Abstract

You will implement several Bayesian networks and sampling algorithms to gain a better understanding of probabilistic systems.

Learning Objectives

Students should be able to understand the importance of Bayesian networks to represent conditional dependencies. Also, be able learn the sampling methods, Gibbs and Metropolis- Hastings and develop an intuition for their convergence criteria (very "researchy").

The Challenge

Many AI systems rely on probabilistic knowledge of the world, rather than absolute knowledge, to execute tasks efficiently: for example, motion planning in robots with unreliable sensors. One type of probabilistic system that is especially useful is the Bayesian network, which encodes a joint probability distribution among dependent variables as a network of conditional probabilities. Your challenge is to implement and test several of these networks, ultimately using a sampling method to approximate a probability distribution.

Figure 1: Example Bayesian network (representing prediction for wet grass).

2. Your Assignment

Your task is to implement a few basic networks as well as several sampling algorithms. You will do this in probability notebook.ipynb, and there are tests along the way to help.
Unlike previous assignments, we will not be grading on performance but rather on completion.

We have provided the following additional classes and files:

BASIC TASK

Warmup 1a: Build a basic Bayesian network representing a power plant.

Warmup 1b: Set the probabilities for the Bayes Net.

Warmup 1c: Use inference to calculate several marginal probabilities within the Net.

Exercise 2a: Build a Bayesian network representing a sports competition.

Exercise 2b: Given the outcomes of 2 matches, calculate likelihoods for the 3rd match.

Exercise 2c: Implement single iteration of Gibbs sampling.

Exercise 2d: Implement single iteration of Metropolis-Hastings sampling.

Exercise 2e: Compare the performance of the 2 sampling methods.