Book Image

Scala for Machine Learning

By : Patrick R. Nicolas
Book Image

Scala for Machine Learning

By: Patrick R. Nicolas

Overview of this book

Table of Contents (20 chapters)
Scala for Machine Learning
About the Author
About the Reviewers

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 p(X,Y) = p(X∩Y). 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 an 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 using graphs [5:1].

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

  • 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...