Consistent algorithms for multi-label classification with macro-at-$k$ metrics
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910507190976512 |
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| author | Schultheis, Erik Kotłowski, Wojciech Wydmuch, Marek Babbar, Rohit Borman, Strom Dembczyński, Krzysztof |
| author_facet | Schultheis, Erik Kotłowski, Wojciech Wydmuch, Marek Babbar, Rohit Borman, Strom Dembczyński, Krzysztof |
| contents | We consider the optimization of complex performance metrics in multi-label classification under the population utility framework. We mainly focus on metrics linearly decomposable into a sum of binary classification utilities applied separately to each label with an additional requirement of exactly $k$ labels predicted for each instance. These "macro-at-$k$" metrics possess desired properties for extreme classification problems with long tail labels. Unfortunately, the at-$k$ constraint couples the otherwise independent binary classification tasks, leading to a much more challenging optimization problem than standard macro-averages. We provide a statistical framework to study this problem, prove the existence and the form of the optimal classifier, and propose a statistically consistent and practical learning algorithm based on the Frank-Wolfe method. Interestingly, our main results concern even more general metrics being non-linear functions of label-wise confusion matrices. Empirical results provide evidence for the competitive performance of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16594 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Consistent algorithms for multi-label classification with macro-at-$k$ metrics Schultheis, Erik Kotłowski, Wojciech Wydmuch, Marek Babbar, Rohit Borman, Strom Dembczyński, Krzysztof Machine Learning We consider the optimization of complex performance metrics in multi-label classification under the population utility framework. We mainly focus on metrics linearly decomposable into a sum of binary classification utilities applied separately to each label with an additional requirement of exactly $k$ labels predicted for each instance. These "macro-at-$k$" metrics possess desired properties for extreme classification problems with long tail labels. Unfortunately, the at-$k$ constraint couples the otherwise independent binary classification tasks, leading to a much more challenging optimization problem than standard macro-averages. We provide a statistical framework to study this problem, prove the existence and the form of the optimal classifier, and propose a statistically consistent and practical learning algorithm based on the Frank-Wolfe method. Interestingly, our main results concern even more general metrics being non-linear functions of label-wise confusion matrices. Empirical results provide evidence for the competitive performance of the proposed approach. |
| title | Consistent algorithms for multi-label classification with macro-at-$k$ metrics |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2401.16594 |