Mean Absolute Percentage Error for regression models

TL;DR

This paper investigates the properties of MAPE as a regression quality measure, proving the existence of optimal models, their consistency, and linking MAPE minimization to weighted MAE regression, with practical kernel regression applications.

Contribution

It establishes the theoretical foundations of MAPE in regression, including optimality, consistency, and its equivalence to weighted MAE regression, with empirical illustration.

Findings

Existence of an optimal MAPE-based model

Universal consistency of MAPE-based empirical risk minimization

Weighted MAE regression is equivalent to MAPE minimization

Abstract

We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We prove the existence of an optimal MAPE model and we show the universal consistency of Empirical Risk Minimization based on the MAPE. We also show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error (MAE) regression, and we apply this weighting strategy to kernel regression. The behavior of the MAPE kernel regression is illustrated on simulated data.