Empirical Bayes Estimation for L1 Regularization: A Detailed Analysis in the One-Parameter Lasso Model
Summary :
Lasso regression based on the L1 regularization is one of the most popular sparse estimation methods. It is often required to set appropriately in advance the regularization parameter that determines the degree of regularization. Although the empirical Bayes approach provides an effective method to estimate the regularization parameter, its solution has yet to be fully investigated in the lasso regression model. In this study, we analyze the empirical Bayes estimator of the one-parameter model of lasso regression and show its uniqueness and its properties. Furthermore, we compare this estimator with that of the variational approximation, and its accuracy is evaluated.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.12 pp.2184-2191
- Publication Date
- 2018/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E101.A.2184
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Machine learning
Authors
Tsukasa YOSHIDA
Toyohashi University of Technology
Kazuho WATANABE
Toyohashi University of Technology
Keyword
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Tsukasa YOSHIDA, Kazuho WATANABE, "Empirical Bayes Estimation for L1 Regularization: A Detailed Analysis in the One-Parameter Lasso Model" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 12, pp. 2184-2191, December 2018, doi: 10.1587/transfun.E101.A.2184.
Abstract: Lasso regression based on the L1 regularization is one of the most popular sparse estimation methods. It is often required to set appropriately in advance the regularization parameter that determines the degree of regularization. Although the empirical Bayes approach provides an effective method to estimate the regularization parameter, its solution has yet to be fully investigated in the lasso regression model. In this study, we analyze the empirical Bayes estimator of the one-parameter model of lasso regression and show its uniqueness and its properties. Furthermore, we compare this estimator with that of the variational approximation, and its accuracy is evaluated.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.2184/_p
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@ARTICLE{e101-a_12_2184,
author={Tsukasa YOSHIDA, Kazuho WATANABE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Empirical Bayes Estimation for L1 Regularization: A Detailed Analysis in the One-Parameter Lasso Model},
year={2018},
volume={E101-A},
number={12},
pages={2184-2191},
abstract={Lasso regression based on the L1 regularization is one of the most popular sparse estimation methods. It is often required to set appropriately in advance the regularization parameter that determines the degree of regularization. Although the empirical Bayes approach provides an effective method to estimate the regularization parameter, its solution has yet to be fully investigated in the lasso regression model. In this study, we analyze the empirical Bayes estimator of the one-parameter model of lasso regression and show its uniqueness and its properties. Furthermore, we compare this estimator with that of the variational approximation, and its accuracy is evaluated.},
keywords={},
doi={10.1587/transfun.E101.A.2184},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Empirical Bayes Estimation for L1 Regularization: A Detailed Analysis in the One-Parameter Lasso Model
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2184
EP - 2191
AU - Tsukasa YOSHIDA
AU - Kazuho WATANABE
PY - 2018
DO - 10.1587/transfun.E101.A.2184
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2018
AB - Lasso regression based on the L1 regularization is one of the most popular sparse estimation methods. It is often required to set appropriately in advance the regularization parameter that determines the degree of regularization. Although the empirical Bayes approach provides an effective method to estimate the regularization parameter, its solution has yet to be fully investigated in the lasso regression model. In this study, we analyze the empirical Bayes estimator of the one-parameter model of lasso regression and show its uniqueness and its properties. Furthermore, we compare this estimator with that of the variational approximation, and its accuracy is evaluated.
ER -
English
