HMM Viterbi & Forward Algorithm tutorial

hmmviterbi.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.viterbi = tf.placeholder(tf.float64)
        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.multiply(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 decode_op(self):
        transitions = tf.matmul(self.viterbi, tf.transpose(self.get_emission(self.obs_idx)))
        weighted_transitions = transitions * self.trans_prob
        viterbi = tf.reduce_max(weighted_transitions, 0)   # y축에 대해서 가장 max 값을 찾음
        return tf.reshape(viterbi, tf.shape(self.viterbi)) # reshape = 1*2 행렬을 2*1 행렬로 바꿔준다.
    
    def backpt_op(self):
        back_transitions = tf.matmul(self.viterbi, np.ones((1, self.N)))  # 2x1 * 1x2 = 2x2
        weighted_back_transitions = back_transitions * self.trans_prob
        return tf.argmax(weighted_back_transitions, 0) # 가장 큰 값을 가진 index 행렬을 리턴한다.


def viterbi_decode(sess, hmm, observations):
    viterbi = sess.run(hmm.forward_init_op(), feed_dict={hmm.obs_idx: observations[0]}) # 0.6 * 0.5, 0.4 * 0.1 행렬
    backpts = np.ones((hmm.N, len(observations)), 'int32') * -1 #2x5의 -1행렬

    for t in range(1, len(observations)):
        viterbi, backpt = sess.run([hmm.decode_op(), hmm.backpt_op()],
                                   feed_dict={hmm.obs_idx: 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]

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

    
# initial_prob = np.array([[0.6], [0.4]])
# trans_prob = np.array([[0.7, 0.3], [0.4, 0.6]])
# obs_prob = np.array([[0.1, 0.4, 0.5], [0.6, 0.3, 0.1]])

initial_prob = np.array([[0.9], [0.05], [0.05]])
trans_prob = np.array([[0.9, 0.05, 0.05], [0.9, 0.05, 0.05], [0.9, 0.05, 0.05]])
obs_prob = np.array([[0.5, 0.5], [0.75, 0.25], [0.25, 0.75]])

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

# observations = [0, 1, 1, 2, 1]
observations = [0]

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

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