Asymptotic properties of mixture-of-experts models

Authors:
M. Olteanu;J. Rynkiewicz
Affiliations:
SAMM, EA 4543, Universite Paris 1, 90 Rue de Tolbiac, 75013 Paris, France;SAMM, EA 4543, Universite Paris 1, 90 Rue de Tolbiac, 75013 Paris, France
Venue:
Neurocomputing
Year:
2011

Citing 4
Cited 0

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On the asymptotic normality of hierarchical mixtures-of-experts for generalized linear models

IEEE Transactions on Information Theory

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Abstract

The statistical properties of the likelihood ratio test statistic (LRTS) for mixture-of-expert models are addressed in this paper. This question is essential when estimating the number of experts in the model. Our purpose is to extend the existing results for simple mixture models (Liu and Shao, 2003 [8]) and mixtures of multilayer perceptrons (Olteanu and Rynkiewicz, 2008 [9]). In this paper we first study a simple example which embodies all the difficulties arising in such models. We find that in the most general case the LRTS diverges but, with additional assumptions, the behavior of such models can be totally explicated.