Re: some hidden markov understanding questions...

3. With continious HMMs I have a problem with the covariance matrices [snip]

I assume that your problem stems from the fact that your covariance
matrix is ill conditioned (e.g. you need to invert it). Adding to the
diagonal of a covariance matrix can work, but you are correct in saying
that it's rather unprincipled (e.g. how do you know what to add?). In
the context of Gaussian Mixture Models, I found that taking the pseudo
inverse worked quite well. This is, IIRC, equivalent to taking the
inverse of the matrix that would be reconstructed from the eigenvectors
of the original matrix which have non-zero eigenvalues (think PCA). You
can do this in Matlab using pinv (though when I used their built-in
version it was slow enough to make me write an optimised mex function
for covariance matrices).

Hope that helps

C

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