  This paper discusses predictive densities under the Kullback--Leibler loss
for high-dimensional Poisson sequence models under sparsity constraints.
Sparsity in count data implies zero-inflation. We present a class of Bayes
predictive densities that attain asymptotic minimaxity in sparse Poisson
sequence models. We also show that our class with an estimator of unknown
sparsity level plugged-in is adaptive in the asymptotically minimax sense. For
application, we extend our results to settings with quasi-sparsity and with
missing-completely-at-random observations. The simulation studies as well as
application to real data illustrate the efficiency of the proposed Bayes
predictive densities.
