hmm.py

import numpy as np
import tensorflow as tf


# initial parameters can be learned on training data
# theory reference https://web.stanford.edu/~jurafsky/slp3/8.pdf
# code reference https://phvu.net/2013/12/06/sweet-implementation-of-viterbi-in-python/
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.obs_prob = obs_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 self.obs_prob.shape[0] == self.N
        self.obs = tf.placeholder(tf.int32)
        self.fwd = tf.placeholder(tf.float64)
        self.viterbi = 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)
        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)))
        weighted_transitions = transitions * self.trans_prob
        fwd = tf.reduce_sum(weighted_transitions, 0)
        return tf.reshape(fwd, tf.shape(self.fwd))

    def decode_op(self):
        transitions = tf.matmul(self.viterbi, tf.transpose(self.get_emission(self.obs)))
        weighted_transitions = transitions * self.trans_prob
        viterbi = tf.reduce_max(weighted_transitions, 0)
        return tf.reshape(viterbi, tf.shape(self.viterbi))

    def backpt_op(self):
        back_transitions = tf.matmul(self.viterbi, np.ones((1, self.N)))
        weighted_back_transitions = back_transitions * self.trans_prob
        return tf.argmax(weighted_back_transitions, 0)


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

def viterbi_decode(sess, hmm, observations):
    viterbi = sess.run(hmm.forward_init_op(), feed_dict={hmm.obs: observations[0]})
    backpts = np.ones((hmm.N, len(observations)), 'int32') * -1
    for t in range(1, len(observations)):
        viterbi, backpt = sess.run([hmm.decode_op(), hmm.backpt_op()],
                                    feed_dict={hmm.obs: observations[t],
                                               hmm.viterbi: viterbi})
        backpts[:, t] = backpt
    tokens = [viterbi[:, -1].argmax()]
    for i in range(len(observations) - 1, 0, -1):
        tokens.append(backpts[tokens[-1], i])
    return tokens[::-1]

if __name__ == '__main__':
    states = ('Healthy', 'Fever')
    observations = ('normal', 'cold', 'dizzy')
    start_probability = {'Healthy': 0.6, 'Fever': 0.4}
    transition_probability = {
        'Healthy': {'Healthy': 0.7, 'Fever': 0.3},
        'Fever': {'Healthy': 0.4, 'Fever': 0.6}
    }
    emission_probability = {
        'Healthy': {'normal': 0.5, 'cold': 0.4, 'dizzy': 0.1},
        'Fever': {'normal': 0.1, 'cold': 0.3, 'dizzy': 0.6}
    }
    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))

        seq = viterbi_decode(sess, hmm, observations)
        print('Most likely hidden states are {}'.format(seq))