Which of the following statements is/are correct in a Bayesian network?
Variable elimination is an approximate inference algorithm
Gibbs sampling is an exact inference algorithm
Variable elimination is used to determine conditional probabilities
Rejection sampling is an approximate inference algorithm
Let's analyse each statement in the context of Bayesian networks and probabilistic inference:
(A) Variable elimination is an approximate inference algorithm
❌ Incorrect
Variable elimination is an exact inference algorithm. It systematically sums out variables to compute exact conditional probabilities.
(B) Gibbs sampling is an exact inference algorithm
❌ Incorrect
Gibbs sampling is a type of Markov Chain Monte Carlo (MCMC) algorithm and provides approximate inference, especially useful in large and complex networks where exact methods are infeasible.
(C) Variable elimination is used to determine conditional probabilities
✅ Correct
The primary purpose of variable elimination is to compute conditional probabilities in a Bayesian network using exact inference.
(D) Rejection sampling is an approximate inference algorithm
✅ Correct
Rejection sampling is an approximate inference method. It generates samples from the prior and rejects those that don’t match the evidence, which is computationally inefficient but still approximate.
✅ Correct options: (C) and (D)
These statements correctly describe inference algorithms in Bayesian networks.