HMMs: generalities
As the name suggests, the series O = (O1,O2 ,O3, .. OT) is observed, while the hidden states S = (S1 ,S2 ,S3 ,……., ST) are not.
S = States {s0,s1,…..,sn}; V = Output alphabet {v0,v1,…..,vm}
A = { aij} = transition probability from si ? sj
B = {bi(j)} = probability outputting vj in state si
What is the most likely sequence of states that produced a given sequence of observations? What is the likelihood of a sequence? Estimate the parameters.
There are elegant algorithms for calculating pr(O|?), arg max? pr(O|?) in certain special cases, and arg maxS pr(S|O,?).