Section 1 : Representation and inference in temporal models

Commentary

Section Goals

• To introduce the concepts and principles of probabilistic reasoning in the context of dynamic worlds that change over time.
• To discuss Markov assumption and Bayesian network structure with states that change over time.
• To discuss four basic inference tasks that must be solved based on temporal models.

Learning Objectives

Learning Objective 1

• Outline state and probabilistic representation in temporal models in the context of the Markov process.
• Explain in detail each of the four basic tasks: filtering, prediction, smoothing, and most likely explanation.
• Explain the algorithm for each of the four tasks: filtering, prediction, smoothing, and most likely sequence finding.
• Explain the following concepts or terms:
  • Time slice
  • Stationary process
  • Markov process or Markov chain
  • Transition model
  • Sensor model or observation model
  • Filtering or monitoring
  • Prediction
  • Smoothing or hindsight
  • Most likely explanation
  • Viterbi algorithm

Objective Readings

Required readings:

Reading topics:

Inference in Temporal Models (see Section 15.1-15.2 of AIMA3ed)

Objective Questions

• What makes a Bayesian network structure different when it is used to represent problems changing with time?
• What methods will you adopt for the Bayesian network if the Markov assumption is only approximate?

Objective Activities

• Compare the representation in conditional probability of the four tasks, and figure out how the probability representation reflects the purposes of the tasks.
• Explore Viterbi algorithms from Web recourses to see how it is used to solve a range of problems.
• Explore the following smoothing algorithm from the textbook's website.
  • Forward-Backward
• Complete Exercise 15.2 of AIMA3ed.