Refined Statistical Bounds for Classification Error Mismatches with Constrained Bayes Error

TL;DR

This paper derives refined bounds on classification error mismatches caused by model distribution errors, using Kullback-Leibler divergence, especially when the Bayes error is low, improving understanding of model accuracy in machine learning.

Contribution

It introduces a new derivation of statistical bounds on classification error mismatch, incorporating a constraint on the Bayes error to refine existing bounds.

Findings

Derived a new error bound based on KL divergence with Bayes error constraint

Reconsidered previous bounds with a different derivation approach

Provided insights into error mismatch when Bayes error is low

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.