Leave-one-out cross-validation
Definition taught in Estimating error rates, part of Statistical learning
Leave-one-out cross-validation
| Type | Definition |
| Taught in | Estimating error rates |
| Part | Statistical learning |
| Questions using it | 3 |
\widehat{\mathrm{Err}}_{\mathrm{LOOCV}} =\frac1n\sum_{i=1}^n Q\bigl(y_i,\eta_{(X_{-i},y_{-i})}(x_i)\bigr),
where -i means that observation i is left out of the fit that is then scored on x_i. The class-specific estimator restricts the average to class g,
\widehat{\mathrm{Err}}_{\mathrm{LOOCV},g} =\frac{\sum_{i=1}^n Q\bigl(y_i,\eta_{(X_{-i},y_{-i})}(x_i)\bigr)\,I(y_i,g)} {\sum_{l=1}^n I(y_l,g)}.
Used in
- Taught in Estimating error rates, where the derivation and examples are.
- Also used in Nearest neighbours
- Questions that use it (3) — A tempting wrong turn (answer) · Costs of cross-validation · A tempting wrong turn (answer)
- All 7 questions on Estimating error rates
See also
Cross-validation · -fold cross-validation · Nested cross-validation · Cross-validation of the likelihood · Estimator · Fixed-rule error · Confusion matrix · Apparent error