Log Cosh

• works like the MSE, but is smoothed towards large errors (presumably caused by outliers) so that the final error score isn’t impacted thoroughly.

We first define the Softplus function $\log \left(e^x+1\right)$

Then , $x=\hat{y}-y$

logcosh = $\mathrm{mean}\left(x+\mathrm{softplus}\left(-2\cdot x\right)-\log \left(2.0\right)\right)$

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