Anumericallystablealgorithmforthesamplingfromdirichletdistributionusingstickbreakingmethod

Abstract

In a model that a Dirichlet prior distribution is given over a set of categorical-valued observations, such as LDA, parameters are estimated using MCMC techniques. When trying to estimate hyperparameters, it is inevitable to sampling from Dirichlet distribution with diverse cases of concentration parameters until convergence. In this paper, a numerically stable algorithm is proposed to generate Dirichlet random variables using stick brekaing method, when one or more concentration parameters are close to 0, which is the case where frequently happens in such as topic models. The most well-used Dirichlet random generators are based on Gamma random generators. But most popular Gamma random generators, Ahrens & Dieter, Best, and Marsaglia methods, are observed to generate randoms the undesirable distribution because of the numerical unstability problem Using stick brekaing method, we overcome this problem.