Statistical Methods for Discrete-Valued High-Dimensional Time Series with Applications to Neuroscience

神经科学中高维时间序列的出现，包括EEG/MEG，fMRI和spike train数据，引发了对多变量时间序列数据分析的新兴趣，特别是破译大脑连接网络的动力学。尽管最近取得了重大进展，但绝大多数用于分析高维时间序列的现有方法都集中在高斯噪声和扰动模型的实值时间序列上。然而，神经科学中的新兴应用涉及离散值时间序列，如点过程和分类观测。该项目旨在开发灵活和可扩展的统计机器学习方法和高效的软件工具，用于使用神经科学的离散值高维时间序列数据推断大脑连接网络。大规模的大脑连接网络通常涉及复杂的非线性和多尺度相互作用，这些相互作用在实践中通常是未知的。 在这种情况下，参数模型的应用可能无法提供准确的大脑动态窗口，特别是如果模型假设被违反。本研究通过开发可扩展的统计机器学习方法和理论来弥合这一差距，以实现高维离散值时间序列的灵活非参数分析。特别是，该项目将开发（i）高维点过程的聚类和变量筛选方法，（ii）从一般类型的点过程中发现网络的有效和通用的非参数估计框架，以及（iii）一种新的正则化估计框架，具有可证明的可识别性保证，用于从高维分类时间序列中重建网络。将对这些方法的理论特性进行调查，并将开发有效的开放源码软件工具，以便利科学界应用这些方法。总之，这些工具为分析各种神经科学应用中出现的高维离散值时间序列提供了一个全面的框架，并将推动统计机器学习方法在高维时间序列分析中的现状。PI还计划发布作为开源开发的软件，并通过确保感兴趣的研究人员能够为所开发软件的代码库做出贡献，围绕该语言建立一个用户社区。这将使该项目得到更广泛的发展。高级网络基础设施办公室的软件集群对此特别感兴趣，该办公室为该奖项提供了共同资助。

The advent of high-dimensional time series from neuroscience, including EEG/MEG, fMRI and spike train data, has sparked a new interest in the analysis of multivariate time series data, particularly, to decipher the dynamics of brain connectivity networks. Despite significant recent progress, the vast majority of existing approaches for analyzing high-dimensional time series focus on real-valued time series from Gaussian noise and perturbation models. However, emerging applications in neuroscience involve discrete-valued time series, such as point processes and categorical observations. This project aims to develop flexible and scalable statistical machine learning methods and efficient software tools for inferring brain connectivity networks using discrete-valued high-dimensional time series data from neuroscience. Large-scale brain connectivity networks often involve complex nonlinear and multi-scale interactions that are usually unknown in practice. Applications of parametric models in such settings may not provide an accurate window into the brain's dynamics, especially if the model assumptions are violated. This research bridges this gap by developing scalable statistical machine learning methods and theory for flexible nonparametric analysis of high-dimensional discrete-valued time series. In particular, this project will develop (i) clustering and variable screening methods for high-dimensional point processes, (ii) an efficient and general nonparametric estimation framework for network discovery from a general class of point processes, and (iii) a novel regularized estimation framework with provable identifiablity guarantees for network reconstruction from high-dimensional categorical time series. Theoretical properties of these methods will be investigated, and efficient open-source software tools will be developed to facilitate the application of the methods by the scientific community. Together, these tools provide a comprehensive framework for analysis of high-dimensional discrete values time series arising in various neuroscience applications, and will advance the current state of statistical machine learning methods for the analysis of high-dimensional time series. The PIs also plan to release the software developed as open source and build a user community around the language by ensuring that interested researchers are able to contribute to the codebase of the software developed. This will allow a wider growth of the project. This aspect is of special interest to the software cluster in the Office of Advanced Cyberinfrastructure, which has provided co-funding for this award.