A commonly used distribution on the probability simplex is the Dirichlet distribution. In this paper we present the linear exponential family as an alternative. The distribution is known in the statistics community, but we present in this paper a numerically stable method to compute its parameters. Although the Dirichlet distribution is known to be a good Bayesian prior for probabilities we believe this paper shows that the linear exponential model offers a good alternative in other contexts, such as when we want to use posterior probabilities as features for automatic speech recognition. We show how to incorporate posterior probabilities as additional features to an existing GMM, and show that the resulting model gives a 0.6% relative gain on a broadcast news speech recognition system.
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