I want to compare different methods (like Poisson regression using Lasso, a convolutional NN, etc.) in terms of prediction error. As error measures I chose the MSE, the MdAPE (median absolute percentage error) and the relMAE (relative mean absolute error).
I wonder if it is senseful to calculate the MSE for the Poisson model w\ lasso regularization, because for the estimation of the regularization parameter $\lambda$ which is done by
cv.glmnet() the deviance is used per default for Poisson models. So I receive a $\lambda$ that has minimum deviance but actually I consider the MSE to compare the models... should I rather use the MSE in
cv.glmnet() to determine $\lambda$?
Or can somebody tell me what's the intuition behind using the deviance as an error measure for Poisson models?