iTechX

Question 1

?/? point (graded)

$X_2$	$B'(X_2)$
0	[q1.1]
1	[q1.2]

$X_2$	$P(E_2=b\|X_2)B'(X_2)$
0	[q1.3]
1	[q1.4]

$X_2$	$B(X_2)$
0	[q1.5]
1	[q1.6]

q1.1 =

q1.2 =

q1.3 =

q1.4 =

q1.5 =

q1.6 =

Question 2

?/? point (graded)

Your answers will be evaluated to 4 decimal places.

coefficient	value
a	[q2.1]
b	[q2.2]
c	[q2.3]
d	[q2.4]

$X_{\infty}$	$\tilde{B}(X_{\infty})$
0	[q2.5]
1	[q2.6]

q2.1 =

q2.2 =

q2.3 =

q2.4 =

q2.5 =

q2.6 =

Question 3

?/? point (graded)

Consider this HMM.

The prior probability $P(X_0)$ , dynamics model $P( X_{t+1} | X_t )$ , and sensor model $P(E_t|X_t)$ are as follows:

If the $E_1 = a, E_2 = b, E_3 = c$ , what is the most likely explanation $X^*_{1:3} = argmax P(X_{1:3} | E_{1:3} )$

Question 4

?/? point (graded)

The Viterbi algorithm finds the most probable sequence of hidden states $X_{1:T}$ , given a sequence of observations $e_{1:T}$ . For the HMM structure above, which of the following probabilities are maximized by the sequence of states returned by the Viterbi algorithm? Select all correct option(s).

Question 5

?/? point (graded)

Consider the following graph, where W₁ and W₂ can be either be R or S, and I₁ and I₂ can be either be T or F:

The conditional probability distributions are given by:

Now we want to try approximate inference through sampling. Applying likelihood weighting, suppose we generate the following six samples given the evidence I₁ = T and I₂ = F: