  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.

Machine Learning;Machine Learning