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

来自神经科学的高维时间序列的出现，包括脑电/脑磁图、功能磁共振成像和棘波训练数据，引起了人们对多变量时间序列数据分析的新兴趣，特别是在破译大脑连接网络的动力学方面。尽管最近取得了显著的进展，但现有的绝大多数高维时间序列分析方法都集中在来自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有效的软件工具，用于使用神经科学的离散值高维时间序列数据来推断大脑连接网络。大规模的大脑连接网络往往涉及复杂的非线性和多尺度的相互作用，而这些相互作用在实践中通常是未知的。在这样的环境中应用参数模型可能无法提供了解大脑动态的准确窗口，特别是在违反模型假设的情况下。这项研究通过开发可扩展的统计机器学习方法和理论来弥补这一差距，以便对高维离散值时间序列进行灵活的非参数分析。具体地说，该项目将开发(I)高维点过程的聚类和变量筛选方法，(Ii)用于从一般点过程发现网络的高效和通用的非参数估计框架，以及(Iii)用于从高维分类时间序列重建网络的具有可证明可辨识性保证的新的正则化估计框架。将调查这些方法的理论性质，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，并将促进用于分析高维时间序列的统计机器学习方法的现状。私人投资机构还计划发布作为开放源码开发的软件，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。这将使该项目有更广泛的增长。这方面对高级数字基础设施办公室的软件集群特别感兴趣，该办公室为这一奖项提供了共同资金。

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.