Explainable global error weighted on feature importance: The xGEWFI metric to evaluate the error of data imputation and data augmentation

Evaluating data imputation and augmentation performance is a critical issue in science. In statistics, methods like Kolmogorov-Smirnov K-S test, Cramér-von Mises $$W^2$$ , Anderson-Darling $$A^2$$ Pearson’s $$\chi ^2$$ Watson’s $$U^2$$ exists for decades to compare the distribution of two datasets. context generation, typical evaluation metrics have same flaw: They calculate feature’s error global on generated without weighting with importance. most cases, importance features imbalanced, it can induce bias errors. This paper proposes novel metric named “Explainable Global Error Weighted Feature Importance” (xGEWFI). new tested whole preprocessing method that 1. Process outliers, 2. impute missing data, 3. augments data. At end process, xGEWFI calculated. The between original calculated using test (K-S test) each feature. Those results are multiplied by respective Random Forest (RF) algorithm. result expressed an explainable format, aiming ethical AI. provides more precise generation process than if only were used.