题 目：Exact Lowest Rank Recovery of Incomplete Matrices
报告人：王学钦 教授
主持人：刘玉坤 教授
时 间：2022年10月21日（周五）14:00-15:00
地 点：腾讯会议ID：194 278 539
报告人简介：
王学钦，中国科学技术大学讲席教授。2003年毕业于纽约州立大学宾厄姆顿分校。他现担任中国现场统计研究会副理事，教育部高等学校统计学类专业教学指导委员会委员、统计学国际期刊《JASA》等的Associate Editor、高等教育出版社《Lecture Notes: Data Science, Statistics and Probability》系列丛书的副主编。
报告内容简介：
Many disciplines of research, including statistics, mathematics, and machine learning, have made extensive use of investigated low-rank approximation approaches. As a measure of how well a model fits the data, rank plays an important role in this approach. Its determination is therefore crucial. A number of works in the literature have offered their estimation methods for the fully observed data, but no works address this topic for missing data, which are highly prevalent in real-world applications, in literature. To restore the rank, we present an optimization framework and a method for solving the optimization issue. The unique rank of the underlying matrix can be recovered from the observed incomplete matrix by providing a suitable low-size bound on the observed entries under a simple entry missing mechanism. We also get the Eckart-Young-Mirsky theorem for incomplete matrices as a natural consequence. Several numerical tests and real data analysis demonstrate the efficacy of our strategy.