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

Shahin Mirshekari, Negin Hayeri Motedayen, Mohammad Ensaf

TL;DR

The study addresses forecasting product sales affected by diverse marketing channels, recognizing non-Gaussian data patterns. It combines data normalization via Yeo-Johnson and quantile transforms with Gaussian Process Regression (GPR) using an ensemble kernel composed of $k_{\text{RBF}}$, $k_{\text{RQ}}$, and $k_{\text{Matérn}}$, and tunes the ensemble weights $ (\alpha_{\text{RBF}}, \alpha_{\text{RQ}}, \alpha_{\text{Matérn}}) $ using Bayesian optimization. The optimized ensemble achieves high predictive accuracy, with $\text{accuracy}=98\%$, $\text{MSE}=0.025$, $\text{MAE}=0.048$, $\text{RMSE}=0.039$, and $R^2=0.974$, and assigns weights $(0.68, 0.21, 0.11)$ that reflect complementary kernel strengths. This work demonstrates that ensemble kernels and Bayesian optimization, coupled with robust data normalization, yield robust and accurate sales forecasts in data-rich marketing contexts, with broad implications for marketing analytics and probabilistic kernel learning.

Abstract

This study introduces an innovative Gaussian Process (GP) model utilizing an ensemble kernel that integrates Radial Basis Function (RBF), Rational Quadratic, and Matérn 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.

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

TL;DR

The study addresses forecasting product sales affected by diverse marketing channels, recognizing non-Gaussian data patterns. It combines data normalization via Yeo-Johnson and quantile transforms with Gaussian Process Regression (GPR) using an ensemble kernel composed of , , and , and tunes the ensemble weights using Bayesian optimization. The optimized ensemble achieves high predictive accuracy, with , , , , and , and assigns weights that reflect complementary kernel strengths. This work demonstrates that ensemble kernels and Bayesian optimization, coupled with robust data normalization, yield robust and accurate sales forecasts in data-rich marketing contexts, with broad implications for marketing analytics and probabilistic kernel learning.

Abstract

This study introduces an innovative Gaussian Process (GP) model utilizing an ensemble kernel that integrates Radial Basis Function (RBF), Rational Quadratic, and Matérn 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 (). 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.
Paper Structure (14 sections, 8 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 14 sections, 8 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Transforming Non-Gaussian Distributions to Gaussian Distribution
  4. Yeo-Johnson Transformation
  5. Quantile Transformation Method
  6. Gaussian Process Regression
  7. Gaussian Process
  8. Regression with Gaussian Processes
  9. Innovative Kernel Methods in Gaussian Process Regression
  10. Ensemble Kernel Method Combining ESS, RQ, and Matérn Kernels
  11. Optimization of Ensemble Kernel Weights alpha in GP
  12. Simulation & Results
  13. Performance Analysis of Gaussian Process Kernels
  14. conclusion

Figures (3)

  • Figure 1: Utilizing Yeo-Johnson and Quantile Transformations Across Various Marketing Channels
  • Figure 2: Heat Map Displaying Correlations Among Various Marketing Channels
  • Figure 3: Implementing RBF, Rational Quadratic, Matern, and Ensemble Kernel in Product Sales Analysis Using Gaussian Process Regression