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lines changed Original file line number Diff line number Diff line change @@ -113,14 +113,14 @@ The logistic loss is given as follows:
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$$loss = -Labels * \log(\sigma(X)) - (1 - Labels) * \log(1 - \sigma(X))$$
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- We know that $$\sigma(X) = (1 / ( 1 + \exp(-X))) $$. By substituting this we get:
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+ We know that $$\sigma(X) = \\frac{1}{ 1 + \exp(-X)} $$. By substituting this we get:
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$$loss = X - X * Labels + \log(1 + \exp(-X))$$
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For stability and to prevent overflow of $$\exp(-X)$$ when X < 0,
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we reformulate the loss as follows:
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- $$loss = \max(X, 0) - X * Labels + \log(1 + \exp(-|X |))$$
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+ $$loss = \max(X, 0) - X * Labels + \log(1 + \exp(-\|X\ |))$$
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Both the input `X` and `Labels` can carry the LoD (Level of Details) information.
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However the output only shares the LoD with input `X`.
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