivariate time series using highly parsimonious models that exploit network structure. This project falls within the EPSRC Statistics and Applied Probability research area.________________________________________

具有明确或隐式网络结构的多元时间序列数据的迅速增加导致对网络时间序列模型的兴趣增加，以预测或网络结构推理。这些模型已用于预测各种研究领域的时间序列，从流行病学到气象学再到社交媒体网络。例如，给定区域中的风速可能取决于同一位置和其地理邻居的过去观察结果，其滞后和效应大小都有不同。准确的风速模型可能是确定新风力涡轮机位置的有用工具，而在长时间内收集所有候选位置的数据是不可成本效果的。最近开发的广义网络自回归（GNAR）模型通过允许对自回归组件的建模系列依赖于多个协变量网络的建模系列，从而为此类数据建模提供了一种灵活的和高度的方法。我的研究旨在扩展GNAR建模框架，并开发与几个领域网络时间序列分析有关的新方法。一个扩展将涉及在没有任何网络先验的情况下开发用于GNAR网络结构推断的新型算法，从而可以将所有多元时间序列数据集作为网络时间序列进行处理。这将基于贝叶斯网络结构推断的现有研究。其次，可以扩展GNAR模型结构以结合节点特异性的外源时间序列回归器，当提供信息的解释变量时，应带来更好的预测和有用的推论。第三，我的研究将尝试将网络时间序列模型推广到张量值时间序列。 For example, in the area of​​ epidemiology, this would allow the parsimonious modelling of network time series where each location (or node in the network) possesses multiple time series representing case numbers, meteorological conditions and other factors relevant to disease transmission.Finally, I will examine the applications of deep learning to big network time series data sets, by using an initial network lifting preprocessing step to detrend and spatially decorrelate the data set.特别有趣的是“混合”深度学习体系结构的扩展，例如最近开发的高斯过程长期记忆（GP-LSTM）模型。 GP-LSTM使用经常性的神经网络嵌入高斯过程的内核矩阵，并以高度可扩展的方式进行推断。除了实现时间序列预测任务的最新性能外，GP-LSTM还可以直接估计传统上“不透明”神经网络的预测中的不确定性。此外，据我所知，在机器学习文献中尚未对使用网络提升方案将数据馈入此类深度学习模型。我希望这些领域的研究能为网络时间序列分析的领域提供新的贡献，这是为了提供方法学工具，以预测使用高速播放网络结构的高速元素时间序列来预测多元素时间序列。该项目属于EPSRC统计数据和应用概率研究领域。