报告人：傅晓（Oregon State University）、蒲文强（Shenzhen Research Institute of Big Data）

时间：2022年09月22日 9:30

腾讯会议ID：886 793 267 

报告摘要：The first part of talk considers the problem of computing the canonical polyadic decomposition (CPD) of large tensors under the least squares loss. Prior works mostly leverage data sparsity to handle this problem, which is not suitable for handling dense tensors that often arise in applications such as medical imaging, computer vision, and remote sensing. Stochastic optimization is known for its low memory cost and per-iteration complexity when handling dense data. However, existing stochastic CPD algorithms are not flexible enough to incorporate a variety of constraints/regularizations that are of interest in signal and data analytics. Convergence properties of many such algorithms are also unclear. In this work, we propose a stochastic optimization framework for large-scale CPD with constraints/regularizations. The framework works under a doubly randomized fashion, and can be regarded as a judicious combination of randomized block coordinate descent (BCD) and stochastic proximal gradient (SPG). The algorithm enjoys lightweight updates and small memory footprint. In addition, this framework entails considerable flexibility---many frequently used regularizers and constraints can be readily handled under the proposed scheme. The approach is also supported by convergence analysis.

The second part of talk extends the idea to CPD under non-Euclidean losses, which are important for non-continuous data analytics. Compared to the least squares loss, the non-Euclidean losses are generally more challenging to handle. Non-Euclidean CPD has attracted considerable interests and a number of prior works exist. However, pressing computational and theoretical challenges, such as scalability and convergence issues, still remain. This work offers a unified stochastic algorithmic framework for large-scale CPD decomposition under a variety of non-Euclidean loss functions. Our key contribution lies in a tensor fiber sampling strategy-based flexible stochastic mirror descent framework. Leveraging the sampling scheme and the multilinear algebraic structure of low-rank tensors, the proposed lightweight algorithm ensures global convergence to a stationary point under reasonable conditions.

报告人简介：傅晓（Xiao Fu） received the Ph.D. degree in Electronic Engineering from The Chinese University of Hong Kong (CUHK), Shatin, N.T., Hong Kong, in 2014. He was a Postdoctoral Associate with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA, from 2014 to 2017. Since 2017, he has been an Assistant Professor with the School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR, USA. His research interests include the broad area of signal processing and machine learning, with emphases on tensor/matrix decomposition and unsupervised deep learning. Dr. Fu received a Best Student Paper Award at ICASSP 2014, and was a recipient of the Outstanding Postdoctoral Scholar Award at University of Minnesota in 2016. His coauthored papers received Best Student Paper Awards from IEEE CAMSAP 2015 and IEEE MLSP 2019, respectively. He received the National Science Foundation CAREER Award in 2022. He serves as a member of the Sensor Array and Multichannel Technical Committee (SAM-TC) of the IEEE Signal Processing Society (SPS). He is also a member of the Signal Processing for Multisensor Systems Technical Area Committee (SPMuS-TAC) of EURASIP. He is the Treasurer of the IEEE SPS Oregon Chapter. He serves as an Editor of Signal Processing and an Associate Editor of IEEE Transactions on Signal Processing. He was a tutorial speaker at ICASSP 2017 and SIAM Conference on Applied Linear Algebra 2021.

蒲文强（Wenqiang Pu） received the B.S. and Ph.D. degrees in electrical engineering from Xidian University, Xi’an, China, in 2013 and 2018, respectively. From Jan. 2019 to Oct. 2020, he was a postdoc researcher at The Chinese University of Hong Kong (Shenzhen). He is currently a research scientist at Shenzhen Research Institute of Big Data. His research interests include signal processing and optimization algorithms.

邀请人：李寒宇

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