Risk-Averse Classification

TL;DR

This paper introduces a novel risk-averse classification framework based on coherent risk measures, allowing for class-specific risk assessments and demonstrating its effectiveness through binary classification experiments and risk-averse SVMs.

Contribution

It develops a new risk-averse classifier design method using coherent risk measures, linking it to existing risk-neutral problems and implementing it in SVMs.

Findings

Effective risk-averse classifiers outperform traditional methods in experiments.

The approach allows for class-specific risk measurement and sharing.

Risk-averse SVMs show promising results on multiple datasets.

Abstract

We develop a new approach to solving classification problems, which is bases on the theory of coherent measures of risk and risk sharing ideas. The proposed approach aims at designing a risk-averse classifier. The new approach allows for associating distinct risk functional to each classes. The risk may be measured by different (non-linear in probability) measures, We analyze the structure of the new classifier design problem and establish its theoretical relation to known risk-neutral design problems. In particular, we show that the risk-sharing classification problem is equivalent to an implicitly defined optimization problem with unequal, implicitly defined but unknown, weights for each data point. We implement our methodology in a binary classification scenario on several different data sets and carry out numerical comparison with classifiers which are obtained using the Huber loss function and other loss functions known in the literature. We formulate specific risk-averse support vector machines in order to demonstrate the viability of our method.