Adversarial consistency and the uniqueness of the adversarial bayes classifier
Minimizing an adversarial surrogate risk is a common technique for learning robust classifiers. Prior work showed that convex surrogate losses are not statistically consistent in the adversarial context – or in other words, a minimizing sequence of the adversarial surrogate risk will not necessarily...
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| Language: | English |
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Cambridge University Press
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| Series: | European Journal of Applied Mathematics |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S0956792525000038/type/journal_article |
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| author | Natalie S. Frank |
| author_facet | Natalie S. Frank |
| author_sort | Natalie S. Frank |
| collection | DOAJ |
| description | Minimizing an adversarial surrogate risk is a common technique for learning robust classifiers. Prior work showed that convex surrogate losses are not statistically consistent in the adversarial context – or in other words, a minimizing sequence of the adversarial surrogate risk will not necessarily minimize the adversarial classification error. We connect the consistency of adversarial surrogate losses to properties of minimizers to the adversarial classification risk, known as adversarial Bayes classifiers. Specifically, under reasonable distributional assumptions, a convex surrogate loss is statistically consistent for adversarial learning iff the adversarial Bayes classifier satisfies a certain notion of uniqueness. |
| format | Article |
| id | doaj-art-1be9ea1a0a024a098d7594c110470c6f |
| institution | OA Journals |
| issn | 0956-7925 1469-4425 |
| language | English |
| publisher | Cambridge University Press |
| record_format | Article |
| series | European Journal of Applied Mathematics |
| spelling | doaj-art-1be9ea1a0a024a098d7594c110470c6f2025-08-20T01:51:53ZengCambridge University PressEuropean Journal of Applied Mathematics0956-79251469-442511910.1017/S0956792525000038Adversarial consistency and the uniqueness of the adversarial bayes classifierNatalie S. Frank0https://orcid.org/0009-0007-5582-4487Mathematics, Courant Institute, New York, NY, USAMinimizing an adversarial surrogate risk is a common technique for learning robust classifiers. Prior work showed that convex surrogate losses are not statistically consistent in the adversarial context – or in other words, a minimizing sequence of the adversarial surrogate risk will not necessarily minimize the adversarial classification error. We connect the consistency of adversarial surrogate losses to properties of minimizers to the adversarial classification risk, known as adversarial Bayes classifiers. Specifically, under reasonable distributional assumptions, a convex surrogate loss is statistically consistent for adversarial learning iff the adversarial Bayes classifier satisfies a certain notion of uniqueness.https://www.cambridge.org/core/product/identifier/S0956792525000038/type/journal_articleStatistics theoryoptimization62A9965K99 |
| spellingShingle | Natalie S. Frank Adversarial consistency and the uniqueness of the adversarial bayes classifier European Journal of Applied Mathematics Statistics theory optimization 62A99 65K99 |
| title | Adversarial consistency and the uniqueness of the adversarial bayes classifier |
| title_full | Adversarial consistency and the uniqueness of the adversarial bayes classifier |
| title_fullStr | Adversarial consistency and the uniqueness of the adversarial bayes classifier |
| title_full_unstemmed | Adversarial consistency and the uniqueness of the adversarial bayes classifier |
| title_short | Adversarial consistency and the uniqueness of the adversarial bayes classifier |
| title_sort | adversarial consistency and the uniqueness of the adversarial bayes classifier |
| topic | Statistics theory optimization 62A99 65K99 |
| url | https://www.cambridge.org/core/product/identifier/S0956792525000038/type/journal_article |
| work_keys_str_mv | AT nataliesfrank adversarialconsistencyandtheuniquenessoftheadversarialbayesclassifier |