Probabilistic Graphical Model Structure

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):
- a Conceptual Hierarchy.
- a Decision Tree Structure.
See: Probability Function, Probabilistic Model, Graph (Mathematics), Conditional Dependence.

References

(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.

(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.

(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 probabilistic networks, reflecting an increased generality in the representations we consider.

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