def build_an_hmm_example():
# i think the characters in each DiscreteDistribution definition, means the emission matrix for each state
# because it says the probability of seeing each character when the system is in that state
d1 = DiscreteDistribution({'A': 0.35, 'C': 0.20, 'G': 0.05, 'T': 0.40})
d2 = DiscreteDistribution({'A': 0.25, 'C': 0.25, 'G': 0.25, 'T': 0.25})
d3 = DiscreteDistribution({'A': 0.10, 'C': 0.40, 'G': 0.40, 'T': 0.10})
s1 = State(d1, name="s1")
s2 = State(d2, name="s2")
s3 = State(d3, name="s3")
model = HiddenMarkovModel('example')
model.add_states([s1, s2, s3])
model.add_transition(model.start, s1, 0.90)
model.add_transition(model.start, s2, 0.10)
model.add_transition(s1, s1, 0.80)
model.add_transition(s1, s2, 0.20)
model.add_transition(s2, s2, 0.90)
model.add_transition(s2, s3, 0.10)
model.add_transition(s3, s3, 0.70)
model.add_transition(s3, model.end, 0.30)
model.bake()
for i in range(len(model.states)):
print(model.states[i].name)
model.plot()
#print(model.log_probability(list('ACGACTATTCGAT')))
#print(", ".join(state.name for i, state in model.viterbi(list('ACGACTATTCGAT'))[1]))
print("forward:", model.forward(list('ACG')))
model.add_transition(s2, s1, 0.4)
model.add_transition(s2, s2, 0.4)
model.add_transition(s2, s3, 0.2)
model.add_transition(s3, s1, 0.05)
model.add_transition(s3, s2, 0.15)
model.add_transition(s3, s3, 0.8)
model.bake()
sequence = [4.8, 5.6, 24.1, 25.8, 14.3, 26.5, 15.9, 5.5, 5.1]
print model.is_infinite()
print "Algorithms On Infinite Model"
sequence = [4.8, 5.6, 24.1, 25.8, 14.3, 26.5, 15.9, 5.5, 5.1]
print "Forward"
print model.forward(sequence)
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
# re-order the rows/columns to match the specified column order
transitions = model.dense_transition_matrix()[:, order_index][order_index, :]
print("The state transition matrix, P(Xt|Xt-1):\n")
print(transitions)
print("\nThe transition probability from Rainy to Sunny is {:.0f}get_ipython().run_line_magic("".format(100", " * transitions[2, 1]))")
# TODO: input a sequence of 'yes'/'no' values in the list below for testing
observations = ['yes', 'no', 'yes']
assert len(observations) > 0, "You need to choose a sequence of 'yes'/'no' observations to test"
# TODO: use model.forward() to calculate the forward matrix of the observed sequence,
# and then use np.exp() to convert from log-likelihood to likelihood
forward_matrix = np.exp(model.forward(observations))
# TODO: use model.log_probability() to calculate the all-paths likelihood of the
# observed sequence and then use np.exp() to convert log-likelihood to likelihood
probability_percentage = np.exp(model.log_probability(observations))
# Display the forward probabilities
print(" " + "".join(s.name.center(len(s.name)+6) for s in model.states))
for i in range(len(observations) + 1):
print(" <start> " if i==0 else observations[i - 1].center(9), end="")
print("".join("{:.0f}get_ipython().run_line_magic("".format(100", " * forward_matrix[i, j]).center(len(s.name) + 6)")
for j, s in enumerate(model.states)))
print("\nThe likelihood over all possible paths " + \
"of this model producing the sequence {} is {:.2f}get_ipython().run_line_magic("\n\n"", "")
.format(observations, 100 * probability_percentage))
model.add_transition(state, state, 0.4) model.add_transition(state, state2, 0.4) model.add_transition(state2, state2, 0.4) model.add_transition(state2, state, 0.4) model.add_transition(model.start, state, 0.5) model.add_transition(model.start, state2, 0.5) model.add_transition(state, model.end, 0.2) model.add_transition(state2, model.end, 0.2) model.bake() sequence = model.sample() print sequence print print model.forward(sequence)[ len(sequence), model.end_index ] print model.backward(sequence)[0,model.start_index] print trans, ems = model.forward_backward(sequence) print trans print ems print model.train( [ sequence ] ) print print model.forward(sequence)[ len(sequence), model.end_index ] print model.backward(sequence)[0,model.start_index] print trans, ems = model.forward_backward(sequence) print trans print ems
# 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])
# 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] )
model.add_transition( s2, s2, 0.4 )
model.add_transition( s2, s3, 0.2 )
model.add_transition( s3, s1, 0.05 )
model.add_transition( s3, s2, 0.15 )
model.add_transition( s3, s3, 0.8 )
model.bake()
sequence = [ 4.8, 5.6, 24.1, 25.8, 14.3, 26.5, 15.9, 5.5, 5.1 ]
print model.is_infinite()
print "Algorithms On Infinite Model"
sequence = [ 4.8, 5.6, 24.1, 25.8, 14.3, 26.5, 15.9, 5.5, 5.1 ]
print "Forward"
print model.forward( sequence )
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
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))
"""
model.add_transition(state, state, 0.4) model.add_transition(state, state2, 0.4) model.add_transition(state2, state2, 0.4) model.add_transition(state2, state, 0.4) model.add_transition(model.start, state, 0.5) model.add_transition(model.start, state2, 0.5) model.add_transition(state, model.end, 0.2) model.add_transition(state2, model.end, 0.2) model.bake() sequence = model.sample() print sequence print print model.forward(sequence)[len(sequence), model.end_index] print model.backward(sequence)[0, model.start_index] print trans, ems = model.forward_backward(sequence) print trans print ems print model.train([sequence]) print print model.forward(sequence)[len(sequence), model.end_index] print model.backward(sequence)[0, model.start_index] print trans, ems = model.forward_backward(sequence) print trans print ems
