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Uniqueness and stability for the solution of a nonlinear least squares problem

黄 猛 博士

（香港科技大学）

报告时间：2021年6月1日星期二 下午4:00-5:00

会议地点：沙河E404（线下）； 腾讯会议ID： 127 416 879（线上）

报告摘要：Nonlinear least squares problems have wide applications in data fitting, function approximation and others in signal processing and machine learning. In this talk, we focus on the problem: min || |Ax|-b ||, which arises in noisy phase retrieval and absolute value rectification neural networks. We first show the solution of this problem is not unique for some “bad” cases. However, under several appropriate conditions, the solution is unique. Next, we turn to the stability of this problem and show the solution is stable if vector b is in any convex set. In this case, an optimal recovery bound has also been established.

报告人简介：黄猛，2019年于中国科学院数学与系统科学研究院获博士学位，导师许志强研究员。2019年至今于香港科技大学从事博士后研究，导师汪扬教授。研究方向为相位恢复、低秩矩阵恢复和压缩感知。现已在包括《Applied and Computational Harmonic Analysis》,《IEEE Transactions on Information Theory》等顶级期刊发表论文数篇。

邀请人： 谢家新