Minimax Lower Bounds for Cost Sensitive Classification

TL;DR

This paper explores the fundamental limits of cost-sensitive classification by extending minimax lower bounds from binary classification, highlighting how misclassification costs influence problem hardness.

Contribution

It extends existing minimax lower bounds to cost-sensitive classification, revealing the impact of cost terms on the problem's difficulty.

Findings

Cost terms significantly affect the hardness of classification.

Extended minimax bounds provide fundamental limits for cost-sensitive problems.

Highlights the importance of considering costs in theoretical analysis.

Abstract

The cost-sensitive classification problem plays a crucial role in mission-critical machine learning applications, and differs with traditional classification by taking the misclassification costs into consideration. Although being studied extensively in the literature, the fundamental limits of this problem are still not well understood. We investigate the hardness of this problem by extending the standard minimax lower bound of balanced binary classification problem (due to \cite{massart2006risk}), and emphasize the impact of cost terms on the hardness.