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from __future__ import (division, print_function)
from pomegranate import *
from numpy.testing import assert_almost_equal
import random
import numpy as np
import json
import pytest
@pytest.fixture
def model():
'''
Build a model that we want to use to test sequences. This model will
be somewhat complicated, in order to extensively test YAHMM. This will be
a three state global sequence alignment HMM. The HMM models a reference of
'ACT', with pseudocounts to allow for slight deviations from this
reference.
'''
random.seed(0)
model = HiddenMarkovModel( "Global Alignment")
# Define the distribution for insertions
i_d = DiscreteDistribution( { 'A': 0.25, 'C': 0.25, 'G': 0.25, 'T': 0.25 } )
# Create the insert states
i0 = State( i_d, name="I0" )
i1 = State( i_d, name="I1" )
i2 = State( i_d, name="I2" )
i3 = State( i_d, name="I3" )
# Create the match states
m1 = State( DiscreteDistribution({ "A": 0.95, 'C': 0.01, 'G': 0.01, 'T': 0.02 }) , name="M1" )
m2 = State( DiscreteDistribution({ "A": 0.003, 'C': 0.99, 'G': 0.003, 'T': 0.004 }) , name="M2" )
m3 = State( DiscreteDistribution({ "A": 0.01, 'C': 0.01, 'G': 0.01, 'T': 0.97 }) , name="M3" )
# Create the delete states
d1 = State( None, name="D1" )
d2 = State( None, name="D2" )
d3 = State( None, name="D3" )
# Add all the states to the model
model.add_states( [i0, i1, i2, i3, m1, m2, m3, d1, d2, d3 ] )
# Create transitions from match states
model.add_transition( model.start, m1, 0.9 )
model.add_transition( model.start, i0, 0.1 )
model.add_transition( m1, m2, 0.9 )
model.add_transition( m1, i1, 0.05 )
model.add_transition( m1, d2, 0.05 )
model.add_transition( m2, m3, 0.9 )
model.add_transition( m2, i2, 0.05 )
model.add_transition( m2, d3, 0.05 )
model.add_transition( m3, model.end, 0.9 )
model.add_transition( m3, i3, 0.1 )
# Create transitions from insert states
model.add_transition( i0, i0, 0.70 )
model.add_transition( i0, d1, 0.15 )
model.add_transition( i0, m1, 0.15 )
model.add_transition( i1, i1, 0.70 )
model.add_transition( i1, d2, 0.15 )
model.add_transition( i1, m2, 0.15 )
model.add_transition( i2, i2, 0.70 )
model.add_transition( i2, d3, 0.15 )
model.add_transition( i2, m3, 0.15 )
model.add_transition( i3, i3, 0.85 )
model.add_transition( i3, model.end, 0.15 )
# Create transitions from delete states
model.add_transition( d1, d2, 0.15 )
model.add_transition( d1, i1, 0.15 )
model.add_transition( d1, m2, 0.70 )
model.add_transition( d2, d3, 0.15 )
model.add_transition( d2, i2, 0.15 )
model.add_transition( d2, m3, 0.70 )
model.add_transition( d3, i3, 0.30 )
model.add_transition( d3, model.end, 0.70 )
# Call bake to finalize the structure of the model.
model.bake()
return model
@pytest.fixture
def multitransition():
'''
Build a model that we want to use to test sequences. This is the same as the
above model, except that it uses the multiple transition methods for building.
