Data Augmentation for Machine Learning on Missing Data

The impact of missing data augmentation and class balancing methods on the prediction accuracy is studied. Results for missing and complete datasets are compared. A new algorithm called “drop-and-replace” for missing data imputation, augmentation, and class balancing is proposed. The quality of the drop-and-replace algorithm is compared to the quality of efficient and widely studied augmentation methods, such as SMOTE and mixup. For comparison, 7 datasets with sizes from 38 up to 70 000 are used. The target metric is balanced accuracy, and the nested cross-validation algorithm is used for validation. For the imputation of small datasets, the mean imputation method is used. The imputation of average or large datasets are performed using the MICE method of multivariate imputation by chained equations. The problem of training machine learning algorithms on missing data is studied in the probably approximately correct learning setting, or PAC learning. The increase of Vapnik–Chervonenkis dimension, or VC dimension, of the function set due to data imputation with one value from a finite set is evaluated. It is shown that the needed dataset size for PAC learning with sufficient accuracy, grows logarithmically slow with an increase in the filling set size. It is proved that drop-and-replace augmentation allows one to maximize balanced accuracy when learning on small linearly separable datasets containing missing values. For larger datasets, SMOTE and mixup augmentation methods are most efficient. For 8 datasets out of 11, data augmentation, which increments data size, increases classification accuracy; in 2 of 3 other cases, dataset balancing alone can improve classification accuracy; in the final case, the initial dataset is balanced and augmentation cannot increase classification accuracy. When learning on average and large datasets, in all 3 cases, augmentation more significantly improves accuracy for incomplete datasets than for complete ones. Thus, augmentation is more efficient when learning on missing data.