class HmmCoinsTest(unittest.TestCase):
def setUp(self):
self.states = ["Coin 1", "Coin 2", "Coin 3"]
self.vocabulary = ["Heads", "Tails"]
self.initial_probabilities = {
"Coin 1": 0.4,
"Coin 2": 0.3,
"Coin 3": 0.3
}
# The probability of moving from state a to state b
# such that the sum of the all the probabilities = 1
self.transition_probabilities = {
"Coin 1": {"Coin 1": 0.6, "Coin 2": 0.3, "Coin 3": 0.1},
"Coin 2": {"Coin 1": 0.2, "Coin 2": 0.5, "Coin 3": 0.3},
"Coin 3": {"Coin 1": 0.3, "Coin 2": 0.2, "Coin 3": 0.5}
}
# the probability of the observation O being generated from the state q
self.emission_probabilities = {
"Coin 1": {"Heads": 0.7, "Tails": 0.3},
"Coin 2": {"Heads": 0.3, "Tails": 0.7},
"Coin 3": {"Heads": 0.5, "Tails": 0.5}
}
self.hmm = HiddenMarkovModel(
self.states, # all the possible hidden states
self.vocabulary, # all possible observation types
self.transition_probabilities,
self.emission_probabilities,
self.initial_probabilities
)
def test_forward(self):
observations = ["Heads", "Heads", "Heads"]
P, forwards = self.hmm.forward(observations)
self.assertEqual(P, 0.14533999999999997)
self.assertEqual(
forwards[0], [0.27999999999999997, 0.16169999999999998, 0.08824199999999997])
self.assertEqual(forwards[1], [0.09, 0.0477, 0.025607999999999995])
def test_backward(self):
observations = ["Heads", "Heads", "Heads"]
P, backwards = self.hmm.backward(observations)
self.assertEqual(P, 0.14534)
self.assertEqual(backwards[0], [0.30080000000000007, 0.56, 1.0])
self.assertEqual(backwards[1], [0.2224, 0.43999999999999995, 1.0])
def test_viterbi(self):
observations = ["Heads", "Heads", "Heads"]
P, backpoints = self.hmm.viterbi(observations)
self.assertEqual(P, 0.049391999999999985)
self.assertEqual(backpoints, ['Coin 1', 'Coin 1', 'Coin 1'])
def test_forward_backward(self):
observations = ["Heads", "Heads", "Heads"]
old_prediction = self.hmm.viterbi(observations)
new_hmm = self.hmm.forward_backward(observations)
prediction = new_hmm.viterbi(observations[:3])
# we should see an increase in the probability output
assert old_prediction[0] < prediction[0]
self.assertEqual(prediction, (0.10346810696178374,
['Coin 1', 'Coin 1', 'Coin 1']))
class HmmWeatherTest(unittest.TestCase):
def setUp(self):
self.states = ["rainy", "sunny"]
self.vocabulary = ["walk", "shop", "clean"]
self.initial_probabilities = {
"rainy": 0.6,
"sunny": 0.4,
}
# The probability of moving from state a to state b
# such that the sum of the all the probabilities = 1
self.transition_probabilities = {
"rainy": {
"rainy": 0.7,
"sunny": 0.3,
},
"sunny": {
"rainy": 0.4,
"sunny": 0.6,
},
}
# the probability of the observation O being generated from the state q
self.emission_probabilities = {
"rainy": {
"walk": 0.1,
"shop": 0.4,
"clean": 0.5,
},
"sunny": {
"walk": 0.6,
"shop": 0.3,
"clean": 0.1,
}
}
self.hmm = HiddenMarkovModel(
self.states, # all the possible hidden states
self.vocabulary, # all possible observation types
self.transition_probabilities,
self.emission_probabilities,
self.initial_probabilities
)
def test_forward(self):
observations = ["walk", "shop", "clean"]
P, forwards = self.hmm.forward(observations)
self.assertEqual(P, 0.033612)
self.assertEqual(forwards[0], [0.06, 0.055200000000000006, 0.02904])
self.assertEqual(forwards[1], [0.24, 0.04859999999999999, 0.004572])
def test_backward(self):
observations = ["walk", "shop", "clean"]
P, backwards = self.hmm.backward(observations)
self.assertEqual(P, 0.033612)
self.assertEqual(backwards[0], [0.1298, 0.38, 1.0])
self.assertEqual(backwards[1], [0.10760000000000002, 0.26, 1.0])
def test_viterbi(self):
observations = ["walk", "shop", "clean"]
P, backpoints = self.hmm.viterbi(observations)
self.assertEqual(P, 0.01344)
self.assertEqual(backpoints, ['sunny', 'rainy', 'rainy'])
def test_forward_backward(self):
observations = ["walk", "shop", "clean"]
new_hmm = self.hmm.forward_backward(observations)
prediction = new_hmm.viterbi(observations[:3])
self.assertEqual(prediction, (0.010994296643152459,
['sunny', 'rainy', 'rainy']))
