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In the documentation of the H2O software (http://docs.h2o.ai/h2o/latest-stable/h2o-docs/data-science/deep-learning.html) it says for the parameter “huber_alpha: Specify the desired quantile for Huber/M-regression (the threshold between quadratic and linear loss). This value must be between 0 and 1.”.

On Wikipedia (https://en.wikipedia.org/wiki/Huber_loss) the Huber loss function is defined as follows:

huber loss

Here y denotes the observed values and f(x) the reconstructed values. Obviously, huber_alpha from the H2O documentation is not equal delta from the Huber loss definition (delta is an absolute value and not a quantile). Now I’m wondering what the relation between the huber_alpha and the delta is. Especially to what “quantile” is the H2O documentation of the “huber_alpha” parameter referring to.

Looking forward to your answer and many thanks in advance.

user4556577
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  • Only just saw this - did my answer at https://stats.stackexchange.com/a/349888/5503 answer this one too? – Darren Cook Jun 05 '18 at 14:11
  • Not really. I already know from the documentation that the parameter is based on a quantile. The question is, to which set of values the quantile function is applied and is the resulting quantile threshold working as a local or a global parameter? – user4556577 Jun 06 '18 at 20:41

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