Why use full covariance in TDE-HMM model?

[FreektenDoesschate]

Dear Diego,

Thanks for your answer on my previous question. Another thing I didn't fully understand is the following:

In the TDE-HMM model, PCA is used on the 'time embedded' space. Subsequently, an HMM with a mv gaussian emission model is run, with zero mean and full covariance matrix (if I understand correctly?). If this is the case, wouldn't the covariance between the different (PCA) signals be near 0, given the signals are orthogonal? So why train the hmm on the covariance?

Thanks again.

Best, Freek

[vidaurre]

Hi Freek,

The covariance across the full data set is zero in the off-diagonal elements for a PCA decomposition; but there can be transient departures from that which is what the HMM is aiming at capturing.

Hope that helps