On the accuracy of the Viterbi alignment
This work addresses a specific issue in statistical modeling for researchers using hidden Markov models, but it appears incremental as it modifies an existing alignment method.
The paper tackles the problem of the Viterbi alignment in hidden Markov models behaving untypically by passing unexpected states, and proposes an iterative procedure to improve it, showing it is more efficient and advantageous compared to a bunch approach.
In a hidden Markov model, the underlying Markov chain is usually hidden. Often, the maximum likelihood alignment (Viterbi alignment) is used as its estimate. Although having the biggest likelihood, the Viterbi alignment can behave very untypically by passing states that are at most unexpected. To avoid such situations, the Viterbi alignment can be modified by forcing it not to pass these states. In this article, an iterative procedure for improving the Viterbi alignment is proposed and studied. The iterative approach is compared with a simple bunch approach where a number of states with low probability are all replaced at the same time. It can be seen that the iterative way of adjusting the Viterbi alignment is more efficient and it has several advantages over the bunch approach. The same iterative algorithm for improving the Viterbi alignment can be used in the case of peeping, that is when it is possible to reveal hidden states. In addition, lower bounds for classification probabilities of the Viterbi alignment under different conditions on the model parameters are studied.