The GATE Grind

GATE 2024 DA – Question 24

Artificial Intelligence · Reasoning under uncertainty: Bayesian networks and inference · 1 mark · Multiple choice

Consider five random variables $U, V, W, X$, and $Y$ whose joint distribution satisfies:
$P(U, V, W, X, Y) = P(U)P(V)P(W|U, V)P(X|W)P(Y|W)$

Which ONE of the following statements is FALSE?

  1. Y is conditionally independent of V given W
  2. X is conditionally independent of U given W
  3. U and V are conditionally independent given W
  4. Y and X are conditionally independent given W

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Show answer and explanation

Correct answer: (C) U and V are conditionally independent given W

Explanation

The network has the edges $U \to W$, $V \to W$, $W \to X$ and $W \to Y$. $W$ blocks every path from $X$ or $Y$ to $U$ and $V$, and from $X$ to $Y$, so A, B and D are true. $U$ and $V$ are independent as parents of $W$, but $W$ is a collider between them, and conditioning on a collider makes them dependent. So C is false.