Mastering Machine Learning Algorithms

Bayesian networks

A Bayesian network is a probabilistic model represented by a direct acyclic graph G = {V, E}, where the vertices are random variables X_i, and the edges determine a conditional dependence among them. In the following diagram, there's an example of simple Bayesian networks with four variables:

Example of Bayesian network

The variable x₄ is dependent on x₃, which is dependent on x₁ and x₂. To describe the network, we need the marginal probabilities P(x₁) and P(x₂) and the conditional probabilities P(x₃|x₁,x₂) and P(x₄|x₃). In fact, using the chain rule, we can derive the full joint probability as:

The previous expression shows ...