title: 斯坦福-隨機圖模型-week2.2
tags: note
notebook: 6- 英文課程-9-Probabilistic Graphical Models 1: Representation
---

斯坦福-隨機圖模型-week2.2

習題

1。第 1 個問題

Markov Assumption.

If a dynamic system X satisfies the Markov assumption for all time t≥0, which of the following statements must be true? You may select 1 or more options.

(X(t+1)⊥X(0:(t?1))|X(t))

正確 

(X(t+1)⊥X(0:(t?1)))

未選擇的是正確的 

P(X(t+1))=P(X(t?1)) for all possible values of X

未選擇的是正確的 

第 2 個問題

正確

1 / 1 分
2。第 2 個問題

Independencies in DBNs.

In the following DBN, which of the following independence assumptions are true? You may select 1 or more options.

(O(t)⊥O(t?1))

未選擇的是正確的 
 

(O(t)⊥X(t?1)∣X(t))

正確 

When X(t) is known, there is no active trail from O(t) to any other node in the network.

(X(t+1)⊥X(t)∣X(t?1))

未選擇的是正確的 

(X(t)⊥X(t?1))

未選擇的是正確的 

第 3 個問題

正確

1 / 1 分
3。第 3 個問題

Applications of DBNs.

For which of the following applications might one use a DBN (i.e. the Markov assumption is satisfied)? You may select 1 or more options.

Modeling data taken at different locations along a road, where the data at each location is influenced by only the data at the same location and at the location directly to the East

正確 

Consider each location to be a time slice, and order the locations from East to West. Viewed in this way, this data satisfies the Markov assumption.

Modeling time-series data, where the events at each time-point are influenced by only the events at the one time-point directly before it

正確 
This perfectly satisfies the Markov assumption.

Predicting the probability that today will be a snow day (school will be closed because of the snow), when this probability depends only on whether yesterday was a snow day.

正確 

Let each day be a time slice, and order the days in chronological order. Viewed in this way, this data satisfies the Markov assumption.

Modeling the behavior of people, where a person‘s behavior is influenced by only the behavior of people in the same generation and the people in his/her parents‘ generation.

正確 
Consider each generation to be a time-slice, and this data satisifes the Markov assumption.

第 4 個問題

正確

1 / 1 分
4。第 4 個問題

Plate Semantics.

"Let A and B be random variables inside a common plate indexed by i. Which of the following statements must be true? You may select 1 or more options.

For each i, A(i) and B(i) are not independent.

未選擇的是正確的 

For each i, A(i) and B(i) are independent.

未選擇的是正確的 

There is an instance of A and an instance of B for every i.

正確 

For each i, A(i) and B(i) have edges connecting them to the same variables outside of the plate.

未選擇的是正確的 

第 5 個問題

錯誤
0 / 1 分
5。第 5 個問題

*Plate Interpretation.

Consider the plate model below (with edges removed). Which of the following might a given instance of X possibly represent in the grounded model? (You may select 1 or more options. Keep in mind that this question addresses the variable‘s semantics, not its CPD.)

Whether a specific teacher T is a tough grader

This model does not have any information about how hard of a grader the teacher is, but it does have information about classes and schools.

Whether someone with expertise E taught something of difficulty D at school S

未選擇的是正確的 

Whether a teacher with expertise E taught a course of difficulty D

未選擇的是正確的 

Whether a specific teacher T taught a specific course C at school S

這應該被選擇 

None of these options can represent X in the grounded model


未選擇的是正確的 

第 6 個問題

錯誤
0 / 1 分
6。第 6 個問題

Grounded Plates.

Using the same plate model, now assume that there are s schools, t teachers in each school, and c courses taught by each teacher. How many instances of the Expertise variable are there?

ct

st

Not enough information given to know

這個選項的答案不正確 

st

第 7 個問題

正確

1 / 1 分
7。第 7 個問題

Template Models. Consider the plate model shown below. Assume we are given K Markets, L Products, M Consumers and N Locations. What is the total number of instances of the variable P in the grounded BN?

K?L?M

正確 
There will be one grounded instance of P for each combination of Market, Consumer, and Product. There will be K?L?M of these combinations.

K?L?M?N

(L?M)K

K?(N+(L?M))

第 8 個問題

正確

1 / 1 分
8。第 8 個問題

Template Models. Consider the plate model from the previous question. What might P represent?

Whether a specific product PROD was consumed by consumer C in market M

正確 
In the grounded model, there will be an instance of P for each combination of Product and Consumer, and there is a combination like this for each Market. Thus, we are looking at a random variable that will say something about a specific product, market, and consumer combination. The correct answer is the only one that does this.

Whether a specific product PROD was consumed by consumer C in all markets

Whether a specific product of brand q was consumed by a consumer with age t in a market of type m that is in location a

Whether a specific product PROD was consumed by consumer C in market M in location L

第 9 個問題

正確

1 / 1 分
9。第 9 個問題

Time-Series Graphs. Which of the time-series graphs satisfies the Markov assumption? You may select 1 or more options.

(a)

未選擇的是正確的 

(b)

正確 
(b) is a time-series graph in which all variables in each time slice are independent of all variables in time slices at least 2 time slices before, given all variables in the previous time slice (X(t+1),Y(t+1),Z(t+1)⊥X(t?1),Y(t?1),Z(t?1)|X(t),Y(t),Z(t)).

(c)

未選擇的是正確的 

第 10 個問題

正確

1 / 1 分
10。第 10 個問題

*Unrolling DBNs. Below are 2-TBNs that could be unrolled into DBNs. Consider these unrolled DBNs (note that there are no edges within the first time-point). In which of them will (X(t)⊥Z(t)∣Y(t)) hold for all t, assuming Obs(t) is observed for all t and X(t) and Z(t) are never observed? You may select 1 or more options.

Hint: Unroll these 2-TBNs into DBNs that are at least 3 time steps long (i.e., involving variables from t?1,t,t+1).

(a)

未選擇的是正確的 

(b)

正確 
The independence assumption holds in this network because knowing Y(t) blocks what was the only active trail from X(t) to Z(t).

(c)

未選擇的是正確的 

斯坦福-隨機圖模型-week2.2_