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Exponential classification risk

For labels

Y \in {- 1, 1}

and a real-valued score

f

, the exponential loss is

ϕ (Y f (X)) = e^{- Y f (X)}

. Its population and empirical risks are

R_{ϕ} (f) = E [e^{- Y f (X)}], R_{ϕ} (f) = \frac{1}{n} \sum_{i = 1}^{n} e^{- Y_{i} f (X_{i})} .

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