The Viterbi algorithm is a dynamic programming algorithm to find optimal paths in the hidden space of an hidden Markov model. It has wide applications, including for Natural Language Processing tasks such as Part-of-Speech tagging. Problem and algorithm descriptions are given below.
Compile and link example.cpp and viterbi.cpp, e.g.:
$ g++ example.cpp viterbi.cpp -o example
$ ./example
You will be prompted to insert the data defining the model, and the input path in observable space.
Let be an hidden Markov model, where:
: hidden space of finite cardinality
: observable space of finite cardinality
: transition matrix
: emission matrix
: start probabilities
Given a path
in observable space,
find a corresponding path
in hidden space
maximizing the conditional probability
or, equivalently, the joint probability
The Viterbi algorithm is a dynamic programming procedure to solve the problem above. It is based on the optimization subproblems:
which can be solved recursively. For more info and pseudocode, c.f. the Wikipedia article.