does anyone know how exactly the Deviances (Poisson, Gamma, Tweedie) are computed in H2O? I cannot find the functions. For interpretation purposes I would like to know the calculations.
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Note for Tweedie there is an error in the docs, you can see the formula actually used in the h2o source, line 395 here: https://github.com/h2oai/h2o-3/blob/master/h2o-algos/src/main/java/hex/glm/GLMModel.java. The formula in this answer shows the correct formula rather than the formula in the docs.
The deviance equations in H2O should be following the general specifications used typically in actuarial sciences. See for instance Modern Actuarial Risk Theory by Kaas et al. page $308$ for the Tweedie Deviance and pages $246$ and $247$ for Poisson and Gamma Deviances. They correspond to the same equations in the accepted answer above, save the weights.