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
Recommendation systems have been integrated into the majority of large online systems to filter and rank information according to user profiles. It thus influences the way users interact with the system and, as a consequence, bias the evaluation of the performance of a recommendation algorithm computed using historical data (via offline evaluation). This paper describes this bias and discuss the relevance of a weighted offline evaluation to reduce this bias for different classes of recommendation algorithms.
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