### Abstract

This entry contains a formalization of hidden Markov models [3] based on Johannes Hölzl's formalization of discrete time Markov chains [1]. The basic definitions are provided and the correctness of two main (dynamic programming) algorithms for hidden Markov models is proved: the forward algorithm for computing the likelihood of an observed sequence, and the Viterbi algorithm for decoding the most probable hidden state sequence. The Viterbi algorithm is made executable including memoization. Hidden markov models have various applications in natural language processing. For an introduction see Jurafsky and Martin [2].

### License

BSD License

### Topics

- Mathematics/Probability theory
- Computer science/Algorithms

### Session Hidden_Markov_Models

- Auxiliary
- Hidden_Markov_Model
- HMM_Implementation
- HMM_Example

### Depends on

- Markov Models
- Monadification, Memoization and Dynamic Programming

## Cite

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Hidden_Markov_Models-AFP

    @article{Hidden_Markov_Models-AFP,
      author  = {Simon Wimmer},
      title   = {Hidden Markov Models},
      journal = {Archive of Formal Proofs},
      month   = {May},
      year    = {2018},
      note    = {\url{https://isa-afp.org/entries/Hidden_Markov_Models.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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