GATE 2025 DA Q.26: solution and answer

Official answer: C, DSource: Official answer key, GATE 2025 DA (IIT Roorkee)

1. Inference in a Bayesian network means computing a posterior such as $P(X\mid \mathbf{e})$ from the joint distribution ${\prod }_{i}P(X_i\mid \text{Parents}(X_i))$. Inference algorithms are either exact or approximate.

2. (A) Variable elimination sums out the hidden variables one at a time and reuses intermediate factors. It returns the exact posterior, so it is an exact algorithm, not an approximate one. (A) is false.

3. (B) Gibbs sampling is a Markov chain Monte Carlo method. It repeatedly resamples one non-evidence variable at a time given its Markov blanket. Its estimates converge to the true posterior only in the limit of many samples, so it is approximate. (B) is false.

4. (C) Variable elimination computes $P(Q\mid \mathbf{e})=\alpha {\sum }_{\text{hidden}}\prod \text{factors}$. It sums out the hidden variables and then normalises, so it is used to determine conditional probabilities. (C) is true.

5. (D) Rejection sampling draws samples from the prior, discards those that disagree with the evidence, and estimates the query from the samples that remain. It is a sampling method, so it is approximate. (D) is true.

6. Correct statements: (C) and (D).