document: Regression error characteristic surfaces This paper presents a generalization of Regression Error Characteristic ( REC ) curves . REC curves describe the cumulative distribution function of the prediction error of models and can be seen as a generalization of ROC curves to regression problems . REC curves provide useful information for analyzing the performance of models , particularly when compared to error statistics like for instance the Mean Squared Error . In this paper we present Regression Error Characteristic ( REC ) surfaces that introduce a further degree of detail by plotting the cumulative distribution function of the errors across the distribution of the target variable , i.e. the joint cumulative distribution function of the errors and the target variable . This provides a more detailed analysis of the performance of models when compared to REC curves . This extra detail is particularly relevant in applications with non-uniform error costs , where it is important to study the performance of models for specific ranges of the target variable . In this paper we present the notion of REC surfaces , describe how to use them to compare the performance of models , and illustrate their use with an important practical class of applications : the prediction of rare extreme values .
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