Improved reduced set density estimator by introducing weighted l1 penalty on the weight coefficients

Gang Yang; Yan Wang

doi:10.1109/WCICA.2014.7052796

Improved reduced set density estimator by introducing weighted l₁ penalty on the weight coefficients

Gang Yang
, Yan Wang

School of Automation Science and Electrical Engineering

Beihang University

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

Abstract

Reduced set density estimator (RSDE), employing a small percentage of available data samples, is an efficient and important nonparametric technique for probability density function estimation. But it still faces the critical challenge in practical applications when training the estimator on large data sets. Dealing with its high complexity both in time and space, an improved reduced set density estimator with weighted l₁ penalty term (WL1-RSDE) is proposed in this paper. To further reduce the complexity, we introduce the weighted l₁ norm as the additional penalty term on the plug-in estimation of weight coefficients, in which small weight coefficients are more likely to be driven to zero. Then, an iterative algorithm is proposed to solve the corresponding minimization problem efficiently. Several examples are employed to demonstrate that the proposed WL1-RSDE is superior to the related methods including the RSDE in sparsity and complexity.

Original language	English
Title of host publication	Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	679-683
Number of pages	5
Edition	March
ISBN (Electronic)	9781479958252
DOIs	https://doi.org/10.1109/WCICA.2014.7052796
State	Published - 2 Mar 2015
Event	2014 11th World Congress on Intelligent Control and Automation, WCICA 2014 - Shenyang, China Duration: 29 Jun 2014 → 4 Jul 2014

Publication series

Name	Proceedings of the World Congress on Intelligent Control and Automation (WCICA)
Number	March
Volume	2015-March

Conference

Conference	2014 11th World Congress on Intelligent Control and Automation, WCICA 2014
Country/Territory	China
City	Shenyang
Period	29/06/14 → 4/07/14

Keywords

Reduced set density estimator
Sequential minimal optimization
Sparsity
Weighted l penalty term

Access to Document

10.1109/WCICA.2014.7052796

Cite this

Yang, G., & Wang, Y. (2015). Improved reduced set density estimator by introducing weighted l₁ penalty on the weight coefficients. In Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014 (March ed., pp. 679-683). Article 7052796 (Proceedings of the World Congress on Intelligent Control and Automation (WCICA); Vol. 2015-March, No. March). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/WCICA.2014.7052796

Yang, Gang ; Wang, Yan. / Improved reduced set density estimator by introducing weighted l₁ penalty on the weight coefficients. Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014. March. ed. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 679-683 (Proceedings of the World Congress on Intelligent Control and Automation (WCICA); March).

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abstract = "Reduced set density estimator (RSDE), employing a small percentage of available data samples, is an efficient and important nonparametric technique for probability density function estimation. But it still faces the critical challenge in practical applications when training the estimator on large data sets. Dealing with its high complexity both in time and space, an improved reduced set density estimator with weighted l1 penalty term (WL1-RSDE) is proposed in this paper. To further reduce the complexity, we introduce the weighted l1 norm as the additional penalty term on the plug-in estimation of weight coefficients, in which small weight coefficients are more likely to be driven to zero. Then, an iterative algorithm is proposed to solve the corresponding minimization problem efficiently. Several examples are employed to demonstrate that the proposed WL1-RSDE is superior to the related methods including the RSDE in sparsity and complexity.",

keywords = "Reduced set density estimator, Sequential minimal optimization, Sparsity, Weighted l penalty term",

author = "Gang Yang and Yan Wang",

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Yang, G & Wang, Y 2015, Improved reduced set density estimator by introducing weighted l₁ penalty on the weight coefficients. in Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014. March edn, 7052796, Proceedings of the World Congress on Intelligent Control and Automation (WCICA), no. March, vol. 2015-March, Institute of Electrical and Electronics Engineers Inc., pp. 679-683, 2014 11th World Congress on Intelligent Control and Automation, WCICA 2014, Shenyang, China, 29/06/14. https://doi.org/10.1109/WCICA.2014.7052796

Improved reduced set density estimator by introducing weighted l₁ penalty on the weight coefficients. / Yang, Gang; Wang, Yan.
Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014. March. ed. Institute of Electrical and Electronics Engineers Inc., 2015. p. 679-683 7052796 (Proceedings of the World Congress on Intelligent Control and Automation (WCICA); Vol. 2015-March, No. March).

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

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AB - Reduced set density estimator (RSDE), employing a small percentage of available data samples, is an efficient and important nonparametric technique for probability density function estimation. But it still faces the critical challenge in practical applications when training the estimator on large data sets. Dealing with its high complexity both in time and space, an improved reduced set density estimator with weighted l1 penalty term (WL1-RSDE) is proposed in this paper. To further reduce the complexity, we introduce the weighted l1 norm as the additional penalty term on the plug-in estimation of weight coefficients, in which small weight coefficients are more likely to be driven to zero. Then, an iterative algorithm is proposed to solve the corresponding minimization problem efficiently. Several examples are employed to demonstrate that the proposed WL1-RSDE is superior to the related methods including the RSDE in sparsity and complexity.

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Yang G, Wang Y. Improved reduced set density estimator by introducing weighted l₁ penalty on the weight coefficients. In Proceeding of the 11th World Congress on Intelligent Control and Automation, WCICA 2014. March ed. Institute of Electrical and Electronics Engineers Inc. 2015. p. 679-683. 7052796. (Proceedings of the World Congress on Intelligent Control and Automation (WCICA); March). doi: 10.1109/WCICA.2014.7052796