Stochastic Iterative Hard Thresholding for Low-Tucker-Rank Tensor Recovery

Rachel Grotheer; Shuang Li; Anna Ma; Deanna Needell; Jing Qin

doi:10.1109/ITA50056.2020.9244965

Stochastic Iterative Hard Thresholding for Low-Tucker-Rank Tensor Recovery

Rachel Grotheer, Shuang Li, Anna Ma, Deanna Needell, Jing Qin

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Low-rank tensor recovery problems have been widely studied in many signal processing and machine learning applications. Tensor rank is typically defined under certain tensor decomposition. In particular, Tucker decomposition is known as one of the most popular tensor decompositions. In recent years, researchers have developed many state-of-the-art algorithms to address the problem of low-Tucker-rank tensor recovery. Motivated by the favorable properties of the stochastic algorithms, such as stochastic gradient descent and stochastic iterative hard thresholding, we aim to extend the stochastic iterative hard thresholding algorithm from vectors to tensors in order to address the problem of recovering a low-Tucker-rank tensor from its linear measurements. We have also developed linear convergence analysis for the proposed method and conducted a series of experiments with both synthetic and real data to illustrate the performance of the proposed method.

Original language	English
Title of host publication	2020 Information Theory and Applications Workshop, ITA 2020
ISBN (Electronic)	9781728141909
DOIs	https://doi.org/10.1109/ITA50056.2020.9244965
State	Published - Feb 2 2020
Event	2020 Information Theory and Applications Workshop, ITA 2020 - San Diego, United States Duration: Feb 2 2020 → Feb 7 2020

Publication series

Name	2020 Information Theory and Applications Workshop, ITA 2020

Conference

Conference	2020 Information Theory and Applications Workshop, ITA 2020
Country/Territory	United States
City	San Diego
Period	2/2/20 → 2/7/20

Bibliographical note

Funding Information:
This material is based upon work supported by the National Security Agency under Grant No. H98230-19-1-0119, The Lyda Hill Foundation, The McGovern Foundation, and Microsoft Research, while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the summer of 2019 as part of the Summer Research for Women in Mathematics (SWiM) program. In addition, Li was supported by the NSF grants CCF-1409258, CCF-1704204, and the DARPA Lagrange Program under ONR/SPAWAR contract N660011824020. Grotheer was supported by the Goucher College Summer Research grant. Needell was supported by NSF CAREER DMS #1348721 and NSF BIGDATA DMS #1740325. Qin was supported by the NSF DMS #1941197.

Publisher Copyright:
© 2020 IEEE.

ASJC Scopus subject areas

Artificial Intelligence
Computational Theory and Mathematics
Computer Science Applications
Information Systems and Management
Control and Optimization

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10.1109/ITA50056.2020.9244965

Cite this

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title = "Stochastic Iterative Hard Thresholding for Low-Tucker-Rank Tensor Recovery",

abstract = "Low-rank tensor recovery problems have been widely studied in many signal processing and machine learning applications. Tensor rank is typically defined under certain tensor decomposition. In particular, Tucker decomposition is known as one of the most popular tensor decompositions. In recent years, researchers have developed many state-of-the-art algorithms to address the problem of low-Tucker-rank tensor recovery. Motivated by the favorable properties of the stochastic algorithms, such as stochastic gradient descent and stochastic iterative hard thresholding, we aim to extend the stochastic iterative hard thresholding algorithm from vectors to tensors in order to address the problem of recovering a low-Tucker-rank tensor from its linear measurements. We have also developed linear convergence analysis for the proposed method and conducted a series of experiments with both synthetic and real data to illustrate the performance of the proposed method.",

author = "Rachel Grotheer and Shuang Li and Anna Ma and Deanna Needell and Jing Qin",

note = "Funding Information: This material is based upon work supported by the National Security Agency under Grant No. H98230-19-1-0119, The Lyda Hill Foundation, The McGovern Foundation, and Microsoft Research, while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the summer of 2019 as part of the Summer Research for Women in Mathematics (SWiM) program. In addition, Li was supported by the NSF grants CCF-1409258, CCF-1704204, and the DARPA Lagrange Program under ONR/SPAWAR contract N660011824020. Grotheer was supported by the Goucher College Summer Research grant. Needell was supported by NSF CAREER DMS #1348721 and NSF BIGDATA DMS #1740325. Qin was supported by the NSF DMS #1941197. Publisher Copyright: {\textcopyright} 2020 IEEE.; null ; Conference date: 02-02-2020 Through 07-02-2020",

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Grotheer, R, Li, S, Ma, A, Needell, D & Qin, J 2020, Stochastic Iterative Hard Thresholding for Low-Tucker-Rank Tensor Recovery. in 2020 Information Theory and Applications Workshop, ITA 2020., 9244965, 2020 Information Theory and Applications Workshop, ITA 2020, 2020 Information Theory and Applications Workshop, ITA 2020, San Diego, United States, 2/2/20. https://doi.org/10.1109/ITA50056.2020.9244965

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AU - Grotheer, Rachel

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N1 - Funding Information: This material is based upon work supported by the National Security Agency under Grant No. H98230-19-1-0119, The Lyda Hill Foundation, The McGovern Foundation, and Microsoft Research, while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the summer of 2019 as part of the Summer Research for Women in Mathematics (SWiM) program. In addition, Li was supported by the NSF grants CCF-1409258, CCF-1704204, and the DARPA Lagrange Program under ONR/SPAWAR contract N660011824020. Grotheer was supported by the Goucher College Summer Research grant. Needell was supported by NSF CAREER DMS #1348721 and NSF BIGDATA DMS #1740325. Qin was supported by the NSF DMS #1941197. Publisher Copyright: © 2020 IEEE.

PY - 2020/2/2

Y1 - 2020/2/2

N2 - Low-rank tensor recovery problems have been widely studied in many signal processing and machine learning applications. Tensor rank is typically defined under certain tensor decomposition. In particular, Tucker decomposition is known as one of the most popular tensor decompositions. In recent years, researchers have developed many state-of-the-art algorithms to address the problem of low-Tucker-rank tensor recovery. Motivated by the favorable properties of the stochastic algorithms, such as stochastic gradient descent and stochastic iterative hard thresholding, we aim to extend the stochastic iterative hard thresholding algorithm from vectors to tensors in order to address the problem of recovering a low-Tucker-rank tensor from its linear measurements. We have also developed linear convergence analysis for the proposed method and conducted a series of experiments with both synthetic and real data to illustrate the performance of the proposed method.

AB - Low-rank tensor recovery problems have been widely studied in many signal processing and machine learning applications. Tensor rank is typically defined under certain tensor decomposition. In particular, Tucker decomposition is known as one of the most popular tensor decompositions. In recent years, researchers have developed many state-of-the-art algorithms to address the problem of low-Tucker-rank tensor recovery. Motivated by the favorable properties of the stochastic algorithms, such as stochastic gradient descent and stochastic iterative hard thresholding, we aim to extend the stochastic iterative hard thresholding algorithm from vectors to tensors in order to address the problem of recovering a low-Tucker-rank tensor from its linear measurements. We have also developed linear convergence analysis for the proposed method and conducted a series of experiments with both synthetic and real data to illustrate the performance of the proposed method.

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Stochastic Iterative Hard Thresholding for Low-Tucker-Rank Tensor Recovery

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