Tensor Decomposition Methods for Statistical Analysis of Spatio-Temporal Infectious Disease Data

"We propose to evaluate and improve tensor decomposition methods and software in application to\n geospatial time-varying data of disease case counts. Tensor decompositions enable efficient analysis of\n a compressed representations of the data, provide access to latent statistical features, and can be used for\n extrapolation/modelling. Tensor completion extends these methods to partially-observed or noisy data.\n We will apply and extend existing parallel software for tensor decomposition and tensor completion to\n a sparse tensor dataset of diagnosis statistics of COVID-19 patients in different locations over time (i.e.,\n a tensor of disease by location by time). We will prototype performance of new tensor decomposition\n methods appropriate for analysis of this type of data, including high-order methods for tensor decom-\n position with constraints and multigrid tensor decompositions with a predefined hierarchy (in our case,\n geospatial). Since the dataset is a large sparse tensor, we plan to make use Stampede2, employing soft-\n ware that has previously been developed and benchmarked for sparse tensor decomposition and tensor\n completion on this supercomputer."