title: 斯坦福-随机图模型-week2.2
tags: note
notebook: 6- 英文课程-9-Probabilistic Graphical Models 1: Representation
---
斯坦福-随机图模型-week2.2
习题
1。第 1 个问题
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))
正确 (X(t+1)⊥X(0:(t−1)))
未选择的是正确的 P(X(t+1))=P(X(t−1)) for all possible values of X
未选择的是正确的 第 2 个问题
正确1 / 1 分
2。第 2 个问题
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))
未选择的是正确的 (O(t)⊥X(t−1)∣X(t))
正确
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))
未选择的是正确的 (X(t)⊥X(t−1))
未选择的是正确的 第 3 个问题
正确1 / 1 分
3。第 3 个问题
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
正确
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
正确
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.
正确
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.
正确
Consider each generation to be a time-slice, and this data satisifes the Markov assumption.第 4 个问题
正确1 / 1 分
4。第 4 个问题
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.
未选择的是正确的 For each i, A(i) and B(i) are independent.
未选择的是正确的 There is an instance of A and an instance of B for every i.
正确 For each i, A(i) and B(i) have edges connecting them to the same variables outside of the plate.
未选择的是正确的 第 5 个问题
错误
0 / 1 分
5。第 5 个问题
*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
未选择的是正确的 Whether a teacher with expertise E taught a course of difficulty D
未选择的是正确的 Whether a specific teacher T taught a specific course C at school S
这应该被选择
None of these options can represent X in the grounded model
未选择的是正确的 第 6 个问题
错误
0 / 1 分
6。第 6 个问题
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
这个选项的答案不正确 st
第 7 个问题
正确1 / 1 分
7。第 7 个问题
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
正确
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 个问题
正确1 / 1 分
8。第 8 个问题
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
正确
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 个问题
正确1 / 1 分
9。第 9 个问题
Time-Series Graphs. Which of the time-series graphs satisfies the Markov assumption? You may select 1 or more options.
(a)
未选择的是正确的 (b)
正确
(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)
未选择的是正确的 第 10 个问题
正确1 / 1 分
10。第 10 个问题
*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)
未选择的是正确的 (b)
正确
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)
未选择的是正确的 