# Factor Graph Model Instance

A Factor Graph Model Instance is a probabilistic graphical model instance where graphical model nodes are joined by factor compatibility function (that outputs a compatibility score between connected variables).

**Context:**- It can represent a Direct Graphical Models, and an Undirected Graphical Model.
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**Example(s):**- a Par-Factor Graph a factor graph with parameterized factors.
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**Counter-Example(s):****See:**Graph, Log-Linear Model, Pair-wise Potential, Potential Function, Ising Model, Factor Graph Software Library.

## References

### 2014

- http://en.wikipedia.org/wiki/Factor_graph
- QUOTE: In probability theory and its applications, a
**factor graph**is a particular type of graphical model, with applications in Bayesian inference, that enables efficient computation of marginal distributions through the sum-product algorithm. One of the important success stories of factor graphs and the sum-product algorithm is the decoding of capacity-approaching error-correcting codes, such as LDPC and turbo codes.A factor graph is an example of a hypergraph, in that an

*arrow*(i.e., a factor node) can connect more than one (normal) node.When there are no free variables, the factor graph of a function

*f*is equivalent to the constraint graph of*f*, which is an instance to a constraint satisfaction problem.

- QUOTE: In probability theory and its applications, a

- http://factorie.cs.umass.edu/usersguide/UsersGuide030Overview.html
*Factor graphs*are a generalization of both directed and undirected graphical models, capable of representing both.When drawn, factor graphs depict variables as circular nodes in the graph (just as in directed and undirected graphical models), however rather than having edges that connect variables directly to each other, edges instead connect variables to factors (which are drawn as black squares). In other words, variables are connected to other variables only through factors. The variables connected to a factor are called the "neighbors" of the factor. A factor graph is a bipartite graph connecting variables and factors.

Factor graphs represent a joint distribution over random variables by a product of (normalized or unnormalized) non-negative values --- one value for each factor in the graph. The factors can be understood as “compatibility functions" that take as input the values of the variables which they neighbor, and outputing a “compatibility score” such that higher scores indicate the combination of values is more likely, and lower scores indicate the combination of values is less likely. A score of 0 indicates the combination is impossible.