Homework 1

ECE 285

1. (25 points) For the following Bayesian network, judge whether the following statements are

true or false. And give a brief explanation for each of your answer.

(I: Intelligent; H: Hardworking; T: good Test taker; U: Understands material; E: high Exam score)

• T and U are independent.

• T and U are conditionally independent given I, E, and H.

• T and U are conditionally independent given I and H.

• E and H are conditionally independent given U.

• E and H are conditionally independent given U, I, and T.

• I and H are conditionally independent given E.

• I and H are conditionally independent given T.

• T and H are independent.

• T and H are conditionally independent given E.

• T and H are conditionally independent given E and U.

2. (15 points) For the above Bayesian network, construct local conditional probability tables.

Assume all variables are binary (1 for true and 0 for false). For example, p(E=1|T=1, U=1) = 0.8.

And give a brief explanation for your specified probabilities. For example, if a student is a good

test taker and understands the material well, the student is very likely to have a high exam

score.

3. (10 points) For the above Bayesian network, write down the joint distribution of all variables.

4. (15 points) Calculate P(E=1|Hardworking=1).

5. (35 points) Consider a task: based on the infected cases in the past week, predict the number

of infected COVID-19 cases for all cities in San Diego County for tomorrow. Design a Markov

random field model to perform this task. In the model, capture the correlation between cities:

nearby cities have similar number of infected cases.