Fitting Gamma Mixture Density Networks with Expectation-Maximization Algorithm

36 Pages Posted: 23 Nov 2020

See all articles by Lukasz Delong

Lukasz Delong

Warsaw School of Economics (SGH) - Institute of Econometrics

Mathias Lindholm

Stockholm University

Mario V. Wuthrich

RiskLab, ETH Zurich

Date Written: October 5, 2020

Abstract

We discuss how mixtures of Gamma distributions with shape and rate parameters depending on explanatory variables can be fitted with neural networks. We develop two versions of the EM algorithm for fitting Gamma Mixture Density Networks which we call the EM network boosting algorithm and the EM forward network algorithm. The key difference between the EM algorithms is how we pass the information about the trained neural networks and the predicted parameters between the iterations of the EM algorithm. We validate our EM algorithms and test different methods of how the algorithms can be efficiently applied in practice. Our algorithms work for general mixtures of any distribution types that have closed form densities.

Keywords: Expectation-Maximization, neural networks, boosting, mixtures of distributions

JEL Classification: G22, C45

Suggested Citation

Delong, Lukasz and Lindholm, Mathias and Wuthrich, Mario V., Fitting Gamma Mixture Density Networks with Expectation-Maximization Algorithm (October 5, 2020). Available at SSRN: https://ssrn.com/abstract=3705225 or http://dx.doi.org/10.2139/ssrn.3705225

Lukasz Delong (Contact Author)

Warsaw School of Economics (SGH) - Institute of Econometrics ( email )

Niepodleglosci 164
Warsaw, 02-554
Poland

Mathias Lindholm

Stockholm University ( email )

Universitetsvägen 10
Stockholm, Stockholm SE-106 91
Sweden

Mario V. Wuthrich

RiskLab, ETH Zurich ( email )

Department of Mathematics
Ramistrasse 101
Zurich, 8092
Switzerland

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