Does the test error typically decrease as model complexity increases?

The statement refers to the relationship between model complexity and test error in the context of machine learning. Generally, as model complexity increases, the model is able to fit more intricate patterns in the training data. However, this doesn’t always translate to a decrease in test error.

With increased complexity, a model is more prone to overfitting, where it learns the training data too well, including its noise and outliers, rather than generalizing to unseen data. As a result, the model may perform exceptionally well on the training data but may struggle to adapt to new, unseen examples, leading to an increase in test error. This phenomenon indicates that while a complex model might have a lower training error, the test error can actually increase.

In summary, model complexity does not guarantee a decrease in test error; instead, it can often lead to overfitting, thereby increasing the test error instead.