给定下图所示的贝叶斯网络，可以推测出什么？

（选择所有适用的选项。）

（图的布局如下：从节点 A 到节点 B 有一个定向边，节点 B 到节点 D 和节点 E 有多个定向边，节点 C 到节点 E 有一个定向边。）

Given a Bayesian Network illustrated in the following figure, what can be inferred?

(Select all that apply.)

(There is a graph with the following configuration: there is a directed edge from Node A to Node B, directed edges from Node B to Node D and Node E, and there is a directed edge from Node C to Node E.)

Question

给定下图所示的贝叶斯网络，可以推测出什么？

（选择所有适用的选项。）

（图的布局如下：从节点 A 到节点 B 有一个定向边，节点 B 到节点 D 和节点 E 有多个定向边，节点 C 到节点 E 有一个定向边。）

Given a Bayesian Network illustrated in the following figure, what can be inferred?

(Select all that apply.)

(There is a graph with the following configuration: there is a directed edge from Node A to Node B, directed edges from Node B to Node D and Node E, and there is a directed edge from Node C to Node E.)

BlackTom AI · Accepted Answer

D-separation rule for a chain A → B → D: conditioning on the middle node B blocks that path, so A and D become independent given B.

1) Relevant knowledge points and concepts
- d-separation: three basic structures (chain X→Y→Z, fork X←Y→Z, collider X→Y←Z) determine conditional independence.
- For a chain or a fork, conditioning on the middle node blocks the path (makes the ends independent). For a collider, conditioning on the collider (or its descendant) opens the path (makes the parents dependent); without conditioning the parents are independent.
- Parent-child relationship: a child is generally dependent on its parent (marginal dependence).

2) Step-by-step reasoning for each candidate statement
- "Given B, D is independent of A." Consider the only path A → B → D (a chain). If B is observed/conditioned, that chain is blocked by d-separation. Therefore A ⟂ D | B. So this statement is true.
- "C and E are dependent." There is a direct edge C → E (C is a parent of E). A parent and its child are generally dependent (E’s distribution depends on C), so C and E are marginally dependent. Thus this statement is true.

3) Intermediate steps (explicit path checking)
- For A and D: paths = {A → B → D}. Condition on B: chain blocked → independence.
- For C and E: direct edge C → E means no blocking; marginal dependence holds.

4) Why the correct answers are correct
- Conditioning on B blocks A→B→D, removing influence of A on D once B is known.
- C directly influences E, so observations of E carry information about C (and vice versa).

5) Why the other options are incorrect
- "B is independent of A." False: there is a direct edge A → B, so B depends on A.
- "E is independent of A." False: A can influence E via A → B → E (a chain). Marginally A and E are dependent (only if you condition on B would they be independent).

6) Conclusion
The correct inferences are: (1) Given B, D is independent of A. (2) C and E are dependent. These match the provided answers.

类似问题

贝叶斯网络不能是有向，即应为无向图。 A Bayesian Network cannot be directed, i.e., it should be an undirected graph.

哪一项陈述最准确地描述了贝叶斯网络的目的？Which statement is most accurate about the purpose of Bayesian networks?

Given a Bayesian network as shown below, Fill in the following blanks. The probability of the alarm sounding when there is an earthquake but no a burglary is [blank1] (keep three decimal places).

Given a Bayesian network as shown below, Fill in the following blanks. The probability of the event in which Mary did not call, given the alarm does not sound, is [Fill in the blank] and the probability of having a Burglary is [Fill in the blank] (keep three decimal places).

Given a Bayesian network as shown below, Fill in the following blank. The probability of the event in which there is no alarm sound when there is a Burglary but no earthquake is [blank1] (keep three decimal places).

Given a Bayesian network as shown below, Fill in the following blanks. The probability of the alarm sounding when there is neither a burglary nor an earthquake is [blank1] (keep three decimal places).

For a Bayesian network, match the components on the left-hand-side to the explanations on the right-hand-side. 1: parent node 2: an edge 3: arrow of an edge

Given a Bayesian network as shown below, Fill in the following blanks. The probability of the event in which John did not call, given the alarm does not sound, is [Fill in the blank] and the probability of having an earthquake is [Fill in the blank] (keep three decimal places).

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