Multivariate gaussian emissions

[ucabqll]

Hello,

I have blank inputs and am trying to reconcile the results between IOHMM and hmmlearn.GaussianHMM. Which I assume should be the standard HMM model.

USHMM = UnSupervisedIOHMM(num_states=2, max_EM_iter=200, EM_tol=1e-6)

USHMM.set_models(model_emissions = [OLS()],  
                                    model_transition=CrossEntropyMNL(solver='lbfgs'), 
                                    model_initial=CrossEntropyMNL(solver='lbfgs'))

USHMM.set_inputs(covariates_initial = [], covariates_transition = [], covariates_emissions = [[]])
USHMM.set_outputs([['feature1'],['feature2'],['feature3'],['feature4']] ) #multiple univariate emissions
USHMM.set_data([train_df])

The above gives me almost same results to

import hmmlearn as hmm

model = hmm.GaussianHMM(n_components = 2, covariance_type = "diag")
model.fit(train_df)

This is expected since "diag" implies that all observations are independent and simply individual emissions. The IOHMM model in this case treats it as 4 independent emissions so the results are not too different and are able to reconcile.

However, if I switch to a full multivariate covariate emission

USHMM = UnSupervisedIOHMM(num_states=2, max_EM_iter=200, EM_tol=1e-6)

USHMM.set_models(model_emissions = [OLS()],  
                                    model_transition=CrossEntropyMNL(solver='lbfgs'), 
                                    model_initial=CrossEntropyMNL(solver='lbfgs'))

USHMM.set_inputs(covariates_initial = [], covariates_transition = [], covariates_emissions = [[]])
USHMM.set_outputs([['feature1','feature2','feature3','feature4']])  #multivariate emission
USHMM.set_data([train_df])

The gives me very different results compared to

model = hmm.GaussianHMM(n_components = 2, covariance_type = "full")
model.fit(train_df)

Where "full" means there would be a pxp covariance matrix under each state which is used as emissions to characterise the multivariate gaussian distribution. Is this expected or did I set-up the model incorrectly? Thanks

Best Regards,