Cross-Validation

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# Cross-Validation ## 3.1 K-Fold Cross-Validation Split data into $k$ folds. Train on $k-1$ folds, test on the remaining fold.

Cross-Validation

3.1 K-Fold Cross-Validation

Split data into

k

folds. Train on

k-1

folds, test on the remaining fold. Repeat

k

times.


python
from sklearn.model_selection import cross_val_score
from sklearn.linear_model import Ridge
import numpy as np
X = np.random.randn(100, 5)
y = X[:, 0] + 0.5 * X[:, 1] + np.random.randn(100) * 0.1
model = Ridge(alpha=1.0)
scores = cross_val_score(model, X, y, cv=5, scoring='r2')
print(f"R2 scores: {scores}, mean: {scores.mean():.3f}")

3.2 LOOCV (Leave-One-Out)

k = n

: train on

n-1

observations, test on the one left out. High variance, computationally expensive.

Bias-Variance Tradeoff

$k=2$ : low variance, high bias
$k=n$ (LOOCV): low bias, high variance
$k=5$ or $k=10$ : good compromise Join Discord PreviousBootstrapNextGradient Descent

What this note is really saying

Cross-Validation

3.1 K-Fold Cross-Validation

3.2 LOOCV (Leave-One-Out)

Bias-Variance Tradeoff

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