forward.py

import numpy as np
import tensorflow as tf


class HMM(object):
    def __init__(self, initial_prob, trans_prob, obs_prob):
        self.N = np.size(initial_prob)
        self.initial_prob = initial_prob
        self.trans_prob = trans_prob
        self.emission = tf.constant(obs_prob)

        assert self.initial_prob.shape == (self.N, 1)
        assert self.trans_prob.shape == (self.N, self.N)
        assert obs_prob.shape[0] == self.N

        self.obs_idx = tf.placeholder(tf.int32)
        self.fwd = tf.placeholder(tf.float64)

    def get_emission(self, obs_idx):
        slice_location = [0, obs_idx]
        num_rows = tf.shape(self.emission)[0]
        slice_shape = [num_rows, 1]
        return tf.slice(self.emission, slice_location, slice_shape)

    def forward_init_op(self):
        obs_prob = self.get_emission(self.obs_idx)
        fwd = tf.mul(self.initial_prob, obs_prob)
        return fwd

    def forward_op(self):
        transitions = tf.matmul(self.fwd, tf.transpose(self.get_emission(self.obs_idx)))
        weighted_transitions = transitions * self.trans_prob
        fwd = tf.reduce_sum(weighted_transitions, 0)
        return tf.reshape(fwd, tf.shape(self.fwd))


def forward_algorithm(sess, hmm, observations):
    fwd = sess.run(hmm.forward_init_op(), feed_dict={hmm.obs_idx: observations[0]})
    for t in range(1, len(observations)):
        fwd = sess.run(hmm.forward_op(), feed_dict={hmm.obs_idx: observations[t], hmm.fwd: fwd})
    prob = sess.run(tf.reduce_sum(fwd))
    return prob

if __name__ == '__main__':
    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]])

    hmm = HMM(initial_prob=initial_prob, trans_prob=trans_prob, obs_prob=obs_prob)

    observations = [0, 1, 1, 2, 1]
    with tf.Session() as sess:
        prob = forward_algorithm(sess, hmm, observations)
        print('Probability of observing {} is {}'.format(observations, prob))