Please select the incorrect statements about k-fold cross-validation and Leave-One-Out Cross-Validation (LOOCV):

Question

BlackTom AI · Accepted Answer

When considering statements about k-fold cross-validation and LOOCV, it helps to recall core properties of how these methods behave with respect to bias, variance, and computational cost.
Option 1: 'Increasing k (closer to the number of observations) typically reduces the variance of the estimate but increases the bias.' This is incorrect. In general, as you increase k, you reduce bias because the training sets become more similar to the full dataset, but the variance tends to increase because each test set is very small and the predictions can be highly variable across folds. The opposite trend is typically observed: higher k reduces bias and may increase variance, but LOOCV (k = n) is known for high variance and low bias; so the stated direction of variance and bias in this option is not accurate.
Option 2: 'LOOCV can be computationally expensive for large datasets since it requires fitting the model n times.' This is true. LOOCV trains the model once per observation, leading to n fits, which can be prohibitive for large n, even though it provides an almost unbiased estimate of generalization error.
Option 3: 'In k-fold cross-validation, using a smaller k generally leads to a lower computational cost.' This is true. Fewer folds mean fewer train-test splits to fit, so the total number of model trainings decreases, reducing computational burden, though it can come with higher bias and possibly different variance characteristics.
Option 4: 'LOOCV is a special case of k-fold cross-validation where k equals the number of observations.' This is true. LOOCV is precisely the situation where each fold contains all but one observation for training and a single observation for testing, i.e., k = n.

Please select the incorrect statements about k-fold cross-validation and Leave-One-Out Cross-Validation (LOOCV):单项选择题

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