The goal of dimension reduction in regression is to reduce the dimension of the predictor space without loss of information on the regression. In many fields, the predictors of a response are count-valued, including species abundance in ecological studies, phrase tokens in text mining, and panel data in econometrics. In this talk, we review the dimension-reduction methodology in regression with count-valued predictors. We follow an inverse regression approach by modeling the conditional distribution of the predictors given the response, using the Poisson independence model and its generalizations. A new proposal is then discussed.