【CSIAM青年学者论坛】【CSIAM大数据与人工智能专委会青年论坛】香港科技大学数学系夏冬博士学术报告通知2022年青工委第十二次活动
讲座题目：Riemannian Optimization for (robust) Low-rank Tensor Estimation
讲座时间：2022年5月27日，星期五，上午10:00-12:00
腾讯会议ID：436 859 312
讲座人： 夏冬博士，香港科技大学
讲座简介：
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or heterogeneous signals that are unexplainable by the low-rank part. The framework is flexible covering both linear and non-linear models, and can easily handle continuous or categorical variables. We propose a fast algorithm by integrating the Riemannian gradient descent and a novel gradient pruning procedure. Under suitable conditions, the algorithm converges linearly and can simultaneously estimate both the low-rank and sparse tensors. The statistical error bounds of final estimates are established in terms of the gradient of loss function. The error bounds are generally sharp under specific statistical models, e.g., the robust tensor PCA and the community detection in hypergraph networks with outlier vertices. Moreover, our method achieves non-trivial error bounds for heavy-tailed tensor PCA whenever the noise has a finite 2+ε moment. We apply our method to analyze the international trade flow dataset and the statistician hypergraph co-authorship network, both yielding new and interesting finding.
讲座人简介：
夏冬博士，香港科技大学数学系助理教授，2016年在佐治亚理工获得博士学位，分别在哥伦比亚大学做博士后和威斯康星大学麦迪逊分校做访问助理教授。夏博士的研究领域为高维统计，机器学习和优化理论。夏博士分别在 AoS, JRSSB 和 JMLR 等统计和机器学习领域顶尖期刊发表学术成果，目前担任JSPI的副主编。
组织者：
王建军西南大学教授
孟德宇西安交通大学教授
赵熙乐电子科技大学教授
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会议主题：线上报告:Riemannian Optimization for (robust) Low-rank Tensor Estimation
会议时间：2022/05/2710:00-12:00 (GMT+08:00) 中国标准时间 - 北京
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#腾讯会议：436-859-312
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