Which of the following describes the behavior of the mean squared error (MSE) as model flexibility increases?

The behavior of the mean squared error (MSE) in relation to model flexibility is crucial in understanding model performance, particularly in the context of overfitting and underfitting. As model flexibility increases, meaning that a model can represent increasingly complex patterns in the training data, the MSE on the training set typically decreases. This is because the model can fit the training data very closely.

However, when interpreting the test mean squared error, which measures how well the model generalizes to unseen data, it’s important to note that while the training MSE decreases, the test MSE does not necessarily behave in the same fashion. Initially, with increasing flexibility, the test MSE may decrease, as the model begins to capture true patterns in the data. However, as flexibility continues to increase, the model can start to fit the noise within the training data, leading to overfitting.

In this scenario, the test MSE will generally decrease to a certain point before stabilizing and potentially beginning to increase due to overfitting. The notion that the test MSE "monotonically decreases" captures the initial trend where an increase in flexibility can lead to improved fit on the test data, only before eventually facing the pitfalls of overfitting