ABSTRACT
This part starts with some notation and a formal definition of MAP. Given a Bayesian network that induces a joint probability distribution Pr, all the variables can be divided into three sets: E, S and M. E stands for evidence variables that have been known and E = e holds; S stands for the variables whose values should be summed out that people don’t care about; M stands for the MAP variables. The MAP probability over variables M given evidence e is defined as
m( , ) Pmax r( , )e m (1)
There may be a number of instantiations m that attains this maximal probability (Darwiche, A. 2012). Each of these instantiations is then a MAP instantiation which is called a MAP solution, where the set of all such instantiations is defined as
m( , ) Pargmax r( , )m (2)
Generally, calculating MAP needs two steps. First, according to Bayer Conditioning (Zhang, L.W. & Guo, H.P. 2006) calculate Equation 3 to get the posterior probability distribution over MAP variables M.
