Leave-One-Out Cross-Validation (LOOCV) Explained with Example

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Cross-validation is a fundamental technique in machine learning to estimate model performance. One of the most extreme forms is Leave-One-Out Cross-Validation (LOOCV).

The Question

For a dataset with 1000 data points and 100 features, the following code will generate how many models during execution?

Code:

from sklearn.model_selection import cross_val_score, LeaveOneOut
from sklearn.linear_model import LinearRegression

lin_reg = LinearRegression()
loocv = LeaveOneOut()
score = cross_val_score(lin_reg, X, y, cv=loocv)

Understanding LOOCV

  • LeaveOneOut() creates as many folds as there are data points.

  • Each iteration:

    • 1 sample is used as the test set.

    • The remaining N-1 samples are used for training.

  • If there are N = 1000 data points, LOOCV runs the model 1000 times.

Calculation

Number of models trained=Number of samples=N\text{Number of models trained} = \text{Number of samples} = N N=1000N = 1000

✅ So, the code will train 1000 models.

Why not other answers?

  • ❌ 100 → Confusion with the number of features (not relevant to LOOCV).

  • ❌ 99 → Misinterpretation (we train with 999 samples each time, but total models = 1000).

  • ✅ 1000 → Correct, one model per data point.

Final Answer

👉 The code will generate 1000 models during execution.

✨ In summary: LOOCV is accurate but computationally expensive. For large datasets, other methods like k-fold cross-validation are preferred.

Would you like me to also compare LOOCV vs K-Fold (with diagrams) for better intuition in your blog?

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