Uncertainty in Artificial Intelligence
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Hierarchical Mixtures-of-Experts for Exponential Family Regression Models with Generalized Linear Mean Functions: A Survey of Approximation and Consistency Results
Wenxin Jiang, Martin Tanner
Abstract:
We investigate a class of hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form psi(ga+fx^Tfgb) are mixed. Here psi(...) is the inverse link function. Suppose the true response y follows an exponential family regression model with mean function belonging to a class of smooth functions of the form psi(h(fx)) where h(...)in W_2^infty (a Sobolev class over [0,1]^{s}). It is shown that the HME probability density functions can approximate the true density, at a rate of O(m^{-2/s}) in L_p norm, and at a rate of O(m^{-4/s}) in Kullback-Leibler divergence. These rates can be achieved within the family of HME structures with no more than s-layers, where s is the dimension of the predictor fx. It is also shown that likelihood-based inference based on HME is consistent in recovering the truth, in the sense that as the sample size n and the number of experts m both increase, the mean square error of the predicted mean response goes to zero. Conditions for such results to hold are stated and discussed.
Keywords: Approximation, consistency, exponential family, generalized linear models,hierarchica
Pages: 296-303
PS Link:
PDF Link: /papers/98/p296-jiang.pdf
BibTex:
@INPROCEEDINGS{Jiang98,
AUTHOR = "Wenxin Jiang and Martin Tanner",
TITLE = "Hierarchical Mixtures-of-Experts for Exponential Family Regression Models with Generalized Linear Mean Functions: A Survey of Approximation and Consistency Results",
BOOKTITLE = "Proceedings of the Fourteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-98)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1998",
PAGES = "296--303"
}


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