Title: On the construction of adaptive predictive densities for sparse count data
Authors: Keisuke Yano - The Institute of Statistical Mathematics (Japan) [presenting]
Ryoya Kaneko - The University of Tokyo (Japan)
Fumiyasu Komaki - The University of Tokyo (Japan)
Abstract: Predictive densities under the Kullback-Leibler loss in high-dimensional sparse count data models are discussed. In particular, we consider Poisson sequence models under sparsity constraints. Sparsity in count data implies zero-inflation or quasi zero-inflation, that is, situations where there exists an excess of zeros or near-zero counts. We investigate the exact asymptotic minimax Kullback-Leibler risks in both sparse and quasi-sparse Poisson sequence models, providing a class of Bayes predictive densities that attain exact asymptotic minimaxity. We also discuss adaptation to an unknown sparsity. Our analysis also discuss the performance of the proposed Bayes predictive densities in settings where current observations are missing completely at random. We show the efficiency of the proposed Bayes predictive densities through both simulation studies and applications to real data.