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import pytest
from nltk.tag import hmm
def _wikipedia_example_hmm():
# Example from wikipedia
# (https://en.wikipedia.org/wiki/Forward%E2%80%93backward_algorithm)
states = ["rain", "no rain"]
symbols = ["umbrella", "no umbrella"]
A = [[0.7, 0.3], [0.3, 0.7]] # transition probabilities
B = [[0.9, 0.1], [0.2, 0.8]] # emission probabilities
pi = [0.5, 0.5] # initial probabilities
seq = ["umbrella", "umbrella", "no umbrella", "umbrella", "umbrella"]
seq = list(zip(seq, [None] * len(seq)))
model = hmm._create_hmm_tagger(states, symbols, A, B, pi)
return model, states, symbols, seq
def test_forward_probability():
from numpy.testing import assert_array_almost_equal
# example from p. 385, Huang et al
model, states, symbols = hmm._market_hmm_example()
seq = [("up", None), ("up", None)]
expected = [[0.35, 0.02, 0.09], [0.1792, 0.0085, 0.0357]]
fp = 2 ** model._forward_probability(seq)
assert_array_almost_equal(fp, expected)
def test_forward_probability2():
from numpy.testing import assert_array_almost_equal
model, states, symbols, seq = _wikipedia_example_hmm()
fp = 2 ** model._forward_probability(seq)
# examples in wikipedia are normalized
fp = (fp.T / fp.sum(axis=1)).T
wikipedia_results = [
[0.8182, 0.1818],
[0.8834, 0.1166],
[0.1907, 0.8093],
[0.7308, 0.2692],
[0.8673, 0.1327],
]
assert_array_almost_equal(wikipedia_results, fp, 4)
def test_backward_probability():
from numpy.testing import assert_array_almost_equal
model, states, symbols, seq = _wikipedia_example_hmm()
bp = 2 ** model._backward_probability(seq)
# examples in wikipedia are normalized
bp = (bp.T / bp.sum(axis=1)).T
wikipedia_results = [
# Forward-backward algorithm doesn't need b0_5,
# so .backward_probability doesn't compute it.
# [0.6469, 0.3531],
[0.5923, 0.4077],
[0.3763, 0.6237],
[0.6533, 0.3467],
[0.6273, 0.3727],
[0.5, 0.5],
]
assert_array_almost_equal(wikipedia_results, bp, 4)
def setup_module(module):
pytest.importorskip("numpy")
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