8
Graphical
Models
Probabilities play a central role in modern pattern recognition. We have seen in
Chapter 1 that probability theory can be expressed in terms of two simple equations
corresponding to the sum rule and the product rule. All of the probabilistic infer-
ence and learning manipulations discussed in this book, no matter how complex,
amount to repeated application of these two equations. We could therefore proceed
to formulate and solve complicated probabilistic models purely by algebraic ma-
nipulation. However, we shall find it highly advantageous to augment the analysis
using diagrammatic representations of probability distributions, calledprobabilistic
graphical models. These offer several useful properties:
- They provide a simple way to visualize the structure of a probabilistic model
and can be used to design and motivate new models. - Insights into the properties of the model, including conditional independence
properties, can be obtained by inspection of the graph.