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

Abstract-We coalgebraically define a unified semantics for systems with an emphasis on the notion of time. Such a semantics intends to formalize system that underly system engineering (i.e. the discipline focusing on the integration mastery of large industrial systems). Moreover, we give a formal meaning to another important aspect of systems engineering : system requirements, constraining the expected properties of a system. To express such requirements, we define a logic that extends µ-calculus to our coalgebraic definition of systems. We establish an important property of this logic: adequacy.

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L’aventure de Pealk, qui a développé une application web à succès et s’est fait racheter par Viadeo, montre que la frontière entre succès et échec reste souvent ambiguë et incertaine. Ce qui ne signifie pas qu’il soit impossible d’en tirer des leçons.

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.