Sparse Estimation of Multivariate Poisson Log-Normal Model and Inverse Covariance for Count Data

Modeling data with multivariate count responses is a challenge problem due to the discrete nature of the responses. Such data are commonly observed in many applications such as biology, epidemiology and social studies. The existing methods for univariate count response cannot be easily extended to the multivariate situation 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 data with count responses. An efficient Monte Carlo EM algorithm is also developed to facilitate the model estimation. By simultaneously estimating the regression coefficients and inverse covariance matrix over the latent variables, the proposed regression model takes advantages of association among multiple count responses to improve the model prediction performance. Simulation studies are conducted to systematically evaluate the performance of the proposed method in comparison with conventional methods. The proposed method is further used to analyze a real influenza-like illness data, showing accurate prediction and forecasting with meaningful interpretation.