斯坦福-随机图模型-week1.1_

斯坦福-随机图模型-week1.1

练习

1。第 1 个问题

Factor product.

Let X,Y and Z be binary variables.

If ϕ1(X,Y) and ϕ2(Y,Z) are the factors shown below, compute the selected entries (marked by a '?') in the factor ψ(X,Y,Z)=ϕ1(X,Y)⋅ϕ2(Y,Z), giving your answer according to the ordering of assignments to variables as shown below.

Separate each of the 3 entries of the factor with spaces, e.g., an answer of

0.1 0.2 0.3

means that ψ(1,1,1)=0.1, ψ(1,2,1)=0.2, and ψ(2,2,2)=0.3. Give your answers as exact decimals without any trailing zeroes.

0.16 0.45 0.6

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1
point

2。第 2 个问题

Factor reduction.

Let X,Z be binary variables, and let Y be a variable that takes on values 1, 2, or 3.

Now say we observe Y=1. If ϕ(X,Y,Z) is the factor shown below, compute the missing entries of the reduced factor ψ(X,Z) given that Y=1, giving your answer according to the ordering of assignments to variables as shown below.

As before, separate the 4 entries of the factor by spaces.

14 60 4 59

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第 3 个问题1
point

3。第 3 个问题

Properties of independent variables.

Assume that A and B are independent random variables. Which of the following options are always true? You may select 1 or more options.

P(B|A)=P(B)

P(A|B)=P(A)

P(A)+P(B)=1

P(A)=P(B)
1
point

4。第 4 个问题

Factor marginalization.

Let X,Z be binary variables, and let Y be a variable that takes on values 1, 2, or 3.

If ϕ(X,Y,Z) is the factor shown below, compute the entries of the factor

ψ(Y,Z)=∑Xϕ(X,Y,Z),

giving your answer according to the ordering of assignments to variables as shown below.

Separate the 4 entries of the factor with spaces, and do not add any extra trailing or leading zeroes or decimal points.

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108 135 79 141