GMM-HMM: Simplifiy / Explicitly refer to literature for implementation #516
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This changes the implementation, so I'm aware that we should be cautious before merging. However, I like that the implementation clearly follows a reference. I've called out in the code where I didn't have any references (nor where I could find a reason for what was going on). |
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@anntzer Thinking of merging this (and the Variational GMM work), and making a release in the coming weeks... thoughts? |
lib/hmmlearn/_emissions.py
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| if 'm' in self.params: # means stats | ||
| stats['m_n'] += np.einsum('ijk,il->jkl', post_comp_mix, X) | ||
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| if 'c' in self.params: # covariance stats | ||
| centered = X[:, None, None, :] - self.means_ |
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From a quick skimming, if I understand correctly (I didn't actually check the formulas), this is something akin replacing var(X) = <(X - <X>)^2> by var(X) = <X^2> - <X>^2? (you don't center the X's anymore)? Do you know if one approach is better/faster/more numerically accurate than the other?
Other than that I guess this looks reasonable? (Again, without actually checking the math...)
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Good question, that I don't immediately know the answer to. Let me look at something.
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Watanabe, Shinji, and Jen-Tzung Chien. Bayesian Speech and Language
Processing. Cambridge University Press, 2015.
which appears simpler than the current implementation. This will make the
VariationalGMMHMM Easier to implement later on.
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Re-implement GMMHMM based upon Newer Reference
Watanabe, Shinji, and Jen-Tzung Chien. Bayesian Speech and Language
Processing. Cambridge University Press, 2015.
which appears simpler than the current implementation. This will make the VariationalGMMHMM Easier to implement later on.