Module posterior_decoding 

Posterior (max-marginal) decoding for discrete HMMs.

Viterbi decoding returns the single jointly-most-probable state path argmax_y P(y | o). Posterior decoding (also “maximum-marginal” or “MPM — maximum posterior marginal” decoding) instead chooses, independently at each time step, the state with the largest marginal posterior:

ŷ_t = argmax_j  γ_t(j) ,   γ_t(j) = P(s_t = j | o_1…o_T)

This minimises the expected number of individually-mislabelled positions (per-symbol error / Hamming risk), whereas Viterbi minimises the whole-sequence 0/1 error. The two can disagree, and the posterior path is not guaranteed to be a legal path (it may traverse a zero-probability transition), so we also expose posterior_path_is_feasible to check it.

The marginals γ come from log-space forward-backward; this module also returns the expected number of correct labels under the model, which is a useful confidence proxy: Σ_t max_j γ_t(j).

Structs

PosteriorDecode

Result of posterior (max-marginal) decoding.

Functions

posterior_decode

Decode an observation sequence by maximum posterior marginal.

posterior_path_is_feasible

Whether a decoded path is feasible under the model — i.e. every visited transition has positive probability and the initial state has positive π.