def backward_log_probabilities(self, sequence, normalize=True):
"""We override this to provide a faster implementation.
@see: forward_log_probability
Returns a numpy 2d array instead of a list of lists.
"""
T = len(sequence)
N = len(self.label_dom)
beta = numpy.zeros((T, N), numpy.float64)
# Initialize
beta[T-1, :] = numpy.log2(1.0/N)
# Iterate backwards over the other timesteps
for t in range(T-2, -1, -1):
for i,si in enumerate(self.label_dom):
# Multiply each next state's prob by the transition prob
# from this state to that and the emission prob in that next
# state
log_probs = [
beta[t+1, j] + self.transition_log_probability(sj, si) + \
self.emission_log_probability(sequence[t+1], sj) \
for j,sj in enumerate(self.label_dom)]
beta[t, i] = sum_logs(log_probs)
# Normalize by dividing all values by the total probability
if normalize:
total = sum_logs(beta[t,:])
for j in range(N):
beta[t,j] -= total
return beta
def backward_log_probabilities(self, sequence, normalize=True):
"""We override this to provide a faster implementation.
@see: forward_log_probability
Returns a numpy 2d array instead of a list of lists.
"""
T = len(sequence)
N = len(self.label_dom)
beta = numpy.zeros((T, N), numpy.float64)
# Initialize
beta[T - 1, :] = numpy.log2(1.0 / N)
# Iterate backwards over the other timesteps
for t in range(T - 2, -1, -1):
for i, si in enumerate(self.label_dom):
# Multiply each next state's prob by the transition prob
# from this state to that and the emission prob in that next
# state
log_probs = [
beta[t+1, j] + self.transition_log_probability(sj, si) + \
self.emission_log_probability(sequence[t+1], sj) \
for j,sj in enumerate(self.label_dom)]
beta[t, i] = sum_logs(log_probs)
# Normalize by dividing all values by the total probability
if normalize:
total = sum_logs(beta[t, :])
for j in range(N):
beta[t, j] -= total
return beta
def forward_log_probabilities(self, sequence, normalize=True, array=False):
"""We override this to provide a faster implementation.
It might also be possible to speed up the superclass' implementation
using numpy, but it's easier here because we know we're using an
HMM, not a higher-order ngram.
This is based on the fwd prob calculation in NLTK's HMM implementation.
@type array: bool
@param array: if True, returns a numpy 2d array instead of a list of
dicts.
"""
T = len(sequence)
N = len(self.label_dom)
alpha = numpy.zeros((T, N), numpy.float64)
# Prepare the first column of the matrix: probs of all states in the
# first timestep
for i,state in enumerate(self.label_dom):
alpha[0,i] = self.transition_log_probability(state, None) + \
self.emission_log_probability(sequence[0], state)
# Iterate over the other timesteps
for t in range(1, T):
for j,sj in enumerate(self.label_dom):
# Multiply each previous state's prob by the transition prob
# to this state and sum them all together
log_probs = [
alpha[t-1, i] + self.transition_log_probability(sj, si) \
for i,si in enumerate(self.label_dom)]
# Also multiply this by the emission probability
alpha[t, j] = sum_logs(log_probs) + \
self.emission_log_probability(sequence[t], sj)
# Normalize by dividing all values by the total probability
if normalize:
for t in range(T):
total = sum_logs(alpha[t,:])
for j in range(N):
alpha[t,j] -= total
if not array:
# Convert this into a list of dicts
matrix = []
for t in range(T):
timestep = {}
for (i,label) in enumerate(self.label_dom):
timestep[label] = alpha[t,i]
matrix.append(timestep)
return matrix
else:
return alpha
def emission_log_probability(self, emission, state):
"""
Gives the probability P(emission | label). Returned as a base 2
log.
The emission should be a pair of (root,label), together defining a
chord.
