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#!/usr/bin/env python
"""Test out HMMs using the Occasionally Dishonest Casino.
This uses the ocassionally dishonest casino example from Biological
Sequence Analysis by Durbin et al.
In this example, we are dealing with a casino that has two types of
dice, a fair dice that has 1/6 probability of rolling any number and
a loaded dice that has 1/2 probability to roll a 6, and 1/10 probability
to roll any other number. The probability of switching from the fair to
loaded dice is .05 and the probability of switching from loaded to fair is
.1.
"""
# standard modules
import random
# biopython
from Bio import Alphabet
from Bio.Seq import MutableSeq
from Bio.Seq import Seq
# HMM stuff we are testing
from Bio.HMM import MarkovModel
from Bio.HMM import Trainer
from Bio.HMM import Utilities
# whether we should print everything out. Set this to zero for
# regression testing
VERBOSE = 0
# -- set up our alphabets
class DiceRollAlphabet(Alphabet.Alphabet):
letters = ['1', '2', '3', '4', '5', '6']
class DiceTypeAlphabet(Alphabet.Alphabet):
letters = ['F', 'L']
# -- useful functions
def _loaded_dice_roll(chance_num, cur_state):
"""Generate a loaded dice roll based on the state and a random number
"""
if cur_state == 'F':
if chance_num <= (float(1) / float(6)):
return '1'
elif chance_num <= (float(2) / float(6)):
return '2'
elif chance_num <= (float(3) / float(6)):
return '3'
elif chance_num <= (float(4) / float(6)):
return '4'
elif chance_num <= (float(5) / float(6)):
return '5'
else:
return '6'
elif cur_state == 'L':
if chance_num <= (float(1) / float(10)):
return '1'
elif chance_num <= (float(2) / float(10)):
return '2'
elif chance_num <= (float(3) / float(10)):
return '3'
elif chance_num <= (float(4) / float(10)):
return '4'
elif chance_num <= (float(5) / float(10)):
return '5'
else:
return '6'
else:
raise ValueError("Unexpected cur_state %s" % cur_state)
def generate_rolls(num_rolls):
"""Generate a bunch of rolls corresponding to the casino probabilities.
Returns:
o The generate roll sequence
o The state sequence that generated the roll.
"""
# start off in the fair state
cur_state = 'F'
roll_seq = MutableSeq('', DiceRollAlphabet())
state_seq = MutableSeq('', DiceTypeAlphabet())
# generate the sequence
for roll in range(num_rolls):
state_seq.append(cur_state)
# generate a random number
chance_num = random.random()
# add on a new roll to the sequence
new_roll = _loaded_dice_roll(chance_num, cur_state)
roll_seq.append(new_roll)
# now give us a chance to switch to a new state
chance_num = random.random()
if cur_state == 'F':
if chance_num <= .05:
cur_state = 'L'
elif cur_state == 'L':
if chance_num <= .1:
cur_state = 'F'
return roll_seq.toseq(), state_seq.toseq()
# -- build a MarkovModel
mm_builder = MarkovModel.MarkovModelBuilder(DiceTypeAlphabet(),
DiceRollAlphabet())
mm_builder.allow_all_transitions()
mm_builder.set_random_probabilities()
"""
mm_builder.set_transition_score('F', 'L', .05)
mm_builder.set_transition_score('F', 'F', .95)
mm_builder.set_transition_score('L', 'F', .10)
mm_builder.set_transition_score('L', 'L', .9)
mm_builder.set_emission_score('F', '1', .17)
mm_builder.set_emission_score('F', '2', .17)
mm_builder.set_emission_score('F', '3', .17)
mm_builder.set_emission_score('F', '4', .17)
mm_builder.set_emission_score('F', '5', .17)
mm_builder.set_emission_score('F', '6', .17)
mm_builder.set_emission_score('L', '1', .1)
mm_builder.set_emission_score('L', '2', .1)
mm_builder.set_emission_score('L', '3', .1)
mm_builder.set_emission_score('L', '4', .1)
mm_builder.set_emission_score('L', '5', .1)
mm_builder.set_emission_score('L', '6', .5)
"""
# just get two different Markov Models -- we'll train one using
# Baum Welch, and one using the Standard trainer
baum_welch_mm = mm_builder.get_markov_model()
standard_mm = mm_builder.get_markov_model()
# get a sequence of rolls to train the markov model with
rolls, states = generate_rolls(3000)
# predicted_states, prob = my_mm.viterbi(rolls, DiceTypeAlphabet())
# print "prob:", prob
# Utilities.pretty_print_prediction(rolls, states, predicted_states)
# -- now train the model
def stop_training(log_likelihood_change, num_iterations):
"""Tell the training model when to stop.
"""
if VERBOSE:
print "ll change:", log_likelihood_change
if log_likelihood_change < 0.01:
return 1
elif num_iterations >= 10:
return 1
else:
return 0
# -- Standard Training with known states
print "Training with the Standard Trainer..."
known_training_seq = Trainer.TrainingSequence(rolls, states)
trainer = Trainer.KnownStateTrainer(standard_mm)
trained_mm = trainer.train([known_training_seq])
if VERBOSE:
print trained_mm.transition_prob
print trained_mm.emission_prob
test_rolls, test_states = generate_rolls(300)
predicted_states, prob = trained_mm.viterbi(test_rolls, DiceTypeAlphabet())
if VERBOSE:
print "Prediction probability:", prob
Utilities.pretty_print_prediction(test_rolls, test_states, predicted_states)
# -- Baum-Welch training without known state sequences
print "Training with Baum-Welch..."
training_seq = Trainer.TrainingSequence(rolls, Seq("", DiceTypeAlphabet()))
trainer = Trainer.BaumWelchTrainer(baum_welch_mm)
trained_mm = trainer.train([training_seq], stop_training)
if VERBOSE:
print trained_mm.transition_prob
print trained_mm.emission_prob
test_rolls, test_states = generate_rolls(300)
predicted_states, prob = trained_mm.viterbi(test_rolls, DiceTypeAlphabet())
if VERBOSE:
print "Prediction probability:", prob
Utilities.pretty_print_prediction(test_rolls, test_states, predicted_states)
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