print "\n".join(state.name for state in model.states)
print "Backward"
print model.backward(sequence)
print "Forward-Backward"
trans, emissions = model.forward_backward(sequence)
print trans
print emissions
print "Viterbi"
prob, states = model.viterbi(sequence)
print "Prob: {}".format(prob)
print "\n".join(state[1].name for state in states)
print
print "MAP"
prob, states = model.maximum_a_posteriori(sequence)
print "Prob: {}".format(prob)
print "\n".join(state[1].name for state in states)
print "Showing that sampling can reproduce the original transition probs."
print "Should produce a matrix close to the following: "
print " [ [ 0.60, 0.10, 0.30 ] "
print " [ 0.40, 0.40, 0.20 ] "
print " [ 0.05, 0.15, 0.80 ] ] "
print
print "Tranition Matrix From 100000 Samples:"
sample, path = model.sample(100000, path=True)
trans = np.zeros((3, 3))
for state, n_state in it.izip(path[1:-2], path[2:-1]):
state_name = float(state.name[1:]) - 1
# the probability of exiting the hmm
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)
# Add transitions to the end of the model
model.add_transition(rainy, model.end, 0.1)
model.add_transition(sunny, model.end, 0.1)
# Finalize the model structure
model.bake(verbose=True)
# Lets sample from this model.
print model.sample()
# Lets call Bob every hour and see what he's doing!
# (aka build up a sequence of observations)
sequence = ['walk', 'shop', 'clean', 'clean', 'clean', 'walk', 'clean']
# What is the probability of seeing this sequence?
print "Probability of Sequence: ", \
math.e**model.forward( sequence )[ len(sequence), model.end_index ]
print "Probability of Cleaning at Time Step 3 Given This Sequence: ", \
math.e**model.forward_backward( sequence )[1][ 2, model.states.index( rainy ) ]
print "Probability of the Sequence Given It's Sunny at Time Step 4: ", \
math.e**model.backward( sequence )[ 3, model.states.index( sunny ) ]
print " ".join(state.name
for i, state in model.maximum_a_posteriori(sequence)[1])
print "\n".join( state.name for state in model.states )
print "Backward"
print model.backward( sequence )
print "Forward-Backward"
trans, emissions = model.forward_backward( sequence )
print trans
print emissions
print "Viterbi"
prob, states = model.viterbi( sequence )
print "Prob: {}".format( prob )
print "\n".join( state[1].name for state in states )
print
print "MAP"
prob, states = model.maximum_a_posteriori( sequence )
print "Prob: {}".format( prob )
print "\n".join( state[1].name for state in states )
print "Showing that sampling can reproduce the original transition probs."
print "Should produce a matrix close to the following: "
print " [ [ 0.60, 0.10, 0.30 ] "
print " [ 0.40, 0.40, 0.20 ] "
print " [ 0.05, 0.15, 0.80 ] ] "
print
print "Tranition Matrix From 100000 Samples:"
sample, path = model.sample( 100000, path=True )
trans = np.zeros((3,3))
for state, n_state in it.izip( path[1:-2], path[2:-1] ):
state_name = float( state.name[1:] )-1
# Transition matrix, with 0.05 subtracted from each probability to add to # the probability of exiting the hmm 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 ) # Add transitions to the end of the model model.add_transition( rainy, model.end, 0.1 ) model.add_transition( sunny, model.end, 0.1 ) # Finalize the model structure model.bake( verbose=True ) # Lets sample from this model. print model.sample() # Lets call Bob every hour and see what he's doing! # (aka build up a sequence of observations) sequence = [ 'walk', 'shop', 'clean', 'clean', 'clean', 'walk', 'clean' ] # What is the probability of seeing this sequence? print "Probability of Sequence: ", \ math.e**model.forward( sequence )[ len(sequence), model.end_index ] print "Probability of Cleaning at Time Step 3 Given This Sequence: ", \ math.e**model.forward_backward( sequence )[1][ 2, model.states.index( rainy ) ] print "Probability of the Sequence Given It's Sunny at Time Step 4: ", \ math.e**model.backward( sequence )[ 3, model.states.index( sunny ) ] print " ".join( state.name for i, state in model.maximum_a_posteriori( sequence )[1] )
def main():
"""Create a Hidden Markov Model."""
