CS228 Weekly Quiz

CS228: Probabilistic Methods in AI
Winter 2008
Weekly Quiz

Overall Score Statistics:
Mean	Median	Mode	Lowest	Highest
84.23%	86%	86% (21)	43%	100%

Score Frequency Table

Frequency of Scores
Score	Number of Students
100%	19
86%	21
71%	11
57%	4
43%	2

Detailed Question/Answer Statistics:

Question 1: Consider the simple Markov chain shown in the figure below. By definition, a stationary distribution for this chain must satisfy which of the following properties? Answers: 1. I, III and V 2. II, IV, and VI 3. I, IV, and V 4. I, IV, and VI 5. None of the above
Type	Answer	Responses	Percent
Correct:	I, IV, and VI	57	100%
Distractor:	I, III and V	0	0%
Distractor:	II, IV, and VI	0	0%
Distractor:	I, IV, and V	0	0%
Distractor:	None of the above	0	0%
Question 2: Which of the following finite state Markov chain structures cannot have a unique statitionary distribution (under any parameterization)? Answers: 1. Markov chain A. 2. Markov chain B. 3. Markov chain C.
Type	Answer	Responses	Percent
Correct:	Markov chain B.	51	89%
Distractor:	Markov chain A.	4	7%
Distractor:	Markov chain C.	2	4%
Question 3: Suppose we are running the Gibbs sampling algorithm on the Bayesian network $X \rightarrow Y \rightarrow Z$ . If the current sample is < x⁰, y⁰, z⁰ >, in a single step of the Gibbs sampler, with what probability will the next sample be < x⁰, y¹, z⁰ >? Answers: 1. P(x⁰, y¹, z⁰) 2. P(y¹ \| x⁰, z⁰) 3. P(y¹ \| x⁰) 4. P(x⁰, z⁰ \| y¹)
Type	Answer	Responses	Percent
Correct:	P(y<sup>1</sup> \| x<sup>0</sup>, z<sup>0</sup>)	52	91%
Distractor:	P(x<sup>0</sup>, y<sup>1</sup>, z<sup>0</sup>)	2	4%
Distractor:	P(y<sup>1</sup> &KPHHASH124; x<sup>0</sup>)	2	4%
Distractor:	P(x<sup>0</sup>, z<sup>0</sup> &KPHHASH124; y<sup>1</sup>)	1	2%
Question 4: Consider the case of exact clique tree inference applied to a DBN. Taking the last clique in the chain to be the root, we need to perform BOTH forward and backward message passing if we wish to solve which inference tasks? Answers: 1. tracking (or filtering) 2. prediction 3. smoothing 4. prediction and smoothing
Type	Answer	Responses	Percent
Correct:	smoothing	50	88%
Distractor:	tracking (or filtering)	0	0%
Distractor:	prediction	0	0%
Distractor:	prediction and smoothing	7	12%
Question 5: In which of the following 2-TBNs will (X^(t) ⊥ Z^(t) \| Y^(t)) hold over time, assuming Obs^(t) is observed for all t and the others are never observed? Answers: 1. (a) 2. (b) 3. (c) 4. All of the above
Type	Answer	Responses	Percent
Correct:	(b)	29	51%
Distractor:	(a)	2	4%
Distractor:	(c)	1	2%
Distractor:	All of the above	25	44%
Question 6: Given the 2-TBN shown below, if we have belief state [0.5, 0.5] at time t, what is the belief state at time t+1? Answers: 1. [0.2, 0.8] 2. [0.8, 0.2] 3. [0.5, 0.5] 4. [0.0, 1.0]
Type	Answer	Responses	Percent
Correct:	[0.5, 0.5]	57	100%
Distractor:	[0.2, 0.8]	0	0%
Distractor:	[0.8, 0.2]	0	0%
Distractor:	[0.0, 1.0]	0	0%
Question 7: Consider the 2-TBN shown below, with O always observed. If we observe O^(t) = 0 at some time t in the unrolled DBN, then which of the following represents the belief state X^(t)? Answers: 1. [1.0, 0.0] 2. [0.2, 0.8] 3. [0.67, 0.33] 4. can't be determined
Type	Answer	Responses	Percent
Correct:	can't be determined	40	70%
Distractor:	[1.0, 0.0]	2	4%
Distractor:	[0.2, 0.8]	0	0%
Distractor:	[0.67, 0.33]	15	26%