# Ch `06`: Concept `01`

## Hidden Markov model forward algorithm

Oof this code's a bit complicated if you don't already know how HMMs work. Please see the book chapter for step-by-step explanations. I'll try to improve the documentation, or feel free to send a pull request with your own documentation!

First, let's import TensorFlow and NumPy:

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import numpy as np
import tensorflow as tf

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Define the HMM model:

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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 == 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)
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))

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Define the forward algorithm:

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def forward_algorithm(sess, hmm, observations):
fwd = sess.run(hmm.forward_init_op(), feed_dict={hmm.obs_idx: observations})
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

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Let's try it out:

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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([[0.1, 0.4, 0.5], [0.6, 0.3, 0.1]])

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))

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Probability of observing [0, 1, 1, 2, 1] is 0.004540300799999999

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