GATE DA 2024 Set 1 — Question 24
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Artificial Intelligence → Uncertainty → Conditional Independence
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Question
Consider five random variables and whose joint distribution satisfies:Which ONE of the following statements is FALSE?
Correct answer
(C) U and V are conditionally independent given W
Solution
The given joint distribution factorization implies the following Bayesian Network structure:
- and are independent parent nodes pointing to ().
- is a parent to both and ().
1.Option (A): . The path is . Since is observed (given), this linear path is blocked. True.
2.Option (B): . The path is . Since is observed, this linear path is blocked. True.
3.Option (C): . The path is . This is a v-structure (collider) at . In a v-structure, the parents are marginally independent but become dependent when the common child () is observed (phenomenon known as explaining away). Thus, and are NOT conditionally independent given . This statement is FALSE.
4.Option (D): . The path is . This is a fork at . Since is observed, the path is blocked. True.
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