Matrix Approximation With Side Information: When Column Sampling Is Enough

A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein full matrix computation is expensive, and partial computations only lead to column information. The proposed algorithm successfully estimates the column and row space of a true matrix given a priori structural knowledge of the true matrix. A theoretical spectral error bound is provided, which captures the possible inaccuracies of the side information. The error bound proves it scales in its signal-to-noise (SNR) ratio as
$\mbox{SNR}^{-1}$
. The proposed algorithm is validated via simulations which enable the characterization of the amount of information provided by the quasi-polynomial side information.