python - 输入输出隐马尔可夫模型在 Python 中的实现

Question

我正在尝试使用输入输出架构实现隐马尔可夫模型，但我找不到任何好的 python 实现。

任何人都可以共享 Python 包来考虑 HMM 的以下实现。

允许连续排放。 允许协变量的功能(即 I/O HMM 中的自变量)。

此刻，我正在努力寻找相同的 python 实现。

我在hmmlearn中找不到相关的例子。

以下是我测试过的几个库:

hmmlearn:hmmlearn 允许将多个特征传递给发射/观察，但不支持包含协变量(即自变量)。

hmms:不支持添加连续排放的功能，也不支持添加自变量。

IOHMM:我能够使用此库训练 HMM 模型，但无法找到训练模型后进行预测的文档。

因此，我正在寻找符合目的的软件包。

from IOHMM import UnSupervisedIOHMM
from IOHMM import OLS, DiscreteMNL, CrossEntropyMNL, forward_backward

SHMM = UnSupervisedIOHMM(num_states=3, max_EM_iter=200, EM_tol=1e-6)

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

SHMM.set_inputs(covariates_initial = [], covariates_transition = [], covariates_emissions = [['Insulin']])


SHMM.set_outputs([['Glucose']])

SHMM.set_data([data])

SHMM.train() 

经过上述训练，我无法弄清楚如何获得发射概率和隐藏状态序列。

Answer 1

引用“https://web.ece.ucsb.edu/Faculty/Rabiner/ece259/Reprints/tutorial%20on%20hmm%20and%20applications.pdf”和库“https://hmmlearn.readthedocs.io/en/latest/”，我找到了这个解决方案:

1- 通过 log_gamma(后验分布):

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-维特比算法:

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)]