On the estimation of integral risk of predictor Lipschitz functions in machine learning models

Abstract

Class imbalance in available training samples for solving machine learning problems in most practical cases complicates the training of predictors that effectively generalize patterns from the training dataset to the general population. This paper investigates the theoretical foundations of the effectiveness of adding synthetic data to the training set. In the assessment of overall risk, two types of errors are highlighted: representation error and deviation error. Practical recommendations are formulated for creating synthetic samples that deviate in their distribution from the representative ones by the density distribution of the argument, with more frequent samples in those areas where the density distribution of the argument has relatively low values, leading to a reduction in the size of the corresponding Voronoi cells and a reduction in the contribution of deviation error to total risk.