There's a special case of this. If the emission is a list, it's
assumed to be a I{distribution} over emissions. The list should
contain (prob,em) pairs, where I{em} is an emission, such as is
normally passed into this function, and I{prob} is the weight to
give to this possible emission. The probabilities of the possible
emissions are summed up, weighted by the I{prob} values.
"""
if type(emission) is list:
# Average probability over the possible emissions
probs = []
for (prob,em) in emission:
probs.append(logprob(prob) + \
self.emission_log_probability(em, state))
return sum_logs(probs)
# Single chord label
state_root,schema = state
chord_root,label = emission
# Probability is 0 if the roots don't match
if state_root != chord_root:
return float('-inf')
else:
return self.emission_dist[schema].logprob(label)
def _get_transition_backoff_scaler(self, context):
# This is just for the schema distribution
if context not in self._discount_cache:
# The prob mass reserved for unseen events can be computed by
# summing probabilities over all seen events and subtracting
# from 1.
# Our discounting model distributes this probability evenly over
# the unseen events, so we can compute the discounted mass by
# getting the probability of one unseen event and multiplying it.
seen_labels = set([lab for lab in self.schemata+[None] if
self.schema_transition_counts[context][lab] > 0])
if len(seen_labels) == 0:
# Not seen anything in this context. All mass is discounted!
self._discount_cache[context] = 0.0
else:
unseen_labels = set(self.schemata+[None]) - seen_labels
# Try getting some event that won't have been seen
# Compute how much mass is reserved for unseen events
discounted_mass = self.schema_transition_dist[context].prob(
"%%% UNSEEN LABEL %%%") \
* len(unseen_labels)
# Compute how much probability the n-1 order model assigns to
# things unseen by this model
backoff_context = context[:-1]
backoff_seen_mass = sum_logs([
self.backoff_model.schema_transition_log_probability_schemata(lab,
*backoff_context)
for lab in unseen_labels])
self._discount_cache[context] = logprob(discounted_mass) - \
backoff_seen_mass
return self._discount_cache[context]
def emission_log_probability(self, emission, state):
"""
Gives the probability P(emission | label). Returned as a base 2
log.
The emission should be a pair of (root,label), together defining a
chord.
There's a special case of this. If the emission is a list, it's
assumed to be a I{distribution} over emissions. The list should
contain (prob,em) pairs, where I{em} is an emission, such as is
normally passed into this function, and I{prob} is the weight to
give to this possible emission. The probabilities of the possible
emissions are summed up, weighted by the I{prob} values.
"""
if type(emission) is list:
# Average probability over the possible emissions
probs = []
for (prob, em) in emission:
probs.append(logprob(prob) + \
self.emission_log_probability(em, state))
return sum_logs(probs)
# Single chord label
state_root, schema = state
chord_root, label = emission
# Probability is 0 if the roots don't match
if state_root != chord_root:
return float('-inf')
else:
return self.emission_dist[schema].logprob(label)
def _get_transition_backoff_scaler(self, context):
# This is just for the schema distribution
if context not in self._discount_cache:
# The prob mass reserved for unseen events can be computed by
# summing probabilities over all seen events and subtracting
# from 1.
# Our discounting model distributes this probability evenly over
# the unseen events, so we can compute the discounted mass by
# getting the probability of one unseen event and multiplying it.
seen_labels = set([
lab for lab in self.schemata + [None]
if self.schema_transition_counts[context][lab] > 0
])
if len(seen_labels) == 0:
# Not seen anything in this context. All mass is discounted!
self._discount_cache[context] = 0.0
else:
unseen_labels = set(self.schemata + [None]) - seen_labels
# Try getting some event that won't have been seen
# Compute how much mass is reserved for unseen events
discounted_mass = self.schema_transition_dist[context].prob(
"%%% UNSEEN LABEL %%%") \
* len(unseen_labels)
# Compute how much probability the n-1 order model assigns to
# things unseen by this model
backoff_context = context[:-1]
backoff_seen_mass = sum_logs([
self.backoff_model.
schema_transition_log_probability_schemata(
lab, *backoff_context) for lab in unseen_labels
])
self._discount_cache[context] = logprob(discounted_mass) - \
backoff_seen_mass
return self._discount_cache[context]
def backward_log_probabilities(self, sequence, normalize=True, array=False):
"""We override this to provide a faster implementation.
