Society of Actuaries (SOA) PA Practice Exam

What does a high model complexity generally lead to in terms of variance?

1. Lower variance and better generalization

2. Higher variance and potential overfitting

3. No effect on variance

4. Increased model interpretability

The correct answer is: Higher variance and potential overfitting

A high model complexity typically leads to higher variance and potential overfitting due to the model's ability to closely fit the training data. When a model has high complexity, it includes more parameters and can capture intricate patterns in the dataset, which allows it to fit not only the underlying trend but also the noise present in the training data. This can result in a model that performs exceptionally well on the training set but struggles to generalize to new, unseen data, as it has effectively 'memorized' the training examples rather than learning the fundamental relationships. In contrast to lower variance models, which tend to generalize better but might overlook important nuances, high complexity models oscillate more dramatically in their predictive performance based on the slight variations in the training data. This phenomenon is why higher variance is associated with a risk of overfitting—where the model learns the data too well and fails to perform well on different datasets. The other possibilities, like lower variance and better generalization or no effect on variance, do not accurately reflect the behavior of high complexity models. Additionally, increased model interpretability is generally associated with simpler models; complex models often lose the clarity needed to understand the relationships they are portraying. Hence, the correct understanding is that complex models can lead