Deriving Log-Loss
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Why we use logarithms for classification error
True Outcome (y)
y = 1 (Passed)
y = 0 (Failed)
Predicted Prob (ŷ)
0.80
The Combined Log-Loss Formula
$$ \text{Loss} = -[ y \cdot \log(\hat{y}) + (1-y) \cdot \log(1-\hat{y}) ] $$