Estimating the covariance structure of multivariate time series is a fundamental problem with a wide-range of real-world applications -- from financial modeling to fMRI analysis. Despite significant recent advances, current state-of-the-art methods are still severely limited in terms of scalability, and do not work well in high-dimensional undersampled regimes. In this work we propose a novel method called Temporal Correlation Explanation, or T-CorEx, that (a) has linear time and memory complexity with respect to the number of variables, and can scale to very large temporal datasets that are not tractable with existing methods; (b) gives state-of-the-art results in highly undersampled regimes on both synthetic and real-world datasets; and (c) makes minimal assumptions about the character of the dynamics of the system. T-CorEx optimizes an information-theoretic objective function to learn a latent factor graphical model for each time period and applies two regularization techniques to induce temporal consistency of estimates. We perform extensive evaluation of T-Corex using both synthetic and real-world data and demonstrate that it can be used for detecting sudden changes in the underlying covariance matrix, capturing transient correlations and analyzing extremely high-dimensional complex multivariate time series such as high-resolution fMRI data.
翻译:估计多变量时间序列的共变结构是一个根本性问题,因为从金融模型到FMRI分析,现实应用的范围很广,从金融模型到FMRI分析,都是一个根本性问题。尽管最近取得了显著的进步,但目前最先进的方法在可缩放性方面仍然受到严重限制,在高维下层抽样制度下效果不佳。在这项工作中,我们提出了一个叫作“时间相关性解释”或“T-CorEx”的新颖方法,即:(a) 变量的数量具有线性时间和记忆复杂性,并且可以扩大到与现有方法不相容的非常大的时间数据集;(b) 在合成和现实世界数据集中,提供高度低采样的系统的最新结果;(c) 对系统动态特性作出最起码的假设。T-CorEx优化信息-理论目标功能,以学习每个时段的隐性系数图形模型,并应用两种正规化技术来促成时间的一致性。我们用合成和现实-数字数据集对T-Corex进行广泛的评估,同时使用合成和真实性数据序列来探测高分辨率数据,并显示其用于快速的多维度数据。