Hi, so I am currently planning on training a layered Hidden Markov Model.
I have 3 stages with the following structures.
The first stage is a 3-state HMM with the
State X: can emit insertion errors State Y: can emit deletion errors State M: can emit either a substitution error or a no error(match)
The second stage is a 2 state HMM with
State Y: can emit deletion errors State M: can emit either a substitution error or a no error(match)
The third stage is a 3-state HMM with the same structure as the first stage but not necessarily the same parameter values.
State X: can emit insertion errors State Y: can emit deletion errors State M: can emit either a substitution error or a no error(match)
In both stage 1 and 3, the states M and X, M and Y can communicate but X and Y cannot communicate.
The HMMs in stage 1,2 and 3 emit error sequences. When these error sequences are applied to the first stage it will output another sequence with some errors. This process is repeated for the second stage where which will emit another sequence with errors and again likewise for the third stage.
Now I have the data for the original sequence before being passed through the error channel and the sequence that comes out of the channel(after the third stage).
Is there any efficient way to find all the model parameters(HMM) so that we can maximise the likelihood of observing the data.
Here is a detailed example of the problem.
The sequence before being passed through the channel.
ACGGTC
Stage 1 HMM emits the following errors.
No error, insertion of A, No error, No error, No error
which results in the following sequence after stage 1.
ACAGGTC
Now for simplicity sake let the error sequence for stages 2 and 3 emit no error. Then we shall obtain the following output sequence after being passed through stages 2 and 3.
ACAGGTC
So I have access to this final data ACAGGTC and the original sequence ACGGTC. GIven these data, how do I efficiently compute the HMM model parameter?
