The process of building a statistical learning model always involves a fundamental tradeoff: you want your model to fit the training data well, but you also need it to generalize to new, unseen data. This balance is at the heart of statistical learning theory and is closely connected to the concepts of risk and model capacity you have already studied. When a model is too simple, it cannot capture the underlying patterns in the data, resulting in high empirical risk and poor performance. On the other hand, a model with too much capacity can fit the training data almost perfectly, but this often leads to overfitting — where the model captures random noise instead of the true signal. Overfitting results in low empirical risk but high true risk when making predictions on new data.

To achieve good generalization, you must carefully manage the complexity of your hypothesis class. The goal is to find a model that is complex enough to capture the relevant structure in the data but not so complex that it memorizes the training examples. The theoretical framework you have learned, including generalization bounds and the VC dimension, provides guidance for navigating this tradeoff. These tools help you understand how the choice of hypothesis class affects the gap between empirical risk and true risk, and they highlight the importance of controlling model capacity to avoid overfitting.