Suggested Method for Prediction Using Gaussian Process Regression Kernel Regression

Abstract

Accurately predicting children's weight is challenging due to measurement inconsistencies. To address this, a hybrid kernel function, combining the squared exponential kernel and the Gaussian kernel with a mixture parameter, is proposed for developing a fuzzy Gaussian process regression model. The integration of fuzzy set theory and a triangular membership function helps handle weight measurement inaccuracies by determining the degrees of membership for each element in the weight vector.

The model is estimated using the spider monkey optimization (SMO) algorithm and implemented in MATLAB Ver. 2023a. The fminunc function is used for optimization, while the fitrgp function applies fuzzy set theory for regression. A dataset consisting of 191 observations from Al-Elwiya Maternity Teaching Hospital in Baghdad (collected between June 1, 2022, and December 31, 2022) is used for evaluation. The dataset is divided into 70% training data (n_train = 129) and 30% testing data (n_test = 55). The standard deviation of explanatory variables is f = 0.9234, and the smoothing parameter l = 0.8 is selected through optimization.

Model performance is assessed using root mean square error (RMSE), mean square error (MSE), and mean absolute percentage error (MAPE). Results indicate a significant difference between actual and predicted values for the squared exponential kernel function, whereas the Gaussian kernel function produces closer predictions. The hybrid kernel function achieves the most accurate predictions, aligning more closely with actual child weight values than the individual kernel functions.

The proposed fuzzy Gaussian process regression model with a hybrid kernel function outperforms both the squared exponential and Gaussian kernel functions in predictive accuracy. By effectively handling measurement uncertainties through fuzzy set theory, the model provides a more reliable approach for predicting children's weights.