Refined Statistical Bounds for Classification Error Mismatches with Constrained Bayes Error

arXiv (Cornell University)

Abstract

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.

Authors 4

1. Zijian Győző Yang Aachen Computer Science Department

   RWTH Aachen University

   Affiliation as printed

   Computer Science Department , RWTH Aachen University , Germany

   Machine Learning and Human Language Technology Group , Lehrstuhl Informatik 6 ,

2. Vahe Eminyan
   Affiliation as printed

   Machine Learning and Human Language Technology Group , Lehrstuhl Informatik 6 ,

3. Ralf Schlüter
4. Hermann Ney Aachen Computer Science Department

   RWTH Aachen University

   Affiliation as printed

   Computer Science Department , RWTH Aachen University , Germany

   Machine Learning and Human Language Technology Group , Lehrstuhl Informatik 6 ,