  In certain applications it is useful to fit multinomial distributions to
observed data with a penalty term that encourages sparsity. For example, in
probabilistic latent audio source decomposition one may wish to encode the
assumption that only a few latent sources are active at any given time. The
standard heuristic of applying an L1 penalty is not an option when fitting the
parameters to a multinomial distribution, which are constrained to sum to 1. An
alternative is to use a penalty term that encourages low-entropy solutions,
which corresponds to maximum a posteriori (MAP) parameter estimation with an
entropic prior. The lack of conjugacy between the entropic prior and the
multinomial distribution complicates this approach. In this report I propose a
simple iterative algorithm for MAP estimation of multinomial distributions with
sparsity-inducing entropic priors.
