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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Hidden Markov Model Example
authors
Step1:  First we will create the states of the model, one uniform and one normal.
Step2:  We will then create the model by creating a HiddenMarkovModel instance. Then we will add the states.
Step3:  Now we'll add the start states to the model.
Step4:  And the transition matrix.
Step5:  Finally the ending states to the model.
Step6:  To finalize the model, we "bake" it.
Step7:  New we'll create a sample sequence using our model.
Step8:  Now we'll feed the sequence through a forward algorithm with our model.
Step9:  Next we'll do the same, except with a backwards algorithm.
Step10:  Then we'll feed the sequence again, through a forward-backward algorithm.
Step11:  Finally we'll train our model with our example sequence.
Step12:  Then repeat the algorithms we fed the sequence through before on our improved model.
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Python Code:
import random
from pomegranate import *
random.seed(0)
Explanation: Hidden Markov Model Example
authors:<br>
Jacob Schreiber [<a href="mailto:jmschreiber91@gmail.com">jmschreiber91@gmail.com</a>]<br>
Nicholas Farn [<a href="mailto:nicholasfarn@gmail.com">nicholasfarn@gmail.com</a>]
A simple example highlighting how to build a model using states, add
transitions, and then run the algorithms, including showing how training
on a sequence improves the probability of the sequence.
End of explanation
state1 = State( UniformDistribution(0.0, 1.0), name="uniform" )
state2 = State( NormalDistribution(0, 2), name="normal" )
Explanation: First we will create the states of the model, one uniform and one normal.
End of explanation
model = HiddenMarkovModel( name="ExampleModel" )
model.add_state( state1 )
model.add_state( state2 )
Explanation: We will then create the model by creating a HiddenMarkovModel instance. Then we will add the states.
End of explanation
model.add_transition( model.start, state1, 0.5 )
model.add_transition( model.start, state2, 0.5 )
Explanation: Now we'll add the start states to the model.
End of explanation
model.add_transition( state1, state1, 0.4 )
model.add_transition( state1, state2, 0.4 )
model.add_transition( state2, state2, 0.4 )
model.add_transition( state2, state1, 0.4 )
Explanation: And the transition matrix.
End of explanation
model.add_transition( state1, model.end, 0.2 )
model.add_transition( state2, model.end, 0.2 )
Explanation: Finally the ending states to the model.
End of explanation
model.bake()
Explanation: To finalize the model, we "bake" it.
End of explanation
sequence = model.sample()
print(sequence)
Explanation: New we'll create a sample sequence using our model.
End of explanation
print(model.forward( sequence )[ len(sequence), model.end_index ])
Explanation: Now we'll feed the sequence through a forward algorithm with our model.
End of explanation
print(model.backward( sequence )[0,model.start_index])
Explanation: Next we'll do the same, except with a backwards algorithm.
End of explanation
trans, ems = model.forward_backward( sequence )
print(trans)
print(ems)
Explanation: Then we'll feed the sequence again, through a forward-backward algorithm.
End of explanation
model.fit( [ sequence ] )
Explanation: Finally we'll train our model with our example sequence.
End of explanation
print("Forward")
print(model.forward( sequence )[ len(sequence), model.end_index ])
print()
print("Backward")
print(model.backward( sequence )[ 0,model.start_index ])
print()
trans, ems = model.forward_backward( sequence )
print(trans)
print(ems)
Explanation: Then repeat the algorithms we fed the sequence through before on our improved model.
End of explanation
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