'''
random.seed(0)
global model
model = HiddenMarkovModel( "Global Alignment")
# Define the distribution for insertions
i_d = DiscreteDistribution( { 'A': 0.25, 'C': 0.25, 'G': 0.25, 'T': 0.25 } )
# Create the insert states
i0 = State( i_d, name="I0" )
i1 = State( i_d, name="I1" )
i2 = State( i_d, name="I2" )
i3 = State( i_d, name="I3" )
# Create the match states
m1 = State( DiscreteDistribution({ "A": 0.95, 'C': 0.01, 'G': 0.01, 'T': 0.02 }) , name="M1" )
m2 = State( DiscreteDistribution({ "A": 0.003, 'C': 0.99, 'G': 0.003, 'T': 0.004 }) , name="M2" )
m3 = State( DiscreteDistribution({ "A": 0.01, 'C': 0.01, 'G': 0.01, 'T': 0.97 }) , name="M3" )
# Create the delete states
d1 = State( None, name="D1" )
d2 = State( None, name="D2" )
d3 = State( None, name="D3" )
# Add all the states to the model
model.add_states( [i0, i1, i2, i3, m1, m2, m3, d1, d2, d3 ] )
# Create transitions from match states
model.add_transitions( model.start, [m1, i0], [0.9, 0.1] )
model.add_transitions( m1, [m2, i1, d2], [0.9, 0.05, 0.05] )
model.add_transitions( m2, [m3, i2, d3], [0.9, 0.05, 0.05] )
model.add_transitions( m3, [model.end, i3], [0.9, 0.1] )
# Create transitions from insert states
model.add_transitions( i0, [i0, d1, m1], [0.7, 0.15, 0.15] )
model.add_transitions( i1, [i1, d2, m2], [0.7, 0.15, 0.15] )
model.add_transitions( i2, [i2, d3, m3], [0.7, 0.15, 0.15] )
model.add_transitions( [i3, i3], [i3, model.end], [0.85, 0.15] )
# Create transitions from delete states
model.add_transitions( d1, [d2, i1, m2], [0.15, 0.15, 0.70] )
model.add_transitions( [d2, d2, d2, d3, d3], [d3, i2, m3, i3, model.end],
[0.15, 0.15, 0.70, 0.30, 0.70 ] )
# Call bake to finalize the structure of the model.
model.bake()
return model
@pytest.fixture
def tied_edge():
'''
Build a model that we want to use to test sequences. This model has
tied edges.
'''
random.seed(0)
model = HiddenMarkovModel( "Global Alignment")
# Define the distribution for insertions
i_d = DiscreteDistribution( { 'A': 0.25, 'C': 0.25, 'G': 0.25, 'T': 0.25 } )
# Create the insert states
i0 = State( i_d, name="I0" )
i1 = State( i_d, name="I1" )
i2 = State( i_d, name="I2" )
i3 = State( i_d, name="I3" )
# Create the match states
m1 = State( DiscreteDistribution({ "A": 0.95, 'C': 0.01, 'G': 0.01, 'T': 0.02 }) , name="M1" )
m2 = State( DiscreteDistribution({ "A": 0.003, 'C': 0.99, 'G': 0.003, 'T': 0.004 }) , name="M2" )
m3 = State( DiscreteDistribution({ "A": 0.01, 'C': 0.01, 'G': 0.01, 'T': 0.97 }) , name="M3" )
# Create the delete states
d1 = State( None, name="D1" )
d2 = State( None, name="D2" )
d3 = State( None, name="D3" )
# Add all the states to the model
model.add_states( [i0, i1, i2, i3, m1, m2, m3, d1, d2, d3 ] )
# Create transitions from match states
model.add_transition( model.start, m1, 0.9 )
model.add_transition( model.start, i0, 0.1 )
model.add_transition( m1, m2, 0.9 )
model.add_transition( m1, i1, 0.05 )
model.add_transition( m1, d2, 0.05 )
model.add_transition( m2, m3, 0.9 )
model.add_transition( m2, i2, 0.05 )
model.add_transition( m2, d3, 0.05 )
model.add_transition( m3, model.end, 0.9 )
model.add_transition( m3, i3, 0.1 )
# Create transitions from insert states
model.add_transition( i0, i0, 0.70, group="i_a" )
model.add_transition( i0, d1, 0.15, group="i_b" )
model.add_transition( i0, m1, 0.15, group="i_c" )
model.add_transition( i1, i1, 0.70, group="i_a" )
model.add_transition( i1, d2, 0.15, group="i_b" )
model.add_transition( i1, m2, 0.15, group="i_c" )
model.add_transition( i2, i2, 0.70, group="i_a" )
model.add_transition( i2, d3, 0.15, group="i_b" )
model.add_transition( i2, m3, 0.15, group="i_c" )
model.add_transition( i3, i3, 0.85, group="i_a" )
model.add_transition( i3, model.end, 0.15 )
# Create transitions from delete states
model.add_transition( d1, d2, 0.15, group="d_a" )
model.add_transition( d1, i1, 0.15, group="d_b" )
model.add_transition( d1, m2, 0.70, group="d_c" )
model.add_transition( d2, d3, 0.15, group="d_a" )
model.add_transition( d2, i2, 0.15, group="d_b" )
model.add_transition( d2, m3, 0.70, group="d_c" )
model.add_transition( d3, i3, 0.30 )
model.add_transition( d3, model.end, 0.70 )
