Factor graph¶
a way to express undirected graphical models with less ambiguity
from the standard notation in MRF, we do not known if the corresponding factor encompasses the whole clique or some of its parts
an example if we have a clique of 3 nodes, we can have a single factor for the whole clique, or we can have 3 factors for each possible pairs
factor graph is a bipartite graph and has the following nodes:
circles: which are random variables as in undirected graphs
squares: factors \(\phi\) of unnormalized probability distribution
variables and factors can be connected with undirected edges, this connection is there if a variable is a argument of a factor in the unnormalized distribution.
there cannot be an connection
variable - variable
factor - factor
an classical undirected graph
a factor graph where we have a single factor for the clique of variables a,b,c
we have 3 factors in the clique a,b,c