Little Bits of Artificial Intelligence

Let’s simulate this using a basic neural network and manual k-Fold CV.

import numpy as np

# --- Generate dummy dataset ---
np.random.seed(42)
X = np.random.rand(100, 1)  # 100 samples, 1 feature
y = 3 * X.squeeze() + np.random.randn(100) * 0.1  # y = 3x + noise

# --- Simple Neural Network Model ---
def train_and_evaluate(X_train, y_train, X_val, y_val, epochs=100, lr=0.01):
    w = np.random.randn()
    b = np.random.randn()
    for epoch in range(epochs):
        y_pred = X_train * w + b
        error = y_pred - y_train
        loss = (error ** 2).mean()

        # Gradient descent
        grad_w = 2 * (error * X_train).mean()
        grad_b = 2 * error.mean()

        w -= lr * grad_w
        b -= lr * grad_b

    # Final evaluation
    val_pred = X_val * w + b
    val_loss = ((val_pred - y_val) ** 2).mean()
    return val_loss

# --- K-Fold Cross Validation ---
def cross_validate(X, y, k=5):
    fold_size = len(X) // k
    losses = []

    for i in range(k):
        start, end = i * fold_size, (i + 1) * fold_size
        X_val, y_val = X[start:end], y[start:end]
        X_train = np.concatenate([X[:start], X[end:]])
        y_train = np.concatenate([y[:start], y[end:]])

        loss = train_and_evaluate(X_train, y_train, X_val, y_val)
        print(f"Fold {i+1} Validation Loss: {loss:.4f}")
        losses.append(loss)

    print(f"\nAverage Validation Loss: {np.mean(losses):.4f}")
    return losses

# --- Run Cross Validation ---
cross_validate(X, y)

How to Know Cross-Validation Is Needed?

Here are signals: