Fast MLE Computation for the Dirichlet Multinomial
This is an incremental improvement for researchers and practitioners working with categorical data and Dirichlet distributions.
The paper tackles the problem of efficiently computing maximum likelihood estimates for Dirichlet multinomial parameters, proposing a single-pass algorithm that reduces running time compared to traditional Newton's method.
Given a collection of categorical data, we want to find the parameters of a Dirichlet distribution which maximizes the likelihood of that data. Newton's method is typically used for this purpose but current implementations require reading through the entire dataset on each iteration. In this paper, we propose a modification which requires only a single pass through the dataset and substantially decreases running time. Furthermore we analyze both theoretically and empirically the performance of the proposed algorithm, and provide an open source implementation.