הערכת מטריצה נמוכת-דרגה: הסרת עומס ויישומים

תקציר מקורי באנגליתarXiv:2109.11057v2 Announce Type: replace-cross Abstract: Weighted low-rank matrix approximation (WLRMA) generalizes classical low-rank approximation and matrix completion by allowing arbitrary elementwise weights. Such formulations arise naturally in a broad class of statistical models, including generalized linear low-rank models, where WLRMA serves as the computational primitive for parameter estimation. Despite its broad applicability, efficient optimization methods for general WLRMA remain relatively underdeveloped. In this paper, we formulate both the rank-constrained and nuclear-norm WLRMA problems within a unified first-order optimization framework by showing that the corresponding iterative algorithms are projected and proximal gradient methods. Building on this perspective, we de