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Unformatted text preview: C260A Lecture 5: Probabilistic Modeling Christopher Lee October 7, 2009 Defining Events vs. Variables event : a subset of our total probability space S . p ( e ) = a number. variable : some slicing of S into disjoint subsets, each labeled with a distinct value . Now p ( X ) = f ( X ) 1 Multiple Variables = Multiple Slicings Each variable just represents another way of slicing up S . Different slicings could be very similar, or very different. Each time we draw one item from S , it is labeled with a value for each of our different variables. 2 Independence? Are events A , B statistically independent? 3 Independence is About Variables Independence is a statement about the function p ( X , Y ) = p ( X ) p ( Y ) over the entire space, i.e. true x , y ! Dont confuse independence with simple set intersection. 4 Event Independence? Create variables X : { A , A } , Y : { B , B } . p ( A , B ) = p ( A ) p ( B ) p ( X , Y ) = p ( X ) p ( Y ) 5 Unconditional Sampling Throw a dart at the dartboard, get one data point ( x , y , z ) yielding a value for each of the variables defined in our information graph. Each time we sample, we get a new value for every vari able, including our hidden variables. By contrast, in in ference we typically draw multiple samples of the observ ables from one specific inference problem (i.e. one value of )....
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This note was uploaded on 04/12/2010 for the course CHEM CHEM 260A taught by Professor Chrislee during the Spring '10 term at UCLA.
 Spring '10
 CHRISLEE
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