# Undirected Graphical Probability Models Family

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An Undirected Graphical Probability Models Family is a Graphical Statistical Model Family that is restricted to undirected edges.

**AKA:**Markov Random Fields, MRFs, Markov Networks.**Context:**- It can be associated with a Undirected Probabilistic Network.
- It can range from being an Undirected Conditional Graphical Model Family to being an Undirected Joint Graphical Model Family.

**Example(s):****Counter-Example(s):****See:**Hidden Markov Model Family, Statistical Model Family.

## References

### 2014

- http://factorie.cs.umass.edu/usersguide/UsersGuide030Overview.html
*Undirected graphical models*(also known as Markov random fields) represent a joint distribution over random variables by a product of unnormalized non-negative values (one value for each clique in the graph). They are convenient models for data in which it is not intuitive to impose an ordering on the variables' generative process. They can represent different patterns of independence constraints than directed models can, and vice versa --- neither one is strictly more expressive than the other.... Factor graphs are a generalization of both directed and undirected graphical models, capable of representing both.

### 2009

- http://www.di.ens.fr/~mschmidt/Software/UGM.html
- UGM is a set of Matlab functions implementing various tasks in probabilistic undirected graphical models of discrete data with pairwise (and unary) potentials. Specifically, it implements a variety of methods for the following four tasks:
- Decoding: Computing the most likely configuration.
- Inference: Computing the partition function and marginal probabilities.
- Sampling: Generating samples from the distribution.
- Parameter Estimation: Given data, computing maximum likelihood (or MAP) estimates of the parameters.

- UGM is a set of Matlab functions implementing various tasks in probabilistic undirected graphical models of discrete data with pairwise (and unary) potentials. Specifically, it implements a variety of methods for the following four tasks:

### 2008

- Doina Precup. (2008). “Lecture 5: Undirected graphical models."
- QUOTE: An undirected graph over a set of random variables <math>{X_1,...,X_n}<math> is called a undirected graphical model or Markov random field (MRF) or Markov network ...
* Undirected models are neither more nor less expressive than directed models; they are simply different.

* The semantics of an undirected model naturally capture correlation of r.v.s, not causation

* If you ever want, in an application, to write a Bayes net with, cycles, it is a sign that the right model is undirected.

- QUOTE: An undirected graph over a set of random variables <math>{X_1,...,X_n}<math> is called a undirected graphical model or Markov random field (MRF) or Markov network ...