Is there an R package which uses neural networks to explicitly model count data?
I skimmed over a paper recently that aims to use Neural Networks as Poisson regression. The method they propose is basically a standard Multi-Layer Perceptron where they use a different loss function, namely:

$$E = -\sum_{n=1}^N[-t_n + y_nlog(t_n)]$$

This is a version without regularization to prevent the overfitting, they use regular weight decay.

They mention that they wrote it in R and Matlab but I don't have a clue if it's available online somewhere, but any neural network package where you can pass your own loss function should suffice.

http://www.mathstat.dal.ca/~hgu/Neural%20Comput%20&amp;%20Applic.pdf