# Probabilistic Graphical Model Family

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A Probabilistic Graphical Model Family is a statistical model family that uses a graph structure to represent probability distributions between random variables.

**AKA:**Statistical Graphical Models, GMs, PGMs.**Context:**- It can be associated with a Graphical Statistical Model Instance.
- It can range from being a Directed Probabilistic Graphical Model Family to being an Undirected Probabilistic Graphical Model Family.
- It can range from being a Conditional Probabilistic Graphical Family to being a Joint Probabilistic Graphical Family
- It can range from being a Generative Probabilistic Graphical Metamodel Model to being a Discriminative Probabilistic Graphical Metamodel.
- It can be used for a Structured Data Modeling Task.

**Example(s):**- a Factor Graph Model Family, for a Factor Graph network.
- a … for a Markov Probabilistic Graphical Model.
- a Bayesian Graph Model Family, for Bayesian networks.
- a Conditional Random Fields, for a CRF network.
- a … for a Markov Random Field.
- a … for a Maximum-Margin Markov Network
- a Latent Dirichlet Allocation Model ? Metamodel.

**Counter-Example(s):****See:**Conceptual Graph Model.

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Graphical_model
- 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

- http://en.wikipedia.org/wiki/Graphical_model#Types_of_graphical_models
- Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a complete distribution over a multi-dimensional space and a graph that is a compact or factorized representation of a set of independences that hold in the specific distribution. Two branches of graphical representations of distributions are commonly used, namely, Bayesian networks and Markov networks. Both families encompass the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution that they induce

- http://factorie.cs.umass.edu/usersguide/UsersGuide030Overview.html
- Graphical models are a formalism in which a graph denotes the conditional dependence structure between random variables. The formalism is the marriage between probability theory and graph theory. It provides an elegant framework that combines uncertainty (probabilities) and logical structure (independence constraints) such that complex joint probability distributions over multiple variables that would have otherwise been intractable to represent or manipulate can instead be represented compactly and often manipulated efficiently. Since graphical models can straightforwardly express so many different probabilistic models, they have become a lingua-franca for statistics, machine learning, and data mining.
In graphical models, variables are depicted by the nodes a graph, drawn as circles, and dependencies among variables are depicted by edges, drawn either as directed (with arrows), or undirected (without arrows).

There are two main types of graphical models. .. Directed graphical models … Undirected graphical models.

- Graphical models are a formalism in which a graph denotes the conditional dependence structure between random variables. The formalism is the marriage between probability theory and graph theory. It provides an elegant framework that combines uncertainty (probabilities) and logical structure (independence constraints) such that complex joint probability distributions over multiple variables that would have otherwise been intractable to represent or manipulate can instead be represented compactly and often manipulated efficiently. Since graphical models can straightforwardly express so many different probabilistic models, they have become a lingua-franca for statistics, machine learning, and data mining.

### 2008

- (Blei, 2008) ⇒ David M. Blei. (2008). “Modeling Science." Presentation. April 17, 2008

### 2006

- (Bishop, 2006) ⇒ Christopher M. Bishop. (2006). “Pattern Recognition and Machine Learning. Springer, Information Science and Statistics.

### 2001

- F. V. Jensen. (2001). Bayesian Networks and Decision Graphs. Springer.
- Introductory book.

### 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

### 1998

- (Jordan, 1998) ⇒ Michael I. Jordan (ed). (1998). “Learning in Graphical Models." MIT Press. ISBN:0-262-60032-3
- (Murphy, 1998) ⇒ Kevin Murphy. (1998). “A Brief Introduction to Graphical Models and Bayesian Networks."

### 1997

- (Jordan, 1997) ⇒ Michael I. Jordan. (1997). “An Introduction to Graphical Models." Tutorial at NIPS-1997.
- Graphical models are a marriage between graph theory and probability theory
- They clarify the relationship between neural networks and related network-based models such as HMMs, MRFs, and Kalman lters
- Indeed, they can be used to give a fully probabilistic interpretation to many neural network architectures
- Some advantages of the graphical model point of view
- inference and learning are treated together
- supervised and unsupervised learning are merged seamlessly
- missing data handled nicely
- a focus on conditional independence and computational issues
- interpretability (if desired)

- (Mitchell, 1997) ⇒ Tom M. Mitchell. (1997). “Machine Learning." McGraw-Hill.

### 1996

- (Lauritzen, 1996) ⇒ S. Lauritzen. (1996). “Graphical Models.” Oxford.
- mathematical exposition of the theory of graphical models.

### 1988

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