|
I was going through some lectures on Graphical Models and came across this expression for a message between node j and node i in a Sum-Product algorithm, where phi(x_j) is the potential at node j given it is an evidence node. I did not fully grasp how we can compute the potentials phi(x_j) and phi(x_i,x_j). Also, are the messages m_ij from the leaves to their parents in the tree just the conditional probability of the leaf given it's parent node? Thanks. |
|
The potentials are given to you at inference time. In a directed network they are the log-probabilities in the conditional probability table for each factor, and in an undirected network they are just unnormalized potentials. For example in an Ising model usually all the potentials are the same, one number for when variables agree and another for when they don't. You can estimate the potentials in many different ways, usually either by maximum likelihood, pseudolikelihood, or Bayesian methods. Thanks. And am I correct in assuming that the messages m_ij from the leaves to their parents in the tree are just the conditional probability of the leaf given it's parent node p(leaf|parent)?
(Jan 21 '14 at 13:28)
Nitin Jain
Yes, they are.
(Jan 22 '14 at 21:58)
Alexandre Passos ♦
|
