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Many real‐world data mining applications involve using imbalanced datasets to obtain predictive models. Imbalanced data can hinder the model performance of learning algorithms in rare cases. Although there are many well‐researched classification task solutions, most of them cannot be directly applied to regression task. One of the challenges in imbalanced regression is to find a suitable evaluation and optimization standard that can improve the predictive ability of the model without severe model bias. Based on the importance of rare cases, this study proposes a new evaluation metric called adapted squared error relevance (ASER) by defining new relevance function and weighting functions. This metric weights data points by defining the importance of rare cases and assigns different weights to losses of the same size at different rare cases, thus enabling the model selected by this evaluation metric to better predict rare cases. ASER is compared with SER on 32 real datasets and 9 simulated datasets to verify the predictive performance of the selected model at rare cases. The experimental results show that the new evaluation metric ASER can obtain a high prediction performance at rare cases, while also not losing too much prediction accuracy in common cases. In order to better evaluate the predictive ability of the model in rare cases, we propose a new evaluation metric for imbalanced regression called adapted squared error relevance (ASER). ASER weights data points by defining the importance of cases and assigns different weights to losses of the same size at different cases. ASER can obtain a high prediction performance at rare cases, while also not losing too much prediction accuracy in common cases. [ABSTRACT FROM AUTHOR]

Feature selection and rebalancing can be seen as two preprocessing ways in class‐imbalanced learning. Recently, there have been many research achievements and applications on LASSO‐type feature selection, whereas most of them are not directly designed for addressing class‐imbalanced data. In this study, we proposed a LASSO‐based stable feature selection algorithm for class‐imbalanced data analysis, and false‐positive selection (FPS) under balanced and imbalanced situations was calculated via selection frequency of each predictor in doing stable selection. The results on simulation studies and real data examples show that class imbalance contributes to avoid overselection caused by LASSO when the data are highly correlated and a lower FPS can be obtained with class‐imbalanced data than balanced one in most of cases in the same settings. A statistical explanation was given for this phenomenon. In addition, it does not need to rebalance the class‐imbalanced data for performing such LASSO‐based feature selection with a stable strategy, and to some degree, intentionally disequilibrating the balanced data could be an alternative strategy to weaken overselection and to perform biomarker identification for finding a few of most important biomarkers. A LASSO‐based stable feature selection algorithm was proposed for imbalanced data. It is not necessary to rebalance the imbalanced data with such stable feature selection strategy. Class imbalance even contributes to avoid overselection caused by LASSO when data are strongly correlated. [ABSTRACT FROM AUTHOR]

Imbalanced domain prediction analysis is currently one of the hot research topics. Many real‐world data mining analyses involve using imbalanced data to obtain predictive models. In the context of imbalance, research on classification problems has been extensive, but research on regression problems is negligible. Rare values rarely occur in imbalanced regression problems, but the focus is on accurately predicting the continuous target variables of rare instances. One of the challenges in imbalanced regression is finding a suitable strategy to rebalance the original dataset in order to improve the predictive performance of the model in rare instances. In this study, two algorithms are proposed: sigma nearest over‐sampling based on convex combination for regression (SNOCCR) and affine combination‐based over‐sampling (ACOS). ACOS rebalances the original dataset by generating new instances through the affine combinations of the original examples. The region where the new instances are generated can be adjusted based on the distribution of the data, ensuring that the generated cases better mimic the distribution of the original examples. The comparison among ACOS, SNOCCR, and other preprocessing methods was conducted on 15 datasets to validate the predictive performance of models trained on rebalanced datasets for rare instances. The experimental results indicate that ACOS outperforms other existing methods. In this study, two over‐sampling algorithms are proposed: sigma nearest over‐sampling based on convex combination for regression (SNOCCR) and affine combination‐based over‐sampling (ACOS) in order to improve the predictive performance of the model in imbalanced regression. The experimental results indicate that ACOS outperforms other existing methods. [ABSTRACT FROM AUTHOR]