Using financial risk measures for analyzing generalization performance of machine learning models

Abstract

We propose a unified machine learning model (UMLM) for two-class classification, regression and outlier (or novelty) detection via a robust optimization approach. The model embraces various machine learning models such as support vector machine-based and minimax probability machine-based classification and regression models. The unified framework makes it possible to compare and contrast existing learning models and to explain their differences and similarities. In this paper, after relating existing learning models to UMLM, we show some theoretical properties for UMLM. Concretely, we show an interpretation of UMLM as minimizing a well-known financial risk measure (worst-case value-at risk (VaR) or conditional VaR), derive generalization bounds for UMLM using such a risk measure, and prove that solving problems of UMLM leads to estimators with the minimized generalization bounds. Those theoretical properties are applicable to related existing learning models.

Keywords: Financial risk measure; Generalization performance; Minimax probability machine; Support vector machine.