HMM inference as belief propagation
The forward-backward algorithm for computing posterior marginals in an HMM can be viewed as a special case of sum-product belief propagation. Similarly, the Viterbi algorithm for computing the most likely state sequence can be viewed as a special case of max-product belief propagation.
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→ Pattern Recognition and Machine Learning
A textbook for a graduate machine learning course, with a focus on Bayesian methods.
Location: Section 13.2.3, pages 625-627
- Following on this result, the Baum-Welch algorithm for learning HMM parameters can be seen as a [speical case](baum_welch_as_em) of [Expectation-Maximization](expectation_maximization) .
- Kalman smoothing can be seen as a [speical case](kalman_as_bp) of the forward-backward algorithm, hence a special case of BP.