Explaining the Performance of Black Box Regression Models The widespread usage of Machine Learning and Data Mining models in several key areas of our societies has raised serious concerns in terms of accountability and ability to justify and interpret the decisions of these models. This is even more relevant when models are too complex and often regarded as black boxes. In this paper we present several tools designed to help in understanding and explaining the reasons for the observed predictive performance of black box regression models. We describe, evaluate and propose several variants of Error Dependence Plots. These plots provide a visual display of the expected relationship between the prediction error of any model and the values of a predictor variable. They allow the end user to understand what to expect from the models given some concrete values of the predictor variables. These tools allow more accurate explanations on the conditions that may lead to some failures of the models. Moreover, our proposed extensions also provide a multivariate perspective of this analysis, and the ability to compare the behaviour of multiple models under different conditions. This comparative analysis empowers the end user with the ability to have a casebased analysis of the risks associated with different models, and thus select the model with lower expected risk for each test case, or even decide not to use any model because the expected error is unacceptable.

A Study on the Impact of Data Characteristics in Imbalanced Regression Tasks The class imbalance problem has been thoroughly studied over the past two decades. More recently, the research community realized that the problem of imbalanced distributions also occurred in other tasks beyond classification. Regression problems are among these newly studied tasks where the problem of imbalanced domains also poses important challenges. Imbalanced regression problems occur in a diversity of real world domains such as meteorological (predicting weather extreme values), financial (extreme stock returns forecasting) or medical (anticipate rare values). In imbalanced regression the enduser preferences are biased towards values of the target variable that are underrepresented on the available data. Several preprocessing methods were proposed to address this problem. These methods change the training set to force the learner to focus on the rare cases. However, as far as we know, the relationship between the data intrinsic characteristics and the performance achieved by these methods has not yet been studied for imbalanced regression tasks. In this paper we describe a study of the impact certain data characteristics may have in the results of applying preprocessing methods to imbalanced regression problems. To achieve this goal, we define potentially interesting data characteristics of regression problems. We then conduct our study using a synthetic data repository build for this purpose. We show that all the different characteristics studied have a different behaviour that is related with the level at which the data characteristic is present and the learning algorithm used. The main contributions of our work are: i) to define interesting data characteristics for regression tasks; ii) to create the first repository of imbalanced regression tasks containing 6000 data sets with controlled data characteristics; and iii) to provide insights on the impact of intrinsic data characteristics in the results of preprocessing methods for handling imbalanced regression tasks.