Expectation - Maximization convergence
I have 2 queries regarding calculation of expected counts in expectation-maximization in AIMA pg 730, namely the formula for conditional probability parameters for a variable(X_i) given it's parents:
THETA_ijk <= N( X_i = x_ij , Pa_i = pa_ik ) \ N( Pa_i = pa_ik ).
1) This equation is to be used if "X_i" is a hidden(latent) variable.
If both X_i & it's parents are observed variables, we can compute theta(parameter) directly from the observed counts in the example set.
However, if X_i is an observed variable, & the parents of X_i consists of observed as well as hidden variables, should we use the above formula(expected counts) for parameter updating, or can we directly estimate the parameter from the observed counts in the example set(as in the case of fully observable case - thus ignoring the hidden parent for X_i) ?
2) The EM algorithm is supposed to iterate i.e. update the parameters until convergence.
How is convergence determined ? i.e. what is the logic which tells the program that the parameters are sufficiently close to true values & it is now time to stop ?