Question: Explain the rationale behind using nonlinearly spaced training set sizes when constructing a learning curve. Discuss the underlying reason for the computational savings and state the condition under which this technique should be applied.

Sample answer: The rationale for using nonlinearly spaced training set sizes is to reduce overall computational expense. Training models on large datasets takes significantly more time than training on small ones. If sizes are spaced linearly (e.g., every 1,000 examples up to 10,000), you are forced to train many large, slow models. By using nonlinear spacing (like 1k, 2k, 4k, 6k, 10k), you still obtain a clear sense of the learning curve's trends but can skip several intermediate large dataset sizes, saving significant time. This technique should only be applied if the computational cost of training all the additional models is significant; if training is very fast, linear spacing is fine.

Key points:

• Reduces computational cost
• Training small datasets is much faster than large datasets
• Still provides a clear sense of learning curve trends
• Relevant only if computational cost is significant

Rubric: The essay should correctly identify reducing computational cost as the primary goal. It must explain that smaller datasets train much faster, and that skipping some evenly spaced larger sizes saves time while preserving the curve's trend. It must explicitly state that the technique is only relevant when training costs are significant.