# Call bake to finalize the structure of the model.
model.bake()
return model
def test_same_length_viterbi(model):
scores = [ -0.5132449003570658, -11.048101241343396, -9.125519674022627,
-5.0879558788604475 ]
sequences = [ list(x) for x in [ 'ACT', 'GGC', 'GAT', 'ACC' ] ]
for seq, score in zip( sequences, scores ):
assert_almost_equal( model.viterbi( seq )[0], score )
with pytest.raises( ValueError ):
model.viterbi( list('XXX') )
def test_variable_length_viterbi(model):
scores = [ -5.406181012423981, -10.88681993576597, -3.6244718790494277,
-3.644880750680635, -10.674332964640293, -10.393824835172445,
-8.67126440174503, -16.903451796110275, -16.451699654050792 ]
sequences = [ list(x) for x in ('A', 'GA', 'AC', 'AT', 'ATCC',
'ACGTG', 'ATTT', 'TACCCTC', 'TGTCAACACT') ]
for seq, score in zip( sequences, scores ):
assert_almost_equal( model.viterbi( seq )[0], score )
def test_log_probability(model):
scores = [ -5.3931, -0.5052, -11.8478, -14.3482 ]
sequences = [ list(x) for x in ( 'A', 'ACT', 'GGCA', 'TACCTGT' ) ]
for seq, score in zip( sequences, scores ):
assert round( model.log_probability( seq ), 4 ) == score
def test_posterior_transitions(model):
a_scores = [ 0.0, 0.0021, 0.2017, 1.5105 ]
b_scores = [ 0.013, 0.0036, 1.9836, 2.145 ]
c_scores = [ 0.013, 0.0035, 0.817, 0.477 ]
d_scores = [ 1.0, 0.0023, 0.2636, 0.3682 ]
t_scores = [ 4.013, 4.0083, 6.457, 8.9812 ]
sequences = [ list(x) for x in ( 'A', 'ACT', 'GGCA', 'TACCTGT' ) ]
indices = { state.name: i for i, state in enumerate( model.states ) }
i, j, k, l = indices['I2'], indices['I0'], indices['D1'], indices['D2']
scores = zip( sequences, a_scores, b_scores, c_scores, d_scores, t_scores )
for seq, a, b, c, d, t in scores:
trans, ems = model.forward_backward( seq )
assert round( trans[i].sum(), 4 ) == a
assert round( trans[j].sum(), 4 ) == b
assert round( trans[k].sum(), 4 ) == c
assert round( trans[l].sum(), 4 ) == d
assert round( trans.sum(), 4 ) == t
def test_posterior_transitions_w_training(model):
sequences = [ list(x) for x in ( 'A', 'ACT', 'GGCA', 'TACCTGT' ) ]
indices = { state.name: i for i, state in enumerate( model.states ) }
transitions = model.dense_transition_matrix()
i0, i1, i2 = indices['I0'], indices['I1'], indices['I2']
d1, d2, d3 = indices['D1'], indices['D2'], indices['D3']
m1, m2, m3 = indices['M1'], indices['M2'], indices['M3']
assert transitions[d1, i1] == transitions[d2, i2]
assert transitions[i0, i0] == transitions[i1, i1]
assert transitions[i0, i0] == transitions[i2, i2]
assert transitions[i0, m1] == transitions[i1, m2]
assert transitions[d1, d2] == transitions[d2, d3]
assert transitions[i0, d1] == transitions[i1, d2]
assert transitions[i0, d1] == transitions[i2, d3]
model.fit( sequences, verbose=False )
transitions = model.dense_transition_matrix()
assert transitions[d1, i1] != transitions[d2, i2]
assert transitions[i0, m1] != transitions[i1, m2]
assert transitions[d1, d2] != transitions[d2, d3]
assert transitions[i0, d1] != transitions[i1, d2]
assert transitions[i0, d1] != transitions[i2, d3]
def test_posterior_transitions_w_vtraining(model):
sequences = [ list(x) for x in ( 'A', 'ACT', 'GGCA', 'TACCTGT' ) ]
