Many applications produce multiway data of exceedingly high dimension. Modeling such multi-way data is important in multichannel signal and video processing where sensors produce multi-indexed data, e.g. over spatial, frequency, and temporal dimensions. We will address the challenges of covariance representation of multiway data and review some of the progress in statistical modeling of multiway covariance over the past two decades, focusing on tensor-valued covariance models and their inference. We will illustrate through a space weather application: predicting the evolution of solar active regions over time.
This work was supported in part by the SOLSTICE Drive Center funded by NASA and National Science Foundation under grant 80NSSC20K0600, the Army Research Office under grants W911NF1910269 and W911NF1510479, and by the National Nuclear Security Administration under grant DE-NA0003921.
Yu Wang. Zeyu Sun. Dogyoon Song. Alfred Hero. "Kronecker-structured covariance models for multiway data." Statist. Surv. 16 238 - 270, 2022. https://doi.org/10.1214/22-SS139