A New Variational Model for Binary Classification in the Supervised Learning Context

TL;DR

This paper introduces a new variational model for binary classification in supervised learning, providing a theoretical framework, numerical solutions, and comparative analysis with existing models using accuracy and AUC metrics.

Contribution

The paper develops a novel variational approach for binary classification, offering a theoretical optimality condition and numerical solutions, with comprehensive performance comparisons.

Findings

The new model achieves competitive accuracy and AUC scores.

Numerical solutions effectively solve the optimality condition.

Model comparisons show competitive performance with existing methods.

Abstract

We examine the supervised learning problem in its continuous setting and give a general optimality condition through techniques of functional analysis and the calculus of variations. This enables us to solve the optimality condition for the desired function u numerically and make several comparisons with other widely utilized supervised learning models. We employ the accuracy and area under the receiver operating characteristic curve as metrics of the performance. Finally, 3 analyses are conducted based on these two mentioned metrics where we compare the models and make conclusions to determine whether or not our method is competitive.