Quasi Polynomial and Interpolative Models for Tensor Approximation

A novel Tucker decomposition based tensor approximation is considered herein: observations based on only a few lateral slices and side structural information of a true tensor are exploited. This work is motivated by quantum chemistry problems wherein full Hessian computation is expensive, but partial computation is available. The proposed method successfully estimates the quasi-polynomial and interpolative structure of frontal and lateral slices given a priori knowledge of the true tensor. A theoretical error bound is provided, which characterizes the impact due to errors in the side information. To the best of our knowledge, this work proposes the first tensor approximation with side information and interpolation.