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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.01309 |
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| _version_ | 1866909322786635776 |
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| author | Yang, Zijian Eminyan, Vahe Schlüter, Ralf Ney, Hermann |
| author_facet | Yang, Zijian Eminyan, Vahe Schlüter, Ralf Ney, Hermann |
| contents | In statistical classification/multiple hypothesis testing and machine learning, a model distribution estimated from the training data is usually applied to replace the unknown true distribution in the Bayes decision rule, which introduces a mismatch between the Bayes error and the model-based classification error. In this work, we derive the classification error bound to study the relationship between the Kullback-Leibler divergence and the classification error mismatch. We first reconsider the statistical bounds based on classification error mismatch derived in previous works, employing a different method of derivation. Then, motivated by the observation that the Bayes error is typically low in machine learning tasks like speech recognition and pattern recognition, we derive a refined Kullback-Leibler-divergence-based bound on the error mismatch with the constraint that the Bayes error is lower than a threshold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01309 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Refined Statistical Bounds for Classification Error Mismatches with Constrained Bayes Error Yang, Zijian Eminyan, Vahe Schlüter, Ralf Ney, Hermann Information Theory In statistical classification/multiple hypothesis testing and machine learning, a model distribution estimated from the training data is usually applied to replace the unknown true distribution in the Bayes decision rule, which introduces a mismatch between the Bayes error and the model-based classification error. In this work, we derive the classification error bound to study the relationship between the Kullback-Leibler divergence and the classification error mismatch. We first reconsider the statistical bounds based on classification error mismatch derived in previous works, employing a different method of derivation. Then, motivated by the observation that the Bayes error is typically low in machine learning tasks like speech recognition and pattern recognition, we derive a refined Kullback-Leibler-divergence-based bound on the error mismatch with the constraint that the Bayes error is lower than a threshold. |
| title | Refined Statistical Bounds for Classification Error Mismatches with Constrained Bayes Error |
| topic | Information Theory |
| url | https://arxiv.org/abs/2409.01309 |