Klassifikation – Interaktive Lern-App

g(z) = 1 / (1 + e^−z), z⁽ⁱ⁾ = b₀ + b₁x₁⁽ⁱ⁾ + ... + b_mx_m⁽ⁱ⁾

Loss = −∑ [ y⁽ⁱ⁾·ln(g(z⁽ⁱ⁾)) + (1−y⁽ⁱ⁾)·ln(1−g(z⁽ⁱ⁾)) ]

∂Loss/∂b_m = ∑ (g(z⁽ⁱ⁾) − y⁽ⁱ⁾) · x_m⁽ⁱ⁾ ← Fehler × Merkmal

Genauigkeit = (TP+TN) / (TP+TN+FP+FN)

Precision = TP / (TP+FP), Recall = TP / (TP+FN)

F1 = 2·P·R / (P+R), Specificity = TN / (TN+FP)

TPR = Recall = TP/(TP+FN), FPR = 1−Specificity = FP/(FP+TN)

Optimum T: maximiere (TPR − FPR) [Youden's J]

softmax(z)_k = e^z_k / ∑_j e^z_j, ŷ = argmax_k softmax(z)_k

b₀ + b₁·x₁ + b₂·x₂ = 0