Fig. 2

Lasso regularization path and optimal lambda selection for regression coefficients. (A) Shows how the mean squared error (MSE) of the Lasso regression model changes with different values of the regularization parameter λ. The x-axis represents λ on a logarithmic scale, and the y-axis shows the MSE. The error bars indicate the MSE range from cross-validation. As λ increases, MSE decreases and stabilizes, but if λ becomes too large, the model underfits and MSE increases again. The dashed vertical line shows the optimal λ, selected through cross-validation. (B) Illustrates how the regression coefficients for various features change with increasing λ. The x-axis represents λ, and the y-axis represents the regression coefficients. Colored curves represent key features (e.g., age, BMI, HCO3-, Lac, MAP, Alb, PT, GCS, and SAPSII), while gray curves show other variables. As λ increases, the coefficients of less important variables shrink towards zero. The dashed vertical line indicates the optimal λ, selected by cross-validation.