Paper , Order, or Assignment Requirements

2.  Your Assignment

Your task is to implement a few basic networks as well as the Gibbs sampling algorithm. There is a bonus section too where you need to implement Metropolis Hastings sampling and compare the results between the two. On completing the bonus section correctly, you will score up to 2% points on your final grade.

You will do this in probability_solution.py, 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 in the “assignment_3-master.zip”

This is meant to be a shorter assignment, so there won’t be much testing required.

3. Grading

BASIC TASK (100 points)

Warmup 1a: Build a basic Bayesian network representing a power plant. (10 points)

Warmup 1b: Answer a question about poly-trees. (5 points)

Warmup 1c: Set the probabilities for the Bayes Net. (10 points)

Warmup 1d: Use inference to calculate several marginal probabilities within the Net. (10points)

Exercise 2a: Build a small Bayesian network representing a sports competition. (15 points)

Exercise 2b: Calculate likelihoods for the 3rd match. (5 points)

Exercise 2c: Implement Gibbs sampling. (20 points)

Exercise 2d: Count the number of iterations it takes to converge to a stable distribution and return the estimated likelihood. (20 points)

Exercise 2e: Answer a question about time complexity. (5 points)

BONUS TASK (optional: up to 2% points added to final class grade)

Exercise 3a: Implement Metropolis-Hastings sampling and convergence. (20 points)

Exercise 3b:

performance of the 2 sampling methods on the Sports network and answer the sampling question. (10 points)