# -*- coding: utf-8 -*-
from __future__ import absolute_import, unicode_literals
from nltk.tag import hmm
def _wikipedia_example_hmm():
# Example from wikipedia
# (http://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
[docs]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)
[docs]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)
[docs]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)
[docs]def setup_module(module):
from nose import SkipTest
try:
import numpy
except ImportError:
raise SkipTest("numpy is required for nltk.test.test_hmm")