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cs-677sp2010:map-inference [2014/12/12 18:19]
ryancha
cs-677sp2010:map-inference [2014/12/12 18:19] (current)
ryancha
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 The Marginal MAP query is very similar to the MAP query, except that it loosens the constraint that $W$ must contain all non-evidence variables. The Marginal MAP query is very similar to the MAP query, except that it loosens the constraint that $W$ must contain all non-evidence variables.
  
-Given a set of random variables, $\Chi$, a set of evidence variables $E$, and a set of query variables $W$ +Given a set of random variables, $\chi$, a set of evidence variables $E$, and a set of query variables $W$ 
-<​blockquote>​$Z = \Chi - W - E$</​blockquote>​+<​blockquote>​$Z = \chi - W - E$</​blockquote>​
  
 The MAP query finds the most likely assignment to the query variables $W$ given the evidence variables $E$. The MAP query finds the most likely assignment to the query variables $W$ given the evidence variables $E$.
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 ==Solution Methods== ==Solution Methods==
-This discussion is simplified by using the, equivalent, factor representation of a joint distribution. ​ Our task is to find $\xi^{MAP}$,​ the most likely assignment to the variables in $\Chi$.  $P_{\Phi}(\Chi)$ is a distribution defined via a set of factors $\Phi$ and an unnormalized density $\tilde{P_{\Phi}}$. ​ $Z$ is a normalizing constant.+This discussion is simplified by using the, equivalent, factor representation of a joint distribution. ​ Our task is to find $\xi^{MAP}$,​ the most likely assignment to the variables in $\chi$.  $P_{\Phi}(\chi)$ is a distribution defined via a set of factors $\Phi$ and an unnormalized density $\tilde{P_{\Phi}}$. ​ $Z$ is a normalizing constant.
  
 <​blockquote>​$\xi^{MAP} = \underset{\xi}{argmax}~P_{\Phi}(\xi)$ <​blockquote>​$\xi^{MAP} = \underset{\xi}{argmax}~P_{\Phi}(\xi)$
cs-677sp2010/map-inference.txt · Last modified: 2014/12/12 18:19 by ryancha
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