Viterbi Algorithm

The Viterbi algorithm is a dynamic programming algorithm used for finding the most likely sequence of hidden states – called the Viterbi path – that results in a sequence of observed events, especially in the context of Markov information sources and Hidden-Markov-Models.

Given an HMM, the Viterbi algorithm can be used to determine the most likely sequence of hidden states that produces a given sequence of observations. This is particularly useful in many applications like speech recognition, computational biology (for gene prediction), and decoding convolutional codes in wireless communication.

The Viterbi algorithm is significantly more efficient than brute force methods for finding the most likely sequence of hidden states in a Hidden Markov Model due to its dynamic programming approach. This results in an $O(L*P^{2})$ time complexity rather than an $O(P^{L})$ time complexity, where $L$ is the length of the sequence and $P$ is the number of hidden states.