Likelihood Weighting
Likelihood Weighting is an approximate inference method for Bayes Nets that avoids sample rejection entirely by fixing evidence variables to their observed values and weighting each sample by how likely the evidence is given the sampled variables.
Each sample is generated as follows:
- Non-evidence variables are sampled normally from their CPTs.
- Evidence variables are not sampled; instead, the sample receives a weight
where the weight is only decided by the likelihoods of evidence variables (hence likelihood weighting).The posterior is estimated by weighted counts:
This ensures that every CPT participates in the probability calculation, correcting the bias introduced by fixing evidence.
Advantage: significantly more efficient than prior or rejection sampling when evidence is rare.
Limitation: weights can become extremely small when there is a long chain of evidence, leading to high variance.