Title: Asymptotically minimax predictive density for sparse Poisson sequence model with different sample sizes
Authors: Ryoya Kaneko - The University of Tokyo (Japan) [presenting]
Keisuke Yano - The University of Tokyo (Japan)
Fumiyasu Komaki - The University of Tokyo (Japan)
Abstract: There is growing demand for high-dimensional sparse count data. Sparsity in count data implies zero-inflation, that is, the situations where there exists an excess of zeros. In handling high-dimensional sparse count data, there often appears inhomogeneity in sample sizes of coordinates. To manage such sparse count data with different sample sizes, we introduce Poisson sequence models with different sample sizes under sparsity constraints on the parameter space, and consider predictive density estimation under Kullback-Leibler loss from a decision-theoretical point of view. We propose a Bayes predictive density that attains exact asymptotic minimax risk over sparse parameter space in Poisson sequence models with different sample sizes. The proposed predictive density has the merit of being adaptive to an unknown sparsity. We also apply the proposed method to real-world datasets and discuss its practical effectiveness.