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Finding a specific probability (Migrated from community.research.microsoft.com)
Question

Kirali posted on 03012011 3:10 AM
The project that I am working on requires me to compute probabilities of the form
P(CarMake = Value1  Evidence)
I am only interested in the probability of value1 and not the other values in the distribution. Currently, I am computing posterior of CarMake and looking at the probability corresponding to Value1. Is there a way in which I can avoid computing the other probabilities, as I need to reduce the computation time wherever possible.
Friday, June 3, 2011 6:26 PM
Answers

minka replied on 03022011 4:08 AM
Yes that is what barren means. If CarMake is not barren, then I don't think any work can be saved.
 Marked as answer by Microsoft Research Friday, June 3, 2011 6:26 PM
Friday, June 3, 2011 6:26 PM
All replies

minka replied on 03012011 3:21 AM
I don't think this is possible. In order to compute the conditional probability of CarMake=Value1, you have to normalize by p(evidence) and this requires summing out CarMake, either explicitly or implicitly in the inference algorithm. The one exception to this is when CarMake is barren, but in that case the probabilities are given directly by the CPT and there is no extra cost in returning the full marginal.
Friday, June 3, 2011 6:26 PM 
minka replied on 03012011 3:29 AM
On further thought, you might be able to save some work in the case CarMake is barren. The marginal in this case is given by a sum over CarMake's parents, and it is cheaper to do this sum for a single value of CarMake than over all values. Is this the situation you are interested in?
Friday, June 3, 2011 6:26 PM 
Kirali replied on 03012011 6:01 PM
Just to make sure that I understand what you said, by CarMake being barren do you mean that every element in {evidence} is a nondescendent of CarMake in the bayesnetwork?
If this interpretation of barren is correct, then my problem is more general. I am not guaranteed that CarMake is always barren.
Friday, June 3, 2011 6:26 PM 
minka replied on 03022011 4:08 AM
Yes that is what barren means. If CarMake is not barren, then I don't think any work can be saved.
 Marked as answer by Microsoft Research Friday, June 3, 2011 6:26 PM
Friday, June 3, 2011 6:26 PM