损失函数friedman_mse

Friedman's mean squared error (Friedman MSE) is a loss function used in gradient boosting regression algorithms. It is a modification of the regular mean squared error (MSE) that adds a penalty term to the residuals in order to reduce overfitting. The penalty term is proportional to the magnitude of the residual, but also takes into account the complexity of the model through a tuning parameter. By adding this penalty term, Friedman MSE encourages the model to select simpler trees with smaller residual errors.

The formula for Friedman MSE is:

MSE(y, f(x)) + α * T

where MSE is the regular mean squared error, y is the true target values, f(x) is the predicted target values, α is the tuning parameter that controls the strength of the penalty term, and T is the complexity of the model (measured as the number of terminal nodes in the decision tree).

Friedman MSE is commonly used in gradient boosting algorithms, such as XGBoost and LightGBM, as it helps to improve the model's generalization performance and prevent overfitting.