As the model flexibility increases in statistical learning methods, what happens to Variance?

As model flexibility increases in statistical learning methods, variance tends to increase. This relationship arises from the trade-off between bias and variance in modeling.

When a model is highly flexible, it has the capacity to fit the training data very closely, capturing even the noise present in the dataset. As a result, such flexible models may perform exceptionally well on training data, demonstrating low bias because they can appropriately accommodate the complexities of the underlying data patterns. However, this increased flexibility comes with a cost: as the model adjusts to these intricacies, it becomes more sensitive to fluctuations and variances in the training data.

Consequently, while a flexible model can result in greater accuracy on the training dataset, its performance on new, unseen data may suffer since it has overfitted to the idiosyncrasies of the training set. This phenomenon is characterized by high variance, where the model's predictions can vary significantly with different samples of data, reflecting its susceptibility to the randomness and noise that doesn't represent the true underlying trend.

It is important to balance model complexity with performance to manage variance effectively while avoiding overfitting when applying statistical learning methods.