Add Method to get n_params and AIC/BIC for GaussianHMM

[richy1996]

Reference Issues/PRs

None

What does this implement/fix? Explain your changes.

• Adds the methods _n_parameters, bic, and aic to the GaussianHMM class.
• Essentially I copied the implementation from sklearn implementation for gaussian mixture model

Any other comments?

I haven't fully implemented the methods for the other classes, e.g. GMMHMM etc. but it's in the works.

[blckmaxima]

Thank you!

• Adding an example of aic/bic being used for model selection would be great.
• Incorporate these methods into the existing test suites.

[anntzer]

This seems related to _get_n_fit_scalars_per_param, and should perhaps also depend on what exactly gets fitted between startprob, transmat, and the emission model?

[richy1996]

Yes it is related to that it seems. Sorry but can you elaborate on the part regarding what gets fitted?

[blckmaxima]

Can we reuse some of https://github.com/hmmlearn/hmmlearn/blob/main/lib/hmmlearn/hmm.py#L184 (_get_n_fit_scalars_per_param) here ?

[richy1996]

yeah it seems so, would you like me to incorporate _get_n_fit_scalars_per_param into aic/bic and scrap _n_parameters?

[blckmaxima]

I think that makes sense, and is inline with what I think @anntzer was thinking too.

[blckmaxima]

We've added aic() and bic() in a separate MR: #500