A comparison of computational approaches for maximum likelihood estimation of the Dirichlet parameters on high dimensional data

Likelihood estimates of the Dirichlet distribution parameters can be obtained only through numerical algorithms. Even though the Dirichlet distribution belongs to the Exponential Family, such algorithms can give estimates outside the correct range for the parameters. In addition, they can require a large amount of iterations to reach convergence. These problems can be exasperated if good starting points are not provided. We discuss several approaches looking at the trade-off between speed and stability. We illustrate the combinations of initialization and estimation methods using both real and simulated data of high dimension