6.25 Resampling methods (3): Leave-one-out cross-validation (LOOCV)

• Q: James et al. (2013) use Figure 5.3 [p.179] to explain the Leave-One-Out Cross-Validation (LOOCV). Please inspect the figure and explain it in a few words.

• Data set split into two parts, whereby a single observation \((x_{1},y_{1})\) is used for validation set
  • Remaining observations \({(x_{2},y_{2}),...,(x_{n},y_{n})}\) make up the training set
  • Statistical learning method is fit on the \(n−1\) training observations and prediction is made for excluded observation
  • Repeated for all splits
• Advantages over validation set approach
  • Less bias because training data is bigger (Why?)
  • Performing LOOCV repeatedly will always produces the same results (Why? No randomness in training/validation set splits)
• Disadvantage: Can be computationally intensive (Why?)

References

James, Gareth, Daniela Witten, Trevor Hastie, and Robert Tibshirani. 2013. An Introduction to Statistical Learning: With Applications in R. Springer Texts in Statistics. Springer.