A Model-Agnostic Algorithm for Bayes Error Determination in Binary Classification

TL;DR

This paper introduces the ILD Algorithm, a model-agnostic method to determine the theoretical performance limit (Bayes error) in binary classification datasets with categorical features, aiding understanding of prediction potential.

Contribution

The paper proposes a novel, model-independent algorithm to compute the Bayes error for binary classification datasets, providing intrinsic performance bounds.

Findings

The ILD Algorithm accurately estimates the Bayes error on real datasets.

It offers a model-agnostic way to understand dataset limitations.

The algorithm's pseudocode facilitates practical implementation.

Abstract

This paper presents the intrinsic limit determination algorithm (ILD Algorithm), a novel technique to determine the best possible performance, measured in terms of the AUC (area under the ROC curve) and accuracy, that can be obtained from a specific dataset in a binary classification problem with categorical features {\sl regardless} of the model used. This limit, namely the Bayes error, is completely independent of any model used and describes an intrinsic property of the dataset. The ILD algorithm thus provides important information regarding the prediction limits of any binary classification algorithm when applied to the considered dataset. In this paper the algorithm is described in detail, its entire mathematical framework is presented and the pseudocode is given to facilitate its implementation. Finally, an example with a real dataset is given.