Large language models like GPT-4 exhibit emergent capabilities across general-purpose
tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks …

We consider the problem of reconstructing a rank-one matrix from a revealed subset of its
entries when some of the revealed entries are corrupted with perturbations that are unknown …

Low-rank matrix completion (LRMC) problems arise in a wide variety of applications.
Previous theory mainly provides conditions for completion under missing-at-random …

Feature missing is a serious problem in many applications, which may lead to low quality of
training data and further significantly degrade the learning performance. While feature …

Steady-state analysis of dynamical systems for biological networks gives rise to algebraic
varieties in high-dimensional spaces whose study is of interest in their own right. We …

Hyperspectral image (HSI) denoising is an essential preprocessing step for improving HSI
applications. Recently, subspace-based nonlocal low-rank approximation (SNLR) methods …

We study the matrix completion problem when the observation pattern is deterministic and
possibly non-uniform. We propose a simple and efficient debiased projection scheme for …

Recent studies in computer vision have shown that, while practically invisible to a human
observer, skin color changes due to blood flow can be captured on face videos and …

Prevalent matrix completion theories reply on an assumption that the locations of the
missing data are distributed uniformly and randomly (ie, uniform sampling). Nevertheless …

Fast transforms correspond to factorizations of the form, where each factor is sparse and
possibly structured. This paper investigates essential uniqueness of such factorizations, ie …