Section 2 : Exact and approximate inference in Bayesian networks

Commentary

Section Goals

• To introduce exact inference in Bayesian networks based on enumeration and variable elimination.
• To introduce randomized sampling algorithms, also called Monte Carlo algorithms, for approximate inference in Bayesian networks

Learning Objectives

Learning Objective 1

• Outline how to perform exact inference in Bayesian networks by enumeration.
• Explain the variable elimination algorithms, focusing on how it can make an exact inference.
• Explain the following concepts or terms:
  • Query variable
  • Evidence variable
  • Hidden variable
  • Variable elimination
  • Causal rule
  • Monte Carlo
  • Rejection sampling
  • Likelihood weighting
  • Markov chain Monte Carlo (MCMC)
  • Transition probability
  • Stationary distribution
  • Gibbs sampler

Objective Readings

Required readings:

Reading topics:

Exact and Approximate Inference in Bayesian Networks (see Sections 14.4 - 14.5 of AIMA3ed)

Objective Questions

• How does likelihood weighting avoid the inefficiency of rejection sampling?
• Why does MCMC work?
• What are the differences between the common types of graphical models?

Objective Activities

• Explore the following probabilistic reasoning algorithms related to this section from the textbook's website.
  • Rejection-Sampling
  • Likelihood-Weighting
  • Gibbs-Ask
• Complete Exercise 14.7 of AIMA3ed.