Sparse Logistic Regression utilizing Cardinality Constraints and Information Criteria

Gabriel Urrutia; Ramon Delgado; Rodrigo Carvajal; Dimitrios Katselis; Juan C. Agüero

doi:10.1109/CCA.2016.7587916

Sparse Logistic Regression utilizing Cardinality Constraints and Information Criteria

Gabriel Urrutia, Ramon Delgado, Rodrigo Carvajal, Dimitrios Katselis, Juan C. Agüero

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

1 Scopus citations

Abstract

In this paper we address the problem of estimating a sparse parameter vector that defines a logistic regression. The problem is then solved using two approaches: i) inequality constrained Maximum Likelihood estimation and ii) penalized Maximum Likelihood which is closely related to Information Criteria such as AIC. For the promotion of sparsity, we utilize a nonlinear constraint based on the ℓ₀ (pseudo) norm of the parameter vector. The corresponding optimization problem is solved using an equivalent representation of the problem that is simpler to solve. We illustrate the benefits of our proposal with an example that is inspired by a gene selection problem in DNA microarrays.

Original language	English
Title of host publication	2016 IEEE Conference on Control Applications, CCA 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	798-803
Number of pages	6
ISBN (Electronic)	9781509007554
DOIs	https://doi.org/10.1109/CCA.2016.7587916
State	Published - 10 Oct 2016
Externally published	Yes
Event	2016 IEEE Conference on Control Applications, CCA 2016 - Buenos Aires, Argentina Duration: 19 Sep 2016 → 22 Sep 2016

Publication series

Name	2016 IEEE Conference on Control Applications, CCA 2016

Conference

Conference	2016 IEEE Conference on Control Applications, CCA 2016
Country/Territory	Argentina
City	Buenos Aires
Period	19/09/16 → 22/09/16

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10.1109/CCA.2016.7587916

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Urrutia, G., Delgado, R., Carvajal, R., Katselis, D., & Agüero, J. C. (2016). Sparse Logistic Regression utilizing Cardinality Constraints and Information Criteria. In 2016 IEEE Conference on Control Applications, CCA 2016 (pp. 798-803). Article 7587916 (2016 IEEE Conference on Control Applications, CCA 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CCA.2016.7587916

@inproceedings{16f5c3d64db94e3786a389797067b7fc,

title = "Sparse Logistic Regression utilizing Cardinality Constraints and Information Criteria",

abstract = "In this paper we address the problem of estimating a sparse parameter vector that defines a logistic regression. The problem is then solved using two approaches: i) inequality constrained Maximum Likelihood estimation and ii) penalized Maximum Likelihood which is closely related to Information Criteria such as AIC. For the promotion of sparsity, we utilize a nonlinear constraint based on the ℓ0 (pseudo) norm of the parameter vector. The corresponding optimization problem is solved using an equivalent representation of the problem that is simpler to solve. We illustrate the benefits of our proposal with an example that is inspired by a gene selection problem in DNA microarrays.",

author = "Gabriel Urrutia and Ramon Delgado and Rodrigo Carvajal and Dimitrios Katselis and Ag{\"u}ero, {Juan C.}",

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year = "2016",

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day = "10",

doi = "10.1109/CCA.2016.7587916",

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Urrutia, G, Delgado, R, Carvajal, R, Katselis, D & Agüero, JC 2016, Sparse Logistic Regression utilizing Cardinality Constraints and Information Criteria. in 2016 IEEE Conference on Control Applications, CCA 2016., 7587916, 2016 IEEE Conference on Control Applications, CCA 2016, Institute of Electrical and Electronics Engineers Inc., pp. 798-803, 2016 IEEE Conference on Control Applications, CCA 2016, Buenos Aires, Argentina, 19/09/16. https://doi.org/10.1109/CCA.2016.7587916

Sparse Logistic Regression utilizing Cardinality Constraints and Information Criteria. / Urrutia, Gabriel; Delgado, Ramon; Carvajal, Rodrigo et al.
2016 IEEE Conference on Control Applications, CCA 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 798-803 7587916 (2016 IEEE Conference on Control Applications, CCA 2016).

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

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AU - Agüero, Juan C.

PY - 2016/10/10

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N2 - In this paper we address the problem of estimating a sparse parameter vector that defines a logistic regression. The problem is then solved using two approaches: i) inequality constrained Maximum Likelihood estimation and ii) penalized Maximum Likelihood which is closely related to Information Criteria such as AIC. For the promotion of sparsity, we utilize a nonlinear constraint based on the ℓ0 (pseudo) norm of the parameter vector. The corresponding optimization problem is solved using an equivalent representation of the problem that is simpler to solve. We illustrate the benefits of our proposal with an example that is inspired by a gene selection problem in DNA microarrays.

AB - In this paper we address the problem of estimating a sparse parameter vector that defines a logistic regression. The problem is then solved using two approaches: i) inequality constrained Maximum Likelihood estimation and ii) penalized Maximum Likelihood which is closely related to Information Criteria such as AIC. For the promotion of sparsity, we utilize a nonlinear constraint based on the ℓ0 (pseudo) norm of the parameter vector. The corresponding optimization problem is solved using an equivalent representation of the problem that is simpler to solve. We illustrate the benefits of our proposal with an example that is inspired by a gene selection problem in DNA microarrays.

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BT - 2016 IEEE Conference on Control Applications, CCA 2016

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ER -

Urrutia G, Delgado R, Carvajal R, Katselis D, Agüero JC. Sparse Logistic Regression utilizing Cardinality Constraints and Information Criteria. In 2016 IEEE Conference on Control Applications, CCA 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 798-803. 7587916. (2016 IEEE Conference on Control Applications, CCA 2016). doi: 10.1109/CCA.2016.7587916

Sparse Logistic Regression utilizing Cardinality Constraints and Information Criteria

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