Stacking density estimation and its oversampling method for continuously imbalanced data in chemometrics

Continuously imbalanced data means that the target variable is continuous and its distribution is uneven. This kind of data is widespread in many practical application areas. However, methods to effectively handle continuously imbalanced data have been relatively scarce, and there is an urgent need to establish corresponding imbalance regression methods to enhance the capability of handling continuously imbalanced data. Firstly, we propose a Stacking-based density estimation (SDE) method to solve the density estimation problem of continuously imbalanced target variables. SDE links density estimation with the Ensemble learning algorithm called Stacking, and its core concept is the “fusion of multiple perspectives for accurate capture”. Performing SDE enhances the model’s understanding of complex data structures and makes it more sensitive and accurate in identifying rare values. Subsequently, we investigate an SDE-based oversampling technique (SDE-OS). SDE-OS uses SDE to synthesize new rare instances in the rare-value region, achieving fine-tuned customization of rare-value additions. In a series of numerical experiments, SDE has been estimated more accurately than the kernel density estimation method on ANLL. SDE-OS outperforms conventional sampling methods such as SMOGN and SMOTER in various metrics. Therefore, the proposed SDE and SDE-OS are highly competitive and effective tools for addressing the imbalanced regression problem.