TensorGraphicalModels: A Julia toolbox for multiway covariance models and ensemble Kalman filter

Abstract

<h2>Abstract</h2> The increasing availability of high dimensional multi-indexed data has created an opportunity for the development of graphical modeling software that bridges the gap between second order statistical and computational models. In this paper, we introduce TensorGraphicalModels, a suite of Julia tools for statistical estimation of high-dimensional multiway (tensor-variate) covariance and precision matrices, with applications to ensemble Kalman filtering. The Julia package implements several state-of-the-art multiway covariance and precision matrix estimators. These are illustrated in the context of a physics-driven forecasting example with an integrated implementation of a tensor ensemble Kalman filter (EnKF).