Refined Statistical Bounds for Classification Error Mismatches with Constrained Bayes Error

IEEE Information Theory Workshop (ITW), pp. 283–288

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 Machine Learning and Human Language Technology Group Lehrstuhl Informatik 6 Computer Science Department

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Machine Learning and Human Language Technology Group, Lehrstuhl Informatik 6,Computer Science Department,Germany

2. Vahe Eminyan Aachen Machine Learning and Human Language Technology Group Lehrstuhl Informatik 6 Computer Science Department

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Machine Learning and Human Language Technology Group, Lehrstuhl Informatik 6,Computer Science Department,Germany

3. Ralf Schlüter Aachen Machine Learning and Human Language Technology Group Lehrstuhl Informatik 6 Computer Science Department

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Machine Learning and Human Language Technology Group, Lehrstuhl Informatik 6,Computer Science Department,Germany

4. Hermann Ney Aachen Machine Learning and Human Language Technology Group Lehrstuhl Informatik 6 Computer Science Department

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Machine Learning and Human Language Technology Group, Lehrstuhl Informatik 6,Computer Science Department,Germany