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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Neal, R.M.: Markov chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics 9(2), 249–265 (2000)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological), 1–38 (1977)
Mayrose, I., Friedman, N., Pupko, T.: A Gamma mixture model better accounts for among site rate heterogeneity. Bioinformatics 21(suppl. 2) (2005)
Almhana, J., Liu, Z., Choulakian, V., McGorman, R.: A recursive algorithm for gamma mixture models. In: IEEE International Conference on Communications, ICC 2006, vol. 1, pp. 197–202 (June 2006)
Venturini, S., Dominici, F., Parmigiani, G.: Gamma shape mixtures for heavy-tailed distributions. The Annals of Applied Statistics 2(2), 756–776 (2008); Zentralblatt MATH identifier: 05591297; Mathematical Reviews number (MathSciNet): MR2524355
Nielsen, F.: k-MLE: A fast algorithm for learning statistical mixture models. CoRR (2012)
Schwander, O., Schutz, A.J., Nielsen, F., Berthoumieu, Y.: k-MLE for mixtures of generalized Gaussians. In: 2012 21st International Conference on Pattern Recognition (ICPR), pp. 2825–2828 (November 2012)
Nielsen, F., Garcia, V.: Statistical exponential families: A digest with flash cards. CoRR 09114863 (2009)
Banerjee, A., Merugu, S., Dhillon, I.S., Ghosh, J.: Clustering with Bregman divergences. The Journal of Machine Learning Research 6, 1705–1749 (2005)
Nielsen, F.: k-MLE: A fast algorithm for learning statistical mixture models. In: 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 869–872 (March 2012)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical recipes: The art of scientific computing, 3rd edn. Cambridge University Press (2007)
Lloyd, S.P.: Least squares quantization in PCM. IEEE Transactions on Information Theory 28(2), 129–137 (1982)
Sim, A.Y., Schwander, O., Levitt, M., Bernauer, J.: Evaluating mixture models for building rna knowledge-based potentials. Journal of Bioinformatics and Computational Biology 10(02) (2012)
Bernauer, J., Huang, X., Sim, A.Y., Levitt, M.: Fully differentiable coarse-grained and all-atom knowledge-based potentials for rna structure evaluation. RNA 17(6), 1066–1075 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schwander, O., Nielsen, F. (2013). Fast Learning of Gamma Mixture Models with k-MLE. In: Hancock, E., Pelillo, M. (eds) Similarity-Based Pattern Recognition. SIMBAD 2013. Lecture Notes in Computer Science, vol 7953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39140-8_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-39140-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39139-2
Online ISBN: 978-3-642-39140-8
eBook Packages: Computer ScienceComputer Science (R0)