IntroductiontoProbabilisticGraphicalModels.ppt

* *** One common application is clustering. For instance, if we have data on tv shows and which users watched them then we can cluster tv shows that have similar users under the assumption that it tells us something about similarity of shows *** Given a new show and the set of users that watch it, we can predict its cluster * *** Another example is given user preferences make recommendations for them *** Take pairs of movies and learn correlation between the variables *** With these learned correlations, can score new movies given some preferences of users * * * * * We will assume knowledge of the following areas. You can read about them in the sections of the book but that will not be sufficient * *** For P to be a probability distribution it has to obey the following three conditions… *** A conditional probability distribution is a measure of the probability that event B will occur, given that event A has already occurred *** The chain rule can then be derived from the conditional probability *** Bayes rule can then be derived from the definitions of the chain rule and the conditional probability. The advantage of Bayes rule is that it allows us to evaluate the conditional distribution of A given B from the conditional distribution of B given A *** A and B are conditionally independent given C if the probability of A given B and C is equal to the probability of A given C, or in other words it means that if we know C, then the probability of A does not depend on whether or not B has happened * Random variable is defined by a function from elements in the space to a value They can be of different types… Conditional independence for RVs extends the definition for probabilities to all values that the RVs can take * *** Expectation over random variables is defined for discrete rvs or for continuous rvs *** Certain properties then hold for rvs such as linearity of expectation which we can prove *** and also product of random variables in case that the variables a