Question: Discuss the trade-offs of using feature selection to reduce variance in a machine learning model. How do the scale of the feature reduction and the size of the training dataset influence the decision to apply this technique?

Sample answer: Feature selection reduces variance by limiting the number or type of input features, but it risks increasing bias by removing potentially useful information. A small reduction in features typically has a minimal effect on bias, whereas a large reduction (e.g., 10x) significantly increases the risk of higher bias. In modern deep learning with plentiful data, it is generally preferred to feed all features into the algorithm and let it learn which ones matter. However, when the training set is small, feature selection remains a highly useful technique to prevent overfitting and manage variance.

Key points:

• Feature selection reduces variance but might increase bias.
• Small feature reductions are unlikely to cause large bias increases, unlike significant reductions.
• With plentiful data in modern deep learning, practitioners generally provide all features to the algorithm.
• Feature selection is very useful when the training set is small.

Rubric: Award full credit if the answer identifies the core trade-off (variance reduction vs. bias increase), explains the impact of reduction scale (small vs. large reductions), and correctly applies the context of dataset size (plentiful data favors using all features; small datasets favor feature selection).