Refined Statistical Bounds for Classification Error Mismatches with Constrained Bayes Error
<|reference_start|>Refined Statistical Bounds for Classification Error Mismatches with Constrained Bayes Error: 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.<|reference_end|>
@article{yang2024refined,
    title={Refined Statistical Bounds for Classification Error Mismatches with
  Constrained Bayes Error},
    author={Zijian Yang, Vahe Eminyan, Ralf Schl"uter, Hermann Ney},
    journal={arXiv preprint arXiv:2409.01309},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.01309},
    primaryClass={cs.IT math.IT}
}