Unformatted text preview: we mainly using deterministic model to describe data, which means a given input always generate the
same output, now we are going to consider generative model of data. In this case, some hidden variables are incorporated and joint probability is assigned between the
nodes so that we can derive results through the bayes rule.
We assume, as we can see in the graph on the right hand side, that we have three random variables,
,,
and where
denotes class , is what we observed here, and is some hidden random variable.
There is a process that there are different classes, and each class can trigger a different hidden random
variable . To understand this, we can assume that, for instance, this random variable has a Gaussian
distribution (it could have any other distribution as well) and that all the ’s have the same distribution
(Gaussian), but with different parameters. From each Gaussian distribution triggered by each class, we are
going to sample some data points. Therefore, in the end, we are going to get a set of data, which are not
strictly Gaussian, but are actually a mixture of Gaussians.
Again, we look at the posterior distribution from Bayes' Rule (http://en.wikipedia.org/wiki/Bayes'_theorem) .
Figure 26.1: RBF Network Classification Demo Since we made the assumption that the data has been generated from a mixture model, we can estimate this conditional probability by
,
which is the class conditional distribution (or probability) of the mixture model. Note, here, if we only have a simple model from
summation. to , then we won’t have this We can substitute this class conditional distribution into Bayes' formula. We can see that the posterior of class
is the summation over
times the probability of given
, times the prior distribution of class , and lastly divided by the marginal probability of . That is, of the probability of given . wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 50/74 10/09/2013 Stat841  Wiki Cour se Notes Since, the prior probability of class , , does not have an index o...
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This document was uploaded on 03/07/2014.
 Winter '13

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