Explainable Global Error Weighted on Feature Importance: The xGEWFI metric to evaluate the error of data imputation and data augmentation

Evaluating the performance of an algorithm is crucial. Evaluating the performance of data imputation and data augmentation can be similar since both generated data can be compared with an original distribution. Although, the typical evaluation metrics have the same flaw: They calculate the feature's error and the global error on the generated data without weighting the error with the feature importance. The result can be good if all of the feature's importance is similar. However, in most cases, the importance of the features is imbalanced, and it can induce an important bias on the features and global errors. This paper proposes a novel metric named "Explainable Global Error Weighted on Feature Importance"(xGEWFI). This new metric is tested in a whole preprocessing method that 1. detects the outliers and replaces them with a null value. 2. imputes the data missing, and 3. augments the data. At the end of the process, the xGEWFI error is calculated. The distribution error between the original and generated data is calculated using a Kolmogorov-Smirnov test (KS test) for each feature. Those results are multiplied by the importance of the respective features, calculated using a Random Forest (RF) algorithm. The metric result is expressed in an explainable format, aiming for an ethical AI.