Exact and empirical estimation of misclassification probability

TL;DR

This paper investigates risk estimation in classification, deriving analytic bounds for bias in empirical risk and exploring their use in empirical risk estimation, with a focus on confidence intervals.

Contribution

It introduces simple analytic approximations for the maximum bias of empirical risk in histogram classifiers and studies their application in risk estimation.

Findings

Derived analytic bounds for empirical risk bias

Analyzed the use of these bounds in risk estimation

Provided insights into confidence interval maximization

Abstract

We discuss the problem of risk estimation in the classification problem, with specific focus on finding distributions that maximize the confidence intervals of risk estimation. We derived simple analytic approximations for the maximum bias of empirical risk for histogram classifier. We carry out a detailed study on using these analytic estimates for empirical estimation of risk.