Squared Log Error

Squared Log Error¶

The equation for Squared Log Error is:

$L_{SLE} = \frac{1}{2}(\log(\hat{y} + 1) - \log(y + 1))^{2}$

We calculate the Gradient:

$G_{SLE} = \frac{\log(\hat{y} + 1) - \log(y + 1)}{\hat{y} + 1}$

We also need to calculate the Hessian:

$H_{SLE} = \frac{- \log(\hat{y} + 1) + \log(y + 1) + 1}{(\hat{y} + 1)^{2}}$