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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See also

  • 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.