Empirical risk minimization is consistent with the mean absolute percentage error

TL;DR

This paper explores the use of MAPE as a regression quality measure, demonstrating its equivalence to weighted MAE and conditions for consistent empirical risk minimization.

Contribution

It establishes the theoretical connection between MAPE and weighted MAE and shows conditions for ERM consistency with MAPE.

Findings

MAPE minimization is equivalent to weighted MAE regression

ERM can be consistent with MAPE under certain assumptions

Provides theoretical foundation for using MAPE in regression models

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 show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error (MAE) regression. We also show that, under some asumptions, universal consistency of Empirical Risk Minimization remains possible using the MAPE.