# Probabilistic Graphical Model Structure

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A Probabilistic Graphical Model Structure is a statistical model structure that is labeled graph structure where the nodes are random variables, and the edges represent a probability function between the connected nodes.

**AKA:**Statistical Network Structure.**Context:**- It must have One or more graphical model output nodes.
- It must have One or more graphical model input nodes.
- It can (typically) be a member of a Probabilistic Graphical Model Family.
- It can range from being a Directed Probabilistic Network (typically a Bayesian Network) to being an Undirected Probabilistic Network (typically a Random Field Network).
- It can queried with a Probabilistic Query by means of Probabilistic Graphical Model Inference.
- It can be produced:
- by an Expert.
- by a Graphical Model Learning Algorithm.

- It can be used to support a Decision System.

**Example(s):**- a Conditional Probability Network, such as a Bayesian network.
- a Random Field Network, such as a Conditional Random Fields network.
- a Markov Logic Network.
- …

**Counter-Example(s):****See:**Probability Function, Probabilistic Model, Graph (Mathematics), Conditional Dependence.

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Graphical_model Retrieved:2014-5-30.
- A
**graphical model**is a probabilistic model for which a graph denotes the conditional dependence structure between random variables. They are commonly used in probability theory, statistics — particularly Bayesian statistics — and machine learning.

- A

### 2000

- (Valpola, 2000) ⇒ Harri Valpola. (2000). “Bayesian Ensemble Learning for Nonlinear Factor Analysis." PhD Dissertation, Helsinki University of Technology.
- QUOTE: graphical model: A graphical representation of the causal structure of a probabilistic model. Variables are denoted by circles and arrows are used for representing the conditional dependences.

### 1999

- (Cowell et al., 1999) ⇒ Robert Cowell, A. Philip Dawid, Steffen Lauritzen, and David Spiegelhalter. (1999). “Probabilistic Networks and Expert Systems." Springer. ISBN:978-0-387-98767-5
- … The best way to do this turns out to be through the imposition of meaningful simplifying conditional independence assumptions. These, in turn, can be expressed by means of a powerful and appealing graphical representations, and the resulting networks are often termed
*Bayesian networks*, although in this book we prefer the term, reflecting an increased generality in the representations we consider.**probabilistic networks**

- … The best way to do this turns out to be through the imposition of meaningful simplifying conditional independence assumptions. These, in turn, can be expressed by means of a powerful and appealing graphical representations, and the resulting networks are often termed

### 1997

- (Richardson, 1977) ⇒ T. Richardson. (1997). “Extensions of undirected and acyclic, directed graphical models.” In: Proceedings of the 6th Conference on Artificial Intelligence in Statistics.

### 1988

- (Pearl, 1988) ⇒ Judea Pearl. (1988). “Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference." Morgan Kaufmann. ISBN:1558604790