Some understanding of PGM

The full name of PGM is called the probability map model, and it doesn't feel good until you learn it. Now that I have studied, I feel that it is of great use. Below on some of my Learning and learning journey record down, will inevitably have some wrong ideas, welcome to pass by friends to correct.

2016.12.23
I am learning prml This classic textbook, now in the study of 8.4.4 Festival, "and-Product algorithm", a few days to write the sentiment of this section, the first few sections later fill up.

1, the algorithm is an efficient algorithm for finding the edge probability distribution of variable x.
2, the algorithm first transforms the graph, the non-direction graph or the multi-tree to the factor graph, then uses the factor graph frame to push.
3, the apostle said useless, the previous example illustrates:

For example, you should first understand that "in a factor graph, a variable node to a factor node or a factor node to a variable node is interactive through information (message)."

This is a 4-node factor graph, and its joint probability distribution can be directly written out:

We aim to require the edge probability distribution of node x2

How to do it. We now assume that with X3 as the root node, x1 and x4 are leaf nodes, then the flow of information between nodes is expressed as follows:

The blue arrow is the direction of the flow of information.

The edge probability of the X2 is equal to the product of the flow of information flowing through the X2. and three green ellipses marked with green arrows. This is the product of all factor nodes (red squares) that are connected to the variable node x2.

So how do you find the red direction?
This actually involves how to analyze: Starting from the leaf node, step-by-step analysis, all the way to the root node. Then the root node is returned, step by step to the leaf node. The middle passes through these factor nodes, and the flow of information in different directions can be calculated.

leaf node to root node:

root node again to leaf node:

The above is the calculation process of the information flow size.

Then the X2 's edge probability can be easily calculated.

At the end of the sentence, the formula for our calculation and the algorithm is actually

OK, this is what I understand and-product algorithm, feel a lot of not understand thoroughly, and then fill it.

print ' Goodnight world! '