Box-constrained optimization for minimax supervised learning***
In this paper, we present the optimization procedure for computing the discrete boxconstrained minimax classifier introduced in [1, 2]. Our approach processes discrete or beforehand discretized features. A box-constrained region defines some bounds for each class proportion independently. The box-co...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2021-08-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://www.esaim-proc.org/articles/proc/pdf/2021/02/proc2107109.pdf |
| _version_ | 1797965229500399616 |
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| author | Gilet Cyprien Barbosa Susana Fillatre Lionel |
| author_facet | Gilet Cyprien Barbosa Susana Fillatre Lionel |
| author_sort | Gilet Cyprien |
| collection | DOAJ |
| description | In this paper, we present the optimization procedure for computing the discrete boxconstrained minimax classifier introduced in [1, 2]. Our approach processes discrete or beforehand discretized features. A box-constrained region defines some bounds for each class proportion independently. The box-constrained minimax classifier is obtained from the computation of the least favorable prior which maximizes the minimum empirical risk of error over the box-constrained region. After studying the discrete empirical Bayes risk over the probabilistic simplex, we consider a projected subgradient algorithm which computes the prior maximizing this concave multivariate piecewise affine function over a polyhedral domain. The convergence of our algorithm is established. |
| first_indexed | 2024-04-11T01:56:43Z |
| format | Article |
| id | doaj.art-ce8d521cef4b4e75883d6c1fca3b5c8f |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T01:56:43Z |
| publishDate | 2021-08-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-ce8d521cef4b4e75883d6c1fca3b5c8f2023-01-03T05:12:21ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592021-08-017110111310.1051/proc/202171109proc2107109Box-constrained optimization for minimax supervised learning***Gilet Cyprien0Barbosa Susana1Fillatre Lionel2University of Côte d’Azur, CNRS, I3S laboratoryUniversity of Côte d’Azur, CNRS, laboratory IPMCUniversity of Côte d’Azur, CNRS, I3S laboratoryIn this paper, we present the optimization procedure for computing the discrete boxconstrained minimax classifier introduced in [1, 2]. Our approach processes discrete or beforehand discretized features. A box-constrained region defines some bounds for each class proportion independently. The box-constrained minimax classifier is obtained from the computation of the least favorable prior which maximizes the minimum empirical risk of error over the box-constrained region. After studying the discrete empirical Bayes risk over the probabilistic simplex, we consider a projected subgradient algorithm which computes the prior maximizing this concave multivariate piecewise affine function over a polyhedral domain. The convergence of our algorithm is established.https://www.esaim-proc.org/articles/proc/pdf/2021/02/proc2107109.pdf |
| spellingShingle | Gilet Cyprien Barbosa Susana Fillatre Lionel Box-constrained optimization for minimax supervised learning*** ESAIM: Proceedings and Surveys |
| title | Box-constrained optimization for minimax supervised learning*** |
| title_full | Box-constrained optimization for minimax supervised learning*** |
| title_fullStr | Box-constrained optimization for minimax supervised learning*** |
| title_full_unstemmed | Box-constrained optimization for minimax supervised learning*** |
| title_short | Box-constrained optimization for minimax supervised learning*** |
| title_sort | box constrained optimization for minimax supervised learning |
| url | https://www.esaim-proc.org/articles/proc/pdf/2021/02/proc2107109.pdf |
| work_keys_str_mv | AT giletcyprien boxconstrainedoptimizationforminimaxsupervisedlearning AT barbosasusana boxconstrainedoptimizationforminimaxsupervisedlearning AT fillatrelionel boxconstrainedoptimizationforminimaxsupervisedlearning |