numpy Computing Probabilities on HMM - vanilla method and forward algorithm based on `BinRoot/TensorFlow-Book`

vanilla_forward.py

from itertools import product
import numpy as np

# >1 vanilla method, computing expensive
def vanilla(initial_prob, trans_prob, obs_prob, observations):
    it = list((product([0, 1], repeat=len(observations))))
    it = np.array(it)
    # [[0 0 0 0 0]
    #  [0 0 0 0 1]
    #  [0 0 0 1 0]
    #       ...
    #  [1 1 0 1 1]
    #  [1 1 1 0 0]
    #  [1 1 1 0 1]
    #  [1 1 1 1 0]
    #  [1 1 1 1 1]]

    prob_o = obs_prob[it, observations]
    prob_o = np.prod(prob_o, axis=1)
    prob_i = initial_prob[it[:, 1], 0]
    for i in range(0, len(observations)-1):
        x = it[:, i]
        y = it[:, i+1]
        prob_i *= trans_prob[x, y]

    prob = np.sum(prob_i * prob_o)
    return prob


# 2 TODO forward algorithm
def forward(initial_prob, trans_prob, obs_prob, observations):
    fwd = initial_prob * obs_prob[:, observations[0]:observations[0]+1]
    for obs in observations[1:]:
        fwd = np.dot(trans_prob.T, fwd) * obs_prob[:, obs:obs+1]
    return np.sum(fwd)

if __name__ == '__main__':
    """
    states = ('Rainy', 'Sunny')
    observations = ('walk', 'shop', 'clean')
    start_probability = {'Rainy': 0.6, 'Sunny': 0.4}
    transition_probability = {
                            'Rainy : {'Rainy': 0.7, 'Sunny': 0.3},
                            'Sunny': {'Rainy': 0.4, 'Sunny': 0.6},
                                }
    emission_probability = {
                            'Rainy : {'walk': 0.1, 'shop': 0.4, 'clean': 0.5},
                            'Sunny': {'walk': 0.6, 'shop': 0.3, 'clean': 0.1},
                            }
    """

    initial_prob = np.array([[0.6],
                             [0.4]])
    trans_prob = np.array([[0.7, 0.3],
                           [0.4, 0.6]])
    obs_prob = np.array([[0.5, 0.4, 0.1],
                         [0.1, 0.3, 0.6]])
    observations = np.array([0, 1, 1, 2, 1])

    print('valina: {:.6f}'.format(vanilla(initial_prob, trans_prob, obs_prob, observations)))
    print('forward: {:.6f}'.format(forward(initial_prob, trans_prob, obs_prob, observations)))

# valina: 0.004412
# forward: 0.004642