2. (15 points) Consider sampling-based inference for the Hidden Markov Model (HMM) in
Figure 2 where Zt are unobservable state variables and Xt are observable evidence variables.
(a) (5 points) Describe the rejection sampling algorithm. Would you use rejection sampling
for the given HMM, why or why not?
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(b) (5 points) Consider likelihood weighting-based inference for the given HMM. Assuming
X13 = {T,T, T}, what is the weight on the following two samples 21! = (F, F, F} and
2? = (T,T,T)?
(c) (5 points) Describe the particle filtering algorithm, clearly discussing the three steps
involved. Would you use particle filtering for the given HMM, why or why not?
1. Extra Credit (5 points) This question considers the value of perfect information (VPI)
VPIE(E;) which evaluates the value of additional information E; given existing information
E. Show that VPI is non-negative, i.e., VPIE(E;) ≥ 0, Vj, E.
1. (15 points) Below is a Bayesian network. Use variable elimination to find P(a, 7d). Note,
you must find the exact probability (you cannot leave it in terms of some value times a).
2. (15 points) Consider sampling-based inference for the Hidden Markov Model (HMM) in
Figure 2 where Zt are unobservable state variables and Xt are observable evidence variables.
(a) (5 points) Describe the rejection sampling algorithm. Would you use rejection sampling
for the given HMM, why or why not?
(b) (5 points) Consider likelihood weighting-based inference for the given HMM. Assuming
= {T,T, T’}, what is the weight on the following two samples 21
= {F. F. F) and
= {T.T.T??
(c) (5 points) Describe the particle filtering algorithm, clearly discussing the three steps
involved. Would you use particle filtering for the given HMM, why or why not?
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