Finding the Best State Sequence II: The Viterbi Algorithm
The Viterbi algorithm efficiently computes the most likely state sequence.
Commonly, we want to find the most likely complete path, that is: argmaxX P(X|O,?)
To do this, it is sufficient to maximize for a fixed O: argmaxX P(X,O|?)
We define ?j(t) = maxX1..Xt-1 P(X1…Xt-1, o1..ot-1, Xt=j|?) ?j(t) records the node of the incoming arc that led to this most probable path.