indices = { state.name: i for i, state in enumerate( model.states ) }
transitions = model.dense_transition_matrix()
i0, i1, i2, i3 = indices['I0'], indices['I1'], indices['I2'], indices['I3']
d1, d2, d3 = indices['D1'], indices['D2'], indices['D3']
m1, m2, m3 = indices['M1'], indices['M2'], indices['M3']
assert transitions[d1, i1] == transitions[d2, i2]
assert transitions[i0, i0] == transitions[i1, i1]
assert transitions[i0, i0] == transitions[i2, i2]
assert transitions[i0, m1] == transitions[i1, m2]
assert transitions[d1, d2] == transitions[d2, d3]
assert transitions[i0, d1] == transitions[i1, d2]
assert transitions[i0, d1] == transitions[i2, d3]
model.fit( sequences, verbose=False, algorithm='viterbi' )
transitions = model.dense_transition_matrix()
assert transitions[i0, i0] != transitions[i1, i1]
assert transitions[d1, d2] != transitions[d2, d3]
assert transitions[i0, d1] != transitions[i1, d2]
assert transitions[i0, d1] != transitions[i2, d3]
def test_posterior_transitions_w_tied_training(tied_edge):
model = tied_edge
sequences = [ list(x) for x in ( 'A', 'ACT', 'GGCA', 'TACCTGT' ) ]
indices = { state.name: i for i, state in enumerate( model.states ) }
transitions = model.dense_transition_matrix()
i0, i1, i2, i3 = indices['I0'], indices['I1'], indices['I2'], indices['I3']
d1, d2, d3 = indices['D1'], indices['D2'], indices['D3']
m1, m2, m3 = indices['M1'], indices['M2'], indices['M3']
assert transitions[d1, i1] == transitions[d2, i2]
assert transitions[i0, i0] == transitions[i1, i1]
assert transitions[i0, i0] == transitions[i2, i2]
assert transitions[i0, m1] == transitions[i1, m2]
assert transitions[d1, d2] == transitions[d2, d3]
assert transitions[i0, d1] == transitions[i1, d2]
assert transitions[i0, d1] == transitions[i2, d3]
model.fit( sequences, verbose=False )
transitions = model.dense_transition_matrix()
assert transitions[i0, i0] == transitions[i1, i1]
assert transitions[d1, d2] == transitions[d2, d3]
assert transitions[i0, d1] == transitions[i1, d2]
assert transitions[i0, d1] == transitions[i2, d3]
def test_posterior_transitions_w_tied_vtraining(tied_edge):
model = tied_edge
sequences = [ list(x) for x in ( 'A', 'ACT', 'GGCA', 'TACCTGT' ) ]
indices = { state.name: i for i, state in enumerate( model.states ) }
transitions = model.dense_transition_matrix()
i0, i1, i2 = indices['I0'], indices['I1'], indices['I2']
d1, d2, d3 = indices['D1'], indices['D2'], indices['D3']
m1, m2, m3 = indices['M1'], indices['M2'], indices['M3']
assert transitions[d1, i1] == transitions[d2, i2]
assert transitions[i0, i0] == transitions[i1, i1]
assert transitions[i0, i0] == transitions[i2, i2]
assert transitions[i0, m1] == transitions[i1, m2]
assert transitions[d1, d2] == transitions[d2, d3]
assert transitions[i0, d1] == transitions[i1, d2]
assert transitions[i0, d1] == transitions[i2, d3]
model.fit( sequences, verbose=False, algorithm='viterbi' )
transitions = model.dense_transition_matrix()
assert transitions[d1, i1] == transitions[d2, i2]
assert transitions[i0, i0] == transitions[i1, i1]
assert transitions[i0, i0] == transitions[i2, i2]
