Q1. Which of the following is true about the MAP (Maximum a posteriori estimate) estimation learning framework?
a. It is equivalent to Maximum Likelihood learning with infinite data
b. It is equivalent to Maximum Likelihood learning if P(θ) is independent of θ
c. it can be used without having any prior knowledge about the parameters
d. The performance of MAP is better with dense data compared to sparse data
Answer:- a, d
Q2. What facts are true about smoothing?
- Smoothed estimates of probabilities fit the evidence better than un-smoothed estimates.
- The process of smoothing can be viewed as imposing a prior distribution over the set of parameters.
- Smoothing allows us to account for data which wasn’t seen in the evidence.
- Smoothing is a form of regularization which prevents overfitting in Bayesian networks.
Answer: a, c
Q3. Consider three boolean variables X, Y, and Z. Consider the following data:
There can be multiple Bayesian networks that can be used to model such a universe. Assume that we assume a Bayesian Network as shown below:
If the value of the parameter P(¬z|x,¬y) is m/n such that m and n have no common factors. Then, what is the value of m+n? Assume add-one smoothing.
Q4. Consider the following Bayesian Network from which we wish to compute P(x|z) using rejection sampling:
Q5. Assume that we toss a biased coin with heads probability p, 100 times. We get heads 66 times out of 100. If the Maximum Likelihood estimate of the parameter p is m/n where m and n don’t have common factors,
then the value of m+n is?
Q6. Now, assume that we had a prior distribution over p as shown below:
Q7. Which of the following task(s) are not suited for a goal based agent?
Answer: b, c
Q8. Which of the following are true ?
- Rejection sampling is very wasteful when the probability of getting the evidence in the samples is very low.
- We perform conditional probability weighting on the samples while doing Gibbs Sampling in MCMC algorithm since we have already fixed the evidence variables.
- We perform random walk while sampling variables in Likelihood Weighting, MCMC with Gibbs sampling, but not in Rejection sampling.
- Likelihood Weighting functions well if we have many evidence wars with some samples having nearly all the total weight
Q9. Consider the following Bayesian Network:
- P(C|A,B,D,F,E) = α. P(C|A). P(C|B)
- P(C|A,B,D,F,E) = α. P(C|A,B)
- P(C|A,B,D,F,E) = α. P(C|A,B). P(D|C,E)
- P(C|A,B,D,F,E) = α. P(C|A,B,D,E)
Answer: b, c
Q10. Which of the following options are correct about the environment of Tic Tac Toe?
- Fully observable
Answer: a, c