报告人：李松教授

报告题目：Low Rank Matrix Recovery with Adversarial Sparse Noise

报告摘要：

（1）Many problems in data science can be treated as recovering a low-rank matrix from a small number of random linear measurements, possibly corrupted with adversarial noise and dense noise. Recently, a bunch of theories on variants of models have been developed for different noises, but with fewer theories on the adversarial noise. In this talk，we study low-rank matrix recovery problem from linear measurements perturbed by l_1-bounded noise and sparse noise that can arbitrarily change an adversarially chosen ω-fraction of the measurement vector.

（2）For Gaussian measurements with nearly optimal number of measurements, we show that the nuclear-norm constrained least absolute deviation (LAD) can successfully estimate the ground-truthmatrix for any ω < 0.239. Similar robust recovery results are also established for an iterative hard thresholding algorithm applied to the rank-constrained LAD considering geometrically decaying step-sizes, and the unconstrained LAD based on matrix factorization as well as its subgradient descent solver.

报告时间：2022年5月21日，上午9：00——12:00

报告形式：腾讯会议；会议号：299 494 443

报告人简介：李松，浙江大学求是特聘教授，钱江特聘专家，主要从事压缩感知、小波分析理论及其应用、采样理论以及相位恢复等理论研究工作，主持了国家自然科学基金重点项目、面上项目以及浙江省重大科技专项等基金项目，作为第一完成人获得教育部自然科学二等奖。