assert transitions[i0, m1] == transitions[i1, m2]
assert transitions[d1, d2] == transitions[d2, d3]
assert transitions[i0, d1] == transitions[i1, d2]
assert transitions[i0, d1] == transitions[i2, d3]
def test_posterior_emissions(model):
a_scores = [ 0.987, 0.9965, 0.183, 0.523 ]
b_scores = [ 0.0, 0.9977, 0.7364, 0.6318 ]
c_scores = [ 0.0, 0.9975, 0.6237, 0.8641 ]
d_scores = [ 0.0, 0.0021, 0.2017, 1.5105 ]
sequences = [ list(x) for x in ( 'A', 'ACT', 'GGCA', 'TACCTGT' ) ]
indices = { state.name: i for i, state in enumerate( model.states ) }
i, j, k, l = indices['M1'], indices['M2'], indices['M3'], indices['I2']
for seq, a, b, c, d in zip( sequences, a_scores, b_scores, c_scores, d_scores ):
trans, ems = model.forward_backward( seq )
ems = np.exp( ems )
assert round( ems[:,i].sum(), 4 ) == a
assert round( ems[:,j].sum(), 4 ) == b
assert round( ems[:,k].sum(), 4 ) == c
assert round( ems[:,l].sum(), 4 ) == d
assert round( ems.sum() ) == len( seq )
def test_posterior_emissions_w_multitransition_setup(multitransition):
model = multitransition
a_scores = [ 0.987, 0.9965, 0.183, 0.523 ]
b_scores = [ 0.0, 0.9977, 0.7364, 0.6318 ]
c_scores = [ 0.0, 0.9975, 0.6237, 0.8641 ]
d_scores = [ 0.0, 0.0021, 0.2017, 1.5105 ]
sequences = [ list(x) for x in ( 'A', 'ACT', 'GGCA', 'TACCTGT' ) ]
indices = { state.name: i for i, state in enumerate( model.states ) }
i, j, k, l = indices['M1'], indices['M2'], indices['M3'], indices['I2']
for seq, a, b, c, d in zip( sequences, a_scores, b_scores, c_scores, d_scores ):
trans, ems = model.forward_backward( seq )
ems = np.exp( ems )
assert round( ems[:,i].sum(), 4 ) == a
assert round( ems[:,j].sum(), 4 ) == b
assert round( ems[:,k].sum(), 4 ) == c
assert round( ems[:,l].sum(), 4 ) == d
assert round( ems.sum() ) == len( seq )
def test_posterior_emissions_w_tied_edge_setup(tied_edge):
model = tied_edge
a_scores = [ 0.987, 0.9965, 0.183, 0.523 ]
b_scores = [ 0.0, 0.9977, 0.7364, 0.6318 ]
c_scores = [ 0.0, 0.9975, 0.6237, 0.8641 ]
d_scores = [ 0.0, 0.0021, 0.2017, 1.5105 ]
sequences = [ list(x) for x in ( 'A', 'ACT', 'GGCA', 'TACCTGT' ) ]
indices = { state.name: i for i, state in enumerate( model.states ) }
i, j, k, l = indices['M1'], indices['M2'], indices['M3'], indices['I2']
for seq, a, b, c, d in zip( sequences, a_scores, b_scores, c_scores, d_scores ):
trans, ems = model.forward_backward( seq )
ems = np.exp( ems )
assert round( ems[:,i].sum(), 4 ) == a
assert round( ems[:,j].sum(), 4 ) == b
assert round( ems[:,k].sum(), 4 ) == c
assert round( ems[:,l].sum(), 4 ) == d
assert round( ems.sum() ) == len( seq )
def test_properties(model):
assert model.edge_count() == 29
assert model.state_count() == 12
assert model.name == "Global Alignment"
def test_to_json(model):
b = json.loads(model.to_json())
assert b['name'] == 'Global Alignment'
assert len(b['edges']) == 29
assert len(b['states']) == 12
assert b['silent_index'] == 7
def test_from_json(model):
hmm = HiddenMarkovModel.from_json( model.to_json() )
assert hmm.edge_count() == 29
assert hmm.state_count() == 12
assert hmm.name == "Global Alignment"
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