Streaming Estimation for the Spectral Density"

最近的技术创新大大提高了许多应用领域的数据生成和数据收集能力，特别是在实时信息采集方面取得了许多进展。传统的分析和建模方法需要在处理数据之前存储和读取数据。根据收集数据的速度，这可能导致我们的算法和模型需要大量的内存和计算能力。此外，在真实的世界应用中，数据生成过程有可能在收集数据时经历改变。这是经典算法的另一个缺点。他们通常有一个固定的假设，即生成过程不会改变，因此一旦我们放松这个假设，就不适合这项任务。这个项目福尔斯EPSRC数字信号处理，统计和应用概率的研究领域。我们的目标是开发旨在处理高频数据的方法，同时也保留一定的适应性，使我们能够处理潜在的随机过程中的变化。这些方法将使我们能够在观察到时间序列时对其进行分析，从而使我们能够对真实的时间变化作出反应。这在网络安全等领域特别有用，因为需要尽快发现和调查偏离规范的异常行为。这样的问题涉及到有最好的最新估计的规范是什么，同时也能够判断任何给定的一组数据点为abnormal.In这个项目中，我们计划开发的方法，专门针对估计的频谱密度的时间序列，因为它在数据收集过程中的演变。由于谱密度捕获了关于随机数据生成过程的绝大多数信息，这些算法将使我们能够跟踪长期季节性和短期趋势的变化。目前的重点领域是非参数变点检测和多变量时间序列分析。我们计划通过结合图形预测和网络分析来扩展后者。目前，季节性很少被用来分析网络的基本结构。在我们的工作中，我们希望解决文献中的这一缺陷，并开发新的网络分析工具。为了最大限度地发挥我们工作的影响力，我们还将开发开源软件-包括文档和演示-我们将在网上分享。

Recent technological innovations have resulted in a large increase in both data generation and data collection capabilities in many application areas, especially given the many advances in real-time information capture. Classical approaches for analysis and modelling require the data to be stored and read before it can be processed. Depending on the speed at which the data is being collected, this could result in our algorithms and models requiring a prohibitive amount of memory and computational power. Furthermore, in real world applications, the data generating process has the possibility of undergoing changes as the data is being collected. This presents another shortcoming of classical algorithms. They usually have a baked-in assumption that the generating process does not change and thus are unsuited for the task once we relax this assumption.This project falls within the EPSRC research areas for Digital Signal Processing, Statistics and Applied probability. We aim to develop methodology designed to process high frequency data, while also retaining a level of adaptability that allows us to deal with changes in the underlying random process. These methods will enable the analysis of time series as they are being observed and thus give us the ability to react to changes in real time. This is particularly useful in areas such as cyber-security, where anomalous behaviour deviating from the norm needs to be detected and investigated as soon as possible. Such a problem involves having the best possible up-to-date estimate for what the norm is, while also being able to judge any given set of datapoints as anomalous.In this project, we plan to develop methodology specifically aimed at estimating the spectral density of a time series as it evolves during the data collection process. With the spectral density capturing the vast majority of the information regarding a random data generating process, these algorithms would enable us to track changes in both the long-term seasonality and the short-term trends. Areas of current focus are non-parametric change-point detection and multivariate time series analysis. The latter we plan to extend by incorporating graph prediction and network analysis. At present, seasonality has rarely been used to analyse the underlying structure of a network. In our work we look to address this shortcoming in the literature and develop new tools for network analysis. To maximise the impact of our work, we will also develop open-source software - with documentation and demonstrations - that we will share online.