Refined Statistical Bounds for Classification Error Mismatches with Constrained Bayes Error

作     者：Yang, Zijian Eminyan, Vahe Schlüter, Ralf Ney, Hermann 

作者机构：Machine Learning and Human Language Technology Group Lehrstuhl Informatik 6 Computer Science Department RWTH Aachen University Germany AppTek GmbH Germany 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Adversarial machine learning 

摘      要：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. Copyright © 2024, The Authors. All rights reserved.