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Multivariate count data are commonly encountered through high-throughputsequencing technologies in bioinformatics, text mining, or in sports analytics.Although the Poisson distribution seems a natural fit to these count data, itsmultivariate extension is computationally expensive.In most cases mutualindependence among the variables is assumed, however this fails to take intoaccount the correlation among the variables usually observed in the data.Recently, mixtures of multivariate Poisson-lognormal (MPLN) models have beenused to analyze such multivariate count measurements with a dependencestructure. In the MPLN model, each count is modeled using an independentPoisson distribution conditional on a latent multivariate Gaussian variable.Due to this hierarchical structure, the MPLN model can account forover-dispersion as opposed to the traditional Poisson distribution and allowsfor correlation between the variables. Rather than relying on a MonteCarlo-based estimation framework which is computationally inefficient, a fastvariational-EM based framework is used here for parameter estimation. Further,a parsimonious family of mixtures of Poisson-lognormal distributions areproposed by decomposing the covariance matrix and imposing constraints on thesedecompositions. Utility of such models is shown using simulated and benchmarkdatasets.

A parsimonious family of multivariate Poisson-lognormal distributions for clustering multivariate count data