Initialize.

Get a maximum likelihood estimation of transition and emmission.

Arguments:

• transition_counts — A dictionary with the total number of counts of transitions between two states.
• emissions_counts — A dictionary with the total number of counts of emmissions of a particular emission letter by a state letter.

This then returns the maximum likelihood estimators for the transitions and emissions, estimated by formulas 3.18 in Durbin et al::

a_{kl} = A_{kl} / sum(A_{kl'})
e_{k}(b) = E_{k}(b) / sum(E_{k}(b'))

Returns: Transition and emission dictionaries containing the maximum likelihood estimators.

Calculate the log likelihood of the training seqs.

Arguments:

• probabilities — A list of the probabilities of each training sequence under the current parameters, calculated using the forward algorithm.

Calculate the maximum likelihood estimator.

This can calculate maximum likelihoods for both transitions and emissions.

Arguments:

• counts — A dictionary of the counts for each item.

See estimate_params for a description of the formula used for calculation.