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Given the following Bayessian Network:

Graphical representation of a probabilistic model

I wonder when is it reasonable to estimate $p(u\mid c)$ as

$$ p(u\mid c) \approx p(c\mid w=w_1,\ldots,w_t)$$

I want to estimate that because I can't calculate $p(u\mid c)$ because $u$ is not observable. I've been looking for inference and reasoning in bayes networks but I couldn't find any inference like this.

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    Are you assuming a particular type of distribution for $u and c$ or is this simply a general exercise?2012-12-15
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    I don't know what you mean. Could you give an example of such a distribution?2012-12-16
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    I what is the functional form of the conditional distribution $p(u|c)$? Is $u$ a discrete variable? Gaussian? What about c?2012-12-16
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    Oh, all the variables are discrete. $u$ are users of a search engine, $c$ are categories where the queries that $u$ search ($q$) and webs sites that they visit ($w$) are classified.2012-12-17
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    See [this document here](http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html#learn) under the subsection "Known Structure, Partial Observability"2012-12-17

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