Sparse Estimation of Multivariate Poisson Log-Normal Models from Count Data

Modeling data with multivariate count responses is a challenging problem due to the discrete nature of the responses. Existing methods for univariate count response cannot be easily extended to the multivariate case since the dependency among multiple responses needs to be properly accommodated. In this paper, we propose a multivariate Poisson log-normal regression model for multivariate count responses by using the latent variables. By simultaneously estimating the regression coefficients and inverse covariance matrix over the latent variables with an efficient Monte Carlo EM algorithm, the proposed model takes advantages of association among multiple count responses to improve the model prediction accuracy. Simulation studies and applications to real world data are conducted to systematically evaluate the performance of the proposed method in comparison with conventional methods.