  We propose a new graphical model inference procedure, called SG-PALM, for
learning conditional dependency structure of high-dimensional tensor-variate
data. Unlike most other tensor graphical models the proposed model is
interpretable and computationally scalable to high dimension. Physical
interpretability follows from the Sylvester generative (SG) model on which
SG-PALM is based: the model is exact for any observation process that is a
solution of a partial differential equation of Poisson type. Scalability
follows from the fast proximal alternating linearized minimization (PALM)
procedure that SG-PALM uses during training. We establish that SG-PALM
converges linearly (i.e., geometric convergence rate) to a global optimum of
its objective function. We demonstrate the scalability and accuracy of SG-PALM
for an important but challenging climate prediction problem: spatio-temporal
forecasting of solar flares from multimodal imaging data.
