Semi-parametric regression models combine elements of parametric and non-parametric regression approaches. Lasso regression, a penalized parametric regression technique, introduces a penalty term to the regression equation to enhance model performance. Regression tree models, a non-parametric approach, partition the data into subsets and build separate models for each subset. By combining these techniques, semi-parametric regression models can capture both linear and non-linear relationships in the data, providing a powerful tool for addressing complex regression problems.