Forward-Backward Algorithm
The forward-backward algorithm is the dynamic-programming recursion that, for a fixed HMM, computes the posterior probability of being in each hidden state at each time step given the whole observation sequence. It works by combining a forward pass (the α recursion, the probability of the observations up to time t and being in state i) with a backward pass (the β recursion, the probability of the remaining observations given state i at time t). It is the inference engine inside the E-step of Baum-Welch Estimation, and it is also what produces “smoothed” per-date state probabilities — the marginal-decoding alternative to Viterbi Decoding. The recursions multiply long chains of small probabilities and underflow on long sequences, so scaling is standard.
Connections
- Baum-Welch Estimation — part-of, source: https://en.wikipedia.org/wiki/Baum%E2%80%93Welch_algorithm
- Viterbi Decoding — relates, source: https://en.wikipedia.org/wiki/Viterbi_algorithm
- Hidden Markov Model Regime Detection — detects_regime, source: https://doi.org/10.1109/5.18626