Noisy tensor completion for tensors with a sparse canonical polyadic factor

Swayambhoo Jain; Alexander Gutierrez; Jarvis Haupt

doi:10.1109/ISIT.2017.8006910

Noisy tensor completion for tensors with a sparse canonical polyadic factor

Swayambhoo Jain, Alexander Gutierrez, Jarvis Haupt

Electrical and Computer Engineering

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

3 Scopus citations

Abstract

'To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award.' In this paper we study the problem of noisy tensor completion for tensors that admit a canonical polyadic or CANDE-COMP/PARAFAC (CP) decomposition with one of the factors being sparse. We present general theoretical error bounds for an estimate obtained by using a complexity-regularized maximum likelihood principle and then instantiate these bounds for the case of additive white Gaussian noise. We also provide an ADMM-type algorithm for solving the complexity-regularized maximum likelihood problem and validate the theoretical finding via experiments on synthetic data set.

Original language	English (US)
Title of host publication	2017 IEEE International Symposium on Information Theory, ISIT 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2153-2157
Number of pages	5
ISBN (Electronic)	9781509040964
DOIs	https://doi.org/10.1109/ISIT.2017.8006910
State	Published - Aug 9 2017
Event	2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: Jun 25 2017 → Jun 30 2017

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8095

Other

Other	2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/Territory	Germany
City	Aachen
Period	6/25/17 → 6/30/17

Bibliographical note

Funding Information:
We thank Professor Nicholas Sidiropoulos for his insightful guidance and discussions on tensors which helped in completion of this work. Swayambhoo Jain and Jarvis Haupt were supported by the DARPA Young Faculty Award, Grant N66001-14-1-4047. Alexander Gutierrez was supported by the NSF Graduate Research Fellowship Program under Grant No. 00039202.

Publisher Copyright:
© 2017 IEEE.

Keywords

CANDECOMP/PARAFAC decomposition
Complexity-regularized maximum likelihood estimation
Noisy tensor completion
Sparse canonical polyadic decomposition
Sparse factor models
Tensor decomposition

Publisher link

10.1109/ISIT.2017.8006910

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Jain, S., Gutierrez, A., & Haupt, J. (2017). Noisy tensor completion for tensors with a sparse canonical polyadic factor. In 2017 IEEE International Symposium on Information Theory, ISIT 2017 (pp. 2153-2157). Article 8006910 (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8006910

Noisy tensor completion for tensors with a sparse canonical polyadic factor. / Jain, Swayambhoo; Gutierrez, Alexander; Haupt, Jarvis.
2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 2153-2157 8006910 (IEEE International Symposium on Information Theory - Proceedings).

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

Jain, S, Gutierrez, A & Haupt, J 2017, Noisy tensor completion for tensors with a sparse canonical polyadic factor. in 2017 IEEE International Symposium on Information Theory, ISIT 2017., 8006910, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 2153-2157, 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, 6/25/17. https://doi.org/10.1109/ISIT.2017.8006910

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abstract = "'To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award.' In this paper we study the problem of noisy tensor completion for tensors that admit a canonical polyadic or CANDE-COMP/PARAFAC (CP) decomposition with one of the factors being sparse. We present general theoretical error bounds for an estimate obtained by using a complexity-regularized maximum likelihood principle and then instantiate these bounds for the case of additive white Gaussian noise. We also provide an ADMM-type algorithm for solving the complexity-regularized maximum likelihood problem and validate the theoretical finding via experiments on synthetic data set.",

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note = "Funding Information: We thank Professor Nicholas Sidiropoulos for his insightful guidance and discussions on tensors which helped in completion of this work. Swayambhoo Jain and Jarvis Haupt were supported by the DARPA Young Faculty Award, Grant N66001-14-1-4047. Alexander Gutierrez was supported by the NSF Graduate Research Fellowship Program under Grant No. 00039202. Publisher Copyright: {\textcopyright} 2017 IEEE.; 2017 IEEE International Symposium on Information Theory, ISIT 2017 ; Conference date: 25-06-2017 Through 30-06-2017",

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AB - 'To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award.' In this paper we study the problem of noisy tensor completion for tensors that admit a canonical polyadic or CANDE-COMP/PARAFAC (CP) decomposition with one of the factors being sparse. We present general theoretical error bounds for an estimate obtained by using a complexity-regularized maximum likelihood principle and then instantiate these bounds for the case of additive white Gaussian noise. We also provide an ADMM-type algorithm for solving the complexity-regularized maximum likelihood problem and validate the theoretical finding via experiments on synthetic data set.

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Noisy tensor completion for tensors with a sparse canonical polyadic factor

Abstract

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