Study of Regression Model Optimization by Means of Regularization

The article addresses the problem of optimizing linear regression models under conditions of high dimensionality and multicollinearity, which are typical for modern machine learning applications. The relevance of the study is обусловлена the need to ensure a balance between model generalization ability and interpretability, especially when dealing with noisy and limited datasets. The aim of the study is to investigate and comparatively analyze the effectiveness of Ridge (L2) and Lasso (L1) regularization methods for regression model optimization through the selection of the optimal regularization hyperparameter. 

The k-fold cross-validation technique is employed to determine the optimal value of the regularization parameter, enabling an objective assessment of model generalization and prevention of overfitting. The open Wine Quality dataset, containing physicochemical characteristics of red wine samples, is used as an experimental benchmark due to its representative nature for problems with correlated features. Data preprocessing, feature scaling, model training, and evaluation were performed using standard machine learning procedures.

The models were assessed based on mean squared error (MSE), mean absolute error (MAE), and the coefficient of determination (R²). The results demonstrate that both approaches provide effective predictive performance but exhibit different properties. The Ridge model shows greater stability and better generalization ability, while the Lasso model enables automatic feature selection by inducing sparsity in the model structure.

The study identifies relationships between the regularization parameter, prediction accuracy, and structural characteristics of the models. The scientific novelty of the research lies in the improvement of the comparative analysis methodology for regularized regression models through a comprehensive evaluation of the regularization parameter using cross-validation and multiple performance criteria. The practical significance of the study consists in the applicability of the proposed approach for developing robust, interpretable, and efficient regression models across various application domains.