# Deviances in H2O

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.

Thank you!

1. Linear: $$D=\sum^{N}_{i=1}{(y_{i}-\hat{y}_{i})^{2}}$$
2. Logistic: $$-D=\sum^{N}_{i=1}{\left(y_{i}\log{(\hat{y}_{i})}+(1-y_{i})\log{(1-\hat{y}_{i})}\right)}$$
3. Poisson: $$D=-2\sum^{N}_{i=1}{\left(y_{i}\log{\left(\frac{y_{i}}{\hat{y}_{i}}\right)}-\left(y_{i}-\hat{y}_{i}\right)\right)}$$
4. Gamma: $$D=2\sum^{N}_{i=1}{\left(-\log{\left(\frac{y_{i}}{\hat{y}_{i}}\right)}+\frac{\left(y_{i}-\hat{y}_{i}\right)}{\hat{y}_{i}}\right)}$$
5. Tweedie: where $$p\neq1$$ and $$p\neq2$$ $$D=-2\sum^{N}_{i=1}{\left(\frac{y_{i}\left(y_{i}^{1-p}-\hat{y}_{i}^{1-p}\right)}{1-p}-\frac{\left(y_{i}^{2-p}-\hat{y}_{i}^{2-p}\right)}{2-p}\right)}$$
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.