# Probabilistic graphical models

Let's start with a refresher course in basic statistics.

Given two events or observations, *X* and *Y*, the joint probability of *X* and *Y* is defined as . If the observations *X* and *Y* are not related, an assumption known as **conditional independence**, then *p(X,Y) = p(X).p(Y)*. The conditional probability of event *Y*, given *X*, is defined as *p(Y|X)=p(X,Y)/p(X)*.

These two definitions are quite simple. However, **probabilistic reasoning** can be difficult to read in the case of large numbers of variables and sequences of conditional probabilities. As a picture is worth a thousand words, researchers introduced graphical models to describe a probabilistic relation between random variables [5:1].

There are two categories of graphs, and therefore, graphical models:

- Directed graphs such as Bayesian networks
- Undirected graphs such as conditional random fields (refer to the
*Conditional random fields*section in Chapter 7,*Sequential Data Models*)

**Directed graphical models** are directed...