Enhancing Predictive Accuracy in Pharmaceutical Sales Through An Ensemble Kernel Gaussian Process Regression Approach

This research employs Gaussian Process Regression (GPR) with an ensemble kernel, integrating Exponential Squared, Revised Mat\'ern, and Rational Quadratic kernels to analyze pharmaceutical sales data. Bayesian optimization was used to identify optimal kernel weights: 0.76 for Exponential Squared, 0.21 for Revised Mat\'ern, and 0.13 for Rational Quadratic. The ensemble kernel demonstrated superior performance in predictive accuracy, achieving an \( R^2 \) score near 1.0, and significantly lower values in Mean Squared Error (MSE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE). These findings highlight the efficacy of ensemble kernels in GPR for predictive analytics in complex pharmaceutical sales datasets.

Integrating Marketing Channels into Quantile Transformation and Bayesian Optimization of Ensemble Kernels for Sales Prediction with Gaussian Process Models

This study introduces an innovative Gaussian Process (GP) model utilizing an ensemble kernel that integrates Radial Basis Function (RBF), Rational Quadratic, and Mat\'ern kernels for product sales forecasting. By applying Bayesian optimization, we efficiently find the optimal weights for each kernel, enhancing the model's ability to handle complex sales data patterns. Our approach significantly outperforms traditional GP models, achieving a notable 98\% accuracy and superior performance across key metrics including Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Coefficient of Determination ($R^2$). This advancement underscores the effectiveness of ensemble kernels and Bayesian optimization in improving predictive accuracy, offering profound implications for machine learning applications in sales forecasting.