@see: forward_log_probability
@type array: bool
@param array: if True, returns a numpy 2d array instead of a list of
dicts.
"""
T = len(sequence)
N = len(self.label_dom)
beta = numpy.zeros((T, N), numpy.float64)
# Initialize with the probabilities of transitioning to the final state
for i,si in enumerate(self.label_dom):
beta[T-1, i] = self.transition_log_probability(None, si)
# Iterate backwards over the other timesteps
for t in range(T-2, -1, -1):
for i,si in enumerate(self.label_dom):
# Multiply each next state's prob by the transition prob
# from this state to that and the emission prob in that next
# state
log_probs = [
beta[t+1, j] + self.transition_log_probability(sj, si) + \
self.emission_log_probability(sequence[t+1], sj) \
for j,sj in enumerate(self.label_dom)]
beta[t, i] = sum_logs(log_probs)
# Normalize by dividing all values by the total probability
if normalize:
total = sum_logs(beta[t,:])
for j in range(N):
beta[t,j] -= total
if not array:
# Convert this into a list of dicts
matrix = []
for t in range(T):
timestep = {}
for (i,label) in enumerate(self.label_dom):
timestep[label] = beta[t,i]
matrix.append(timestep)
return matrix
else:
return beta
def emission_log_probability(self, emission, state):
"""
Gives the probability P(emission | label). Returned as a base 2
log.
The emission should be a pair of (root,label), together defining a
chord.
There's a special case of this. If the emission is a list, it's
assumed to be a I{distribution} over emissions. The list should
contain (prob,em) pairs, where I{em} is an emission, such as is
normally passed into this function, and I{prob} is the weight to
give to this possible emission. The probabilities of the possible
emissions are summed up, weighted by the I{prob} values.
"""
if type(emission) is list:
# Average probability over the possible emissions
probs = []
for (prob, em) in emission:
probs.append(logprob(prob) + \
self.emission_log_probability(em, state))
return sum_logs(probs)
# Single chord label
point, function = state
chord_root, label = emission
X, Y, x, y = point
# Work out the chord substitution
subst = (chord_root - coordinate_to_et_2d((x, y))) % 12
# Generate the substitution given the chord function
subst_prob = self.subst_emission_dist[function].logprob(subst)
# Generate the label given the subst and chord function
label_prob = self.type_emission_dist[(subst, function)].logprob(label)
return subst_prob + label_prob
def emission_log_probability(self, emission, state):
"""
Gives the probability P(emission | label). Returned as a base 2
log.
The emission should be a pair of (root,label), together defining a
chord.
There's a special case of this. If the emission is a list, it's
assumed to be a I{distribution} over emissions. The list should
contain (prob,em) pairs, where I{em} is an emission, such as is
normally passed into this function, and I{prob} is the weight to
give to this possible emission. The probabilities of the possible
emissions are summed up, weighted by the I{prob} values.
"""
if type(emission) is list:
# Average probability over the possible emissions
probs = []
for (prob,em) in emission:
probs.append(logprob(prob) + \
self.emission_log_probability(em, state))
return sum_logs(probs)
# Single chord label
point,function = state
chord_root,label = emission
X,Y,x,y = point
# Work out the chord substitution
subst = (chord_root - coordinate_to_et_2d((x,y))) % 12
# Generate the substitution given the chord function
subst_prob = self.subst_emission_dist[function].logprob(subst)
# Generate the label given the subst and chord function
label_prob = self.type_emission_dist[(subst,function)].logprob(label)
return subst_prob + label_prob