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Generalizing Gaussian regression
the likelihoods may be modeled by a mixture of Gaussians

(331) 
where the normalization factor is found as
.
Hence, is here specified by mixing coefficients
and a vector of regression functions
specifying the dependent location of the th cluster centroid
of the mixture model.
A simple prior for
is a smoothness prior diagonal in the cluster components.
As any density can be approximated arbitrarily
well by a mixture with large enough
such cluster regression models
allows to interpolate between Gaussian regression
and more flexible density estimation.
The posterior density becomes for independent data

(332) 
Maximizing that posterior is
 for fixed , uniform and 
equivalent to the clustering approach
of Rose, Gurewitz, and Fox
for squared distance costs [203].
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Joerg_Lemm
20010121