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The multinomial and related distributions have long been used to modelcategorical, count-based data in fields ranging from bioinformatics to naturallanguage processing. Commonly utilized variants include the standardmultinomial and the Dirichlet multinomial distributions due to theircomputational efficiency and straightforward parameter estimation process.However, these distributions make strict assumptions about the mean, variance,and covariance between the categorical features being modeled. If theseassumptions are not met by the data, it may result in poor parameter estimatesand loss in accuracy for downstream applications like classification. Here, weexplore efficient parameter estimation and supervised classification methodsusing an alternative distribution, called the Beta-Liouville multinomial, whichrelaxes some of the multinomial assumptions. We show that the Beta-Liouvillemultinomial is comparable in efficiency to the Dirichlet multinomial forNewton-Raphson maximum likelihood estimation, and that its performance onsimulated data matches or exceeds that of the multinomial and Dirichletmultinomial distributions. Finally, we demonstrate that the Beta-Liouvillemultinomial outperforms the multinomial and Dirichlet multinomial on two out offour gold standard datasets, supporting its use in modeling data with low tomedium class overlap in a supervised classification context.

Fast Maximum Likelihood Estimation and Supervised Classification for the Beta-Liouville Multinomial