# Name of the model
model = HiddenMarkovModel(name="Names")
# Load probability distributions for each token set
fn_dist = utils.load_dict_from_file(config.input_dir +
config.token_files['first_name'])
pfn_dist = utils.load_dict_from_file(config.input_dir +
config.token_files['part_first_name'])
ln1_dist = utils.load_dict_from_file(config.input_dir +
config.token_files['last_name1'])
pln1_dist = utils.load_dict_from_file(
config.input_dir + config.token_files['part_last_name1'])
ln2_dist = utils.load_dict_from_file(config.input_dir +
config.token_files['last_name2'])
pln2_dist = utils.load_dict_from_file(
config.input_dir + config.token_files['part_last_name2'])
# Calculate discrete distributions
fn_dist = discrete_distribution(fn_dist, pfn_dist, ln1_dist, pln1_dist,
ln2_dist, pln2_dist)
pfn_dist = discrete_distribution(pfn_dist, fn_dist, ln1_dist, pln1_dist,
ln2_dist, pln2_dist)
ln1_dist = discrete_distribution(ln1_dist, fn_dist, pfn_dist, pln1_dist,
ln2_dist, pln2_dist)
pln1_dist = discrete_distribution(pln1_dist, fn_dist, pfn_dist, ln1_dist,
ln2_dist, pln2_dist)
ln2_dist = discrete_distribution(ln2_dist, fn_dist, pfn_dist, ln1_dist,
pln1_dist, pln2_dist)
pln2_dist = discrete_distribution(pln2_dist, fn_dist, pfn_dist, ln1_dist,
pln1_dist, ln2_dist)
# States of the model
fn = State(DiscreteDistribution(fn_dist), name='FirstName')
pfn = State(DiscreteDistribution(pfn_dist), name='ParticleFirstName')
ln1 = State(DiscreteDistribution(ln1_dist), name='LastName1')
pln1 = State(DiscreteDistribution(pln1_dist), name='ParticleLastName1')
ln2 = State(DiscreteDistribution(ln2_dist), name='LastName2')
pln2 = State(DiscreteDistribution(pln2_dist), name='ParticleLastName2')
# Transition probabilities
if config.graph_type == config.graph_types[0]:
# Graph for FirstName LastName1 LastName2 sequences
model.add_transition(model.start, fn, 1)
model.add_transition(fn, fn, 0.256251576)
model.add_transition(fn, pfn, 0.028472397)
model.add_transition(fn, ln1, 0.704144114)
model.add_transition(fn, pln1, 0.011131913)
model.add_transition(pfn, pfn, 0.150)
model.add_transition(pfn, fn, 0.850)
model.add_transition(ln1, ln1, 0.007015434)
model.add_transition(ln1, pln1, 0.007017087)
model.add_transition(ln1, ln2, 0.960638112)
model.add_transition(ln1, pln2, 0.014719859)
model.add_transition(ln1, model.end, 0.010609508)
model.add_transition(pln1, pln1, 0.150)
model.add_transition(pln1, ln1, 0.850)
model.add_transition(ln2, ln2, 0.004290151)
model.add_transition(ln2, pln2, 0.006801967)
model.add_transition(ln2, model.end, 0.988907882)
model.add_transition(pln2, pln2, 0.150)
model.add_transition(pln2, ln2, 0.850)
else:
# Graph for LastName1 LastName2 FirstName sequences
model.add_transition(model.start, ln1, 0.984436899)
model.add_transition(model.start, pln1, 0.015563101)
model.add_transition(ln1, ln1, 0.007015434)
model.add_transition(ln1, pln1, 0.007017087)
model.add_transition(ln1, ln2, 0.960638112)
model.add_transition(ln1, pln2, 0.014719859)
model.add_transition(ln1, fn, 0.010609508)
model.add_transition(pln1, pln1, 0.150)
model.add_transition(pln1, ln1, 0.850)
model.add_transition(ln2, ln2, 0.004290151)
model.add_transition(ln2, pln2, 0.006801967)
model.add_transition(ln2, fn, 0.988907882)
model.add_transition(pln2, pln2, 0.150)
model.add_transition(pln2, ln2, 0.850)
model.add_transition(fn, fn, 0.256251576)
model.add_transition(fn, pfn, 0.028472397)
model.add_transition(fn, model.end, 0.715276027)
model.add_transition(pfn, pfn, 0.150)
model.add_transition(pfn, fn, 0.850)
# "Bake" the model, finalizing its structure
model.bake(verbose=True)
# Testing the model
parse_errors = 0
value_errors = 0
tagged_names = utils.load_dict_from_file(config.test_set_file)
for key, value in tagged_names.items():
print('Observation: ' + value['observation'])
norm_observation = utils.normalize(value['observation'],
config.text_case)
words = re.findall(config.word_pattern, norm_observation)
token_sequence = []
for word in words:
token_sequence.append(utils.to_token(word, config.token_length))
test_dict = {
'FirstName': '',
'LastName1': '',
'LastName2': '',
}
try:
j = 0
for i, state in model.maximum_a_posteriori(token_sequence)[1]:
if state.name[-4:] == 'Name':
test_dict['FirstName'] += words[j] + ' '
if state.name[-5:] == 'Name1':
test_dict['LastName1'] += words[j] + ' '
if state.name[-5:] == 'Name2':
test_dict['LastName2'] += words[j] + ' '
j += 1
# compare results with tagged names
test_dict['FirstName'] = test_dict['FirstName'].rstrip()
test_dict['LastName1'] = test_dict['LastName1'].rstrip()
test_dict['LastName2'] = test_dict['LastName2'].rstrip()
print('Parsed: ' + str(test_dict))
# Probability of this sequence
print('P(sequence) = ' + str(math.e**model.forward(token_sequence)[
len(token_sequence), model.end_index]))
result = ''
for state in ['FirstName', 'LastName1', 'LastName2']:
if test_dict[state] == value[state]:
result += ''
else:
result += state + ' differs. '
if result == '':
result = 'Correct.'
else:
parse_errors += 1
print('Result: ' + result)
except ValueError as ve:
print(ve)
value_errors += 1
print('--')
# Final statistics
print('Summary\n=======')
print('Number of observations: ' + str(len(tagged_names)))
print('Parse errors:' + str(parse_errors))
print('Value errors: ' + str(value_errors))
"""
