Approximate Maximum A Posteriori Inference with Entropic Priors

Details Approximate Maximum A Posteriori Inference with Entropic Priors Approximate Maximum A Posteriori Inference with Entropic Priors

2010-09-29

arxiv.org/abs/1009.5761v1

Computer Science

Sound

Scientific paper

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.

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