authors:
Jacob Schreiber [jmschreiber91@gmail.com]
Nicholas Farn [nicholasfarn@gmail.com]
This is an example of a sunny-rainy hidden markov model using yahmm. The example is drawn from the Wikipedia article on Hidden Markov Models describing what Bob likes to do on rainy or sunny days.
In [1]:
from pomegranate import *
import random
import math
random.seed(0)
We first create a HiddenMarkovModel object, and name it "Rainy-Sunny".
In [2]:
model = HiddenMarkovModel( name="Rainy-Sunny" )
We then create the two possible states of the model, "rainy" and "sunny". We make them both discrete distributions, with the possibilities of Bob either walking, shopping, or cleaning.
In [3]:
rainy = State( DiscreteDistribution({ 'walk': 0.1, 'shop': 0.4, 'clean': 0.5 }), name='Rainy' )
sunny = State( DiscreteDistribution({ 'walk': 0.6, 'shop': 0.3, 'clean': 0.1 }), name='Sunny' )
We then add the transitions probabilities, starting with the probability the model starts as sunny or rainy.
In [4]:
model.add_transition( model.start, rainy, 0.6 )
model.add_transition( model.start, sunny, 0.4 )
We then add the transition matrix. We make sure to subtract 0.05 from each probability to add to the probability of exiting the hmm.
In [5]:
model.add_transition( rainy, rainy, 0.65 )
model.add_transition( rainy, sunny, 0.25 )
model.add_transition( sunny, rainy, 0.35 )
model.add_transition( sunny, sunny, 0.55 )
Last, we add transitions to mark the end of the model.
In [6]:
model.add_transition( rainy, model.end, 0.1 )
model.add_transition( sunny, model.end, 0.1 )
Finally we "bake" the model, finalizing its structure.
In [7]:
model.bake( verbose=True )
Now lets check on Bob each hour and see what he is doing! In other words lets create a sequence of observations.
In [8]:
sequence = [ 'walk', 'shop', 'clean', 'clean', 'clean', 'walk', 'clean' ]
Now lets check the probability of observing this sequence.
In [9]:
print(math.e**model.forward( sequence )[ len(sequence), model.end_index ])
Then the probability that Bob will be cleaning a step 3 in this sequence.
In [10]:
print(math.e**model.forward_backward( sequence )[1][ 2, model.states.index( rainy ) ])
The probability of the sequence occurring given it is Sunny at step 4 in the sequence.
In [11]:
print(math.e**model.backward( sequence )[ 3, model.states.index( sunny ) ])
Finally the probable series of states given the above sequence.
In [12]:
print(" ".join( state.name for i, state in model.maximum_a_posteriori( sequence )[1] ))