Using Smoothing and Regression Models to Predict the Skin Permeability of Compounds

Introduction/Objective: Machine learning is widely used across several areas of research. The approach is also useful for predicting skin permeability. The objective of this research project was to use smoothing and regression models for skin permeability prediction. Methods: Performance was evaluated using a curated Sun et al. dataset to assess the performance of variational ridge regression, kernel smoothing, stepwise regression, Huber regression, and Bayesian ridge regression. Kernel smoothing is a nonparametric method used for the computation of underlying structures such as regression curves and density functions without rigid parametric assumptions. Essentially, kernel smoothing, such as the Nadaraya–Watson regression kernel density estimation, utilizes a bandwidth and a kernel function to attach weights to observations based on their proximity to a target point, producing a smooth estimate of the investigated function. Results: The Mean Square Error (MSE) and the coefficient of correlation (R²) were used as the evaluation metrics. The mean squared error and the coefficient of regression (R²) when variational ridge regression was applied to the curated Sun et al. dataset were 1.10 and 0.51, respectively. In contrast, the utilization of kernel smoothing on the same dataset resulted in a mean squared error of 1.03 and a coefficient of regression (R²) of 0.54. Interestingly, when the stepwise regression approach was used, the R-squared was 0.52, and the mean squared error was 1.09. When the Huber regression technique was applied to the dataset, the mean squared error was 1.22, and the R² was 0.46. We observed that the MSE and R² after using the Bayesian ridge regression method were 1.18 and 0.48, respectively. Discussion: Kernel regression surpassed ridge regression in terms of the two metrics of evaluation (R² and MSE). Its smoothness reflects continuous variation in molecular characteristics. Stepwise regression was similar to variational ridge regression, while Huber regression showed moderate predictive reliability. Bayesian ridge regression displayed reliable prediction intervals and a balanced bias-variance trade-off. Conclusion: Kernel smoothing was the most effective technique, while variational and Bayesian ridge methods were beneficial for regularization and interpretability.