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[Description] This worksheet demonstrates binary classification using logistic regression with sigmoid activation.
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Logistic Regression Binary Classification Practice Worksheet
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[Learning Objectives]
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1. Understand binary classification problem using Logistic Regression
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2. Role and calculation of Sigmoid activation function
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3. Understand Binary Cross-Entropy (BCE) loss function
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4. Derive simplified gradient of BCE + Sigmoid
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5. Update weights through backpropagation
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[Network Structure]
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• Input matrix X: 10 samples × 8 features (10×8 matrix)
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• Weight matrix W: 8 features × 1 output (8×1 vector)
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• Bias b: Scalar
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• Linear combination Z: Z = X · W + b
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• Activation function: Sigmoid → Y_pred = σ(Z) = 1/(1+e^(-Z))
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• Output Y_pred: 10 × 1 (probability values between 0~1)
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• Ground truth Y_true: 10 × 1 (0 or 1 - binary label)
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• Loss function: Binary Cross-Entropy (BCE)
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[Mathematical Expression]
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Forward:
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 Z = X · W + b (Linear combination)
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 Y_pred = σ(Z) = 1 / (1 + e^(-Z)) (Sigmoid activation)
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Loss (BCE):
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 L = -(1/n) × Σ[y_true × log(y_pred) + (1-y_true) × log(1-y_pred)]
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Gradient (BCE + Sigmoid simplified):
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 ∂L/∂Z = (1/n) × (Y_pred - Y_true) ★ Key formula!
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 ∂L/∂W = X^T · ∂L/∂Z
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 ∂L/∂b = Σ(∂L/∂Z)
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Update:
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 W_new = W - lr × ∂L/∂W
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 b_new = b - lr × ∂L/∂b
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[Sigmoid Function]
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• Output range: 0 < σ(z) < 1 (interpretable as probability)
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• When z = 0: σ(0) = 0.5
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• When z > 0: σ(z) > 0.5 (classified as positive class)
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• When z < 0: σ(z) < 0.5 (classified as negative class)
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• Derivative: σ'(z) = σ(z) × (1 - σ(z))
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[Color Legend]
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 ■ Input matrix (X)
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 ■ Weight (W)
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 ■ Linear combination (Z)
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 ■ Sigmoid output (Y_pred)
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 ■ Output/Result
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 ■ Gradient
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 ■ Student input cell
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 ■ Answer
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 ■ Wrong
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[How to Use]
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1. Enter calculation results in yellow cells in Forward_Propagation sheet
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2. Check ✓(correct) or ✗(wrong) in verification cells
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3. Tolerance: 0.0001 (up to 4 decimal places)
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4. Hint: When calculating Sigmoid, first compute e^(-z), then 1/(1+e^(-z))
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