Referring to "https://web.ece.ucsb.edu/Faculty/Rabiner/ece259/Reprints/tutorial%20on%20hmm%20and%20applications.pdf" and library "https://hmmlearn.readthedocs.io/en/latest/" I have found this solution:

1- Through log_gamma (posterior distribution):

state_sequences = []
for i in range(100):
    for j in range(lengths[i]):
        state_sequences.append(np.argmax(np.exp(SHMM.log_gammas[i])[j]))
pred_state_seq = [state_sequences[df[df['unit'] == i].index[0]:df[df['unit'] == i].index[-1] + 1] for i in
                              range(1, df_A['unit'].max() + 1)]

2- Viterbi Algorithm:

from hmmlearn import _hmmc

transmat = np.empty((num_states, num_states))
for i in range(num_states):
    transmat = np.concatenate((transmat, np.exp(SHMM.model_transition[i].predict_log_proba(np.array([[]])))))
transmat = transmat[num_states:]

startprob = np.exp(SHMM.model_initial.predict_log_proba(np.array([[]]))).squeeze()


def log_mask_zero(a):
    """
    Compute the log of input probabilities masking divide by zero in log.

    Notes
    -----
    During the M-step of EM-algorithm, very small intermediate start
    or transition probabilities could be normalized to zero, causing a
    *RuntimeWarning: divide by zero encountered in log*.

    This function masks this unharmful warning.
    """
    a = np.asarray(a)
    with np.errstate(divide="ignore"):
        return np.log(a)


def _do_viterbi_pass(framelogprob):
    n_samples, n_components = framelogprob.shape
    state_sequence, logprob = _hmmc._viterbi(n_samples, n_components, log_mask_zero(startprob),
                                             log_mask_zero(transmat), framelogprob)
    return logprob, state_sequence


def _decode_viterbi(X):
    framelogprob = SHMM.log_Eys[X]
    return _do_viterbi_pass(framelogprob)


def decode():
    decoder = {"viterbi": _decode_viterbi}["viterbi"]
    logprob = 0
    sub_state_sequences = []
    for sub_X in range(100):
        # XXX decoder works on a single sample at a time!
        sub_logprob, sub_state_sequence = decoder(sub_X)
        logprob += sub_logprob
        sub_state_sequences.append(sub_state_sequence)
    return logprob, np.concatenate(sub_state_sequences)


def predict():
    """
    Find most likely state sequence corresponding to ``X``.

    Parameters
    ----------
    X : array-like, shape (n_samples, n_features)
        Feature matrix of individual samples.
    lengths : array-like of integers, shape (n_sequences, ), optional
        Lengths of the individual sequences in ``X``. The sum of
        these should be ``n_samples``.

    Returns
    -------
    state_sequence : array, shape (n_samples, )
        Labels for each sample from ``X``.
    """
    logprob, state_sequence = decode()
    return logprob, state_sequence


_, state_seq = predict()

pred_state_seq = [state_seq[df[df['unit'] == i].index[0]:df[df['unit'] == i].index[-1] + 1] for i in
                  range(1, df_A['unit'].max() + 1)]

building on top of this, using log-gamma can decode the sequence of hidden states.

To fit testing data, one could set the data using the testing set and re-run the E-step to get a new set of log-gammas. (this does not update the transitions and emissions, so would be still using the trained transitions and emissions). Using these new log-gammas, re-run the decoding function as above.

USHMM.set_data([testing]) #this initializes the new set of log-gammas
USHMM.E_step() #fitting the log-gammas to the testing set

how to do prediction? #20

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