论文标题
带有附带信息的矩阵近似：当列采样足够时
Matrix Approximation with Side Information: When Column Sampling is Enough
论文作者
论文摘要
本文考虑了一个新的矩阵近似问题：基于一些完全采样的列的观察和准多物质结构侧信息。该框架是由完整矩阵计算昂贵的量子化学问题激励的，部分计算仅导致列信息。所提出的算法成功地估算了真矩阵的真实矩阵的列和行空间，并且给定对真矩阵的先验结构知识。提供了一个理论频谱误差绑定，该误差捕获了侧面信息的可能不准确性。误差绑定证明其缩放以其信噪比（SNR）比率。提出的算法通过模拟验证，该算法能够表征准多项式侧信息提供的信息量。
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. The proposed algorithm is validated via simulations which enable the characterization of the amount of information provided by the quasi-polynomial side information.
