Fast learning of gamma mixture models with k-MLE

Author

Schwander, Olivier and Nielsen, Frank

Abstract

We introduce a novel algorithm to learn mixtures of Gamma distributions. This is an extension of the k-Maximum Likelihood Estimator algorithm for mixtures of exponential families. Although Gamma distributions are exponential families, we cannot rely directly on the exponential families tools due to the lack of closed-form formula and the cost of numerical approximation: our method uses Gamma distributions with a fixed rate parameter and a special step to choose this parameter is added in the algorithm. Since it converges locally and is computationally faster than an Expectation-Maximization method for Gamma mixture models, our method can be used beneficially as a drop-in replacement in any application using this kind of statistical models.