If I use Baum-Welch algorithm to best estimate the parameters for hidden Markov model, then I was thinking, instead of using Viterbi algorithm, why can't I just find the most likely hidden state for current time T by finding the most likely hidden state for 1 time sequence before via argmax of product of the forward and backward pass i.e. alpha*beta for T-1, then find the most likely hidden state for T? Would this work? Or, is it necessary that I use Viterbi algorithm?
u can do so, but viterbi reduces time complexity. It does't include the hidden states which are least likely to be in decoding phase.- https://www.youtube.com/watch?v=E3qrns5f3Fw and other 2 consecutive videos would help you more.