class FBGMM(object):
"""
A finite Bayesian Gaussian mixture model (FBGMM).
See `GaussianComponents` or `GaussianComponentsDiag` for an overview of the
parameters not mentioned below.
Parameters
----------
alpha : float
Concentration parameter for the symmetric Dirichlet prior over the
mixture weights.
K : int
The number of mixture components. This is actually a maximum number,
and it is possible to empty out some of these components.
assignments : vector of int or str
If vector of int, this gives the initial component assignments. The
vector should therefore have N entries between 0 and `K`. Values of
-1 is also allowed, indicating that the data vector does not belong to
any component. Alternatively, `assignments` can take one of the
following values:
- "rand": Vectors are assigned randomly to one of `K` components.
- "each-in-own": Each vector is assigned to a component of its own.
covariance_type : str
String describing the type of covariance parameters to use. Must be
one of "full", "diag" or "fixed".
lms : float
Language model scaling factor.
"""
def __init__(self, X, prior, alpha, K, assignments="rand",
covariance_type="full", lms=1.0):
self.alpha = alpha
self.prior = prior
self.covariance_type = covariance_type
self.lms = lms
self.setup_components(K, assignments, X)
# N, D = X.shape
# # Initial component assignments
# if assignments == "rand":
# assignments = np.random.randint(0, K, N)
# # Make sure we have consequetive values
# for k in xrange(assignments.max()):
# while len(np.nonzero(assignments == k)[0]) == 0:
# assignments[np.where(assignments > k)] -= 1
# if assignments.max() == k:
# break
# elif assignments == "each-in-own":
# assignments = np.arange(N)
# else:
# # `assignments` is a vector
# pass
# if covariance_type == "full":
# self.components = GaussianComponents(X, prior, assignments, K_max=K)
# elif covariance_type == "diag":
# self.components = GaussianComponentsDiag(X, prior, assignments, K_max=K)
# elif covariance_type == "fixed":
# self.components = GaussianComponentsFixedVar(X, prior, assignments, K_max=K)
# else:
# assert False, "Invalid covariance type."
def setup_components(self, K, assignments="rand", X=None):
"""
Setup the `components` attribute.
See parameters of `FBGMM` for parameters not described below. This
function is also useful for resetting the `components`, e.g. if you
want to change the maximum number of possible components.
Parameters
----------
X : NxD matrix or None
The data matrix. If None, then it is assumed that the `components`
attribute has already been initialized and that this function is
called to reset the `components`; in this case the data is taken
from the previous initialization.
"""
if X is None:
assert hasattr(self, "components")
X = self.components.X
N, D = X.shape
# Initial component assignments
if isinstance(assignments, basestring) and assignments == "rand":
assignments = np.random.randint(0, K, N)
elif isinstance(assignments, basestring) and assignments == "each-in-own":
assignments = np.arange(N)
else:
# `assignments` is a vector
pass
# Make sure we have consequetive values
for k in xrange(assignments.max()):
while len(np.nonzero(assignments == k)[0]) == 0:
assignments[np.where(assignments > k)] -= 1
if assignments.max() == k:
break
if self.covariance_type == "full":
self.components = GaussianComponents(X, self.prior, assignments, K_max=K)
elif self.covariance_type == "diag":
self.components = GaussianComponentsDiag(X, self.prior, assignments, K_max=K)
elif self.covariance_type == "fixed":
self.components = GaussianComponentsFixedVar(X, self.prior, assignments, K_max=K)
else:
assert False, "Invalid covariance type."
def set_K(self, K, reassign=True):
"""
Set the number of components `K`.
The `K` largest existing components are kept, and the rest of the data
vectors are re-assigned to one of these (if `reassign` is True).
"""
if self.components.K <= K:
# The active components are already less than the new K
self.components.K_max = K
return
sizes = self.components.counts
old_assignments = self.components.assignments
# Keep only the `K` biggest assignments
assignments_to_keep = list(np.argsort(sizes)[-K:])
new_assignments = [
i if i in assignments_to_keep else -1 for i in old_assignments
]
mapping = dict([(assignments_to_keep[i], i) for i in range(K)])
mapping[-1] = -1
new_assignments = np.array([mapping[i] for i in new_assignments])
# Make sure we have consequetive assignment values
for k in xrange(new_assignments.max()):
while len(np.nonzero(new_assignments == k)[0]) == 0:
new_assignments[np.where(new_assignments > k)] -= 1
if new_assignments.max() == k:
break
# Create new `components` attribute
self.setup_components(K, list(new_assignments))
# Now add back those vectors which were assigned before but are unassigned now
if reassign:
for i, old_assignment in enumerate(old_assignments):
new_assignment = new_assignments[i]
if old_assignment == -1 or new_assignment != -1:
continue
self.gibbs_sample_inside_loop_i(i)
# sizes = self.components.counts
# cur_assignments = self.components.assignments
# print cur_assignments[:100]
# # Keep only the `K` biggest assignments
# assignments_to_keep = list(np.argsort(sizes)[-K:])
# print assignments_to_keep
# new_assignments = [
# i if i in assignments_to_keep else -1 if i == -1 else
# random.choice(assignments_to_keep) for i in cur_assignments
# ]
# mapping = dict([(assignments_to_keep[i], i) for i in range(K)])
# print mapping
# mapping[-1] = -1
# new_assignments = np.array([mapping[i] for i in new_assignments])
# print new_assignments[:100]
# # Make sure we have consequetive assignment values
# for k in xrange(new_assignments.max()):
# while len(np.nonzero(new_assignments == k)[0]) == 0:
# new_assignments[np.where(new_assignments > k)] -= 1
# if new_assignments.max() == k:
# break
# self.setup_components(K, list(new_assignments))
def log_prob_z(self):
"""
Return the log marginal probability of component assignment P(z).
See (24.24) in Murphy, p. 842.
"""
log_prob_z = (
gammaln(self.alpha)
- gammaln(self.alpha + np.sum(self.components.counts))
+ np.sum(
gammaln(
self.components.counts
+ float(self.alpha)/self.components.K_max
)
- gammaln(self.alpha/self.components.K_max)
)
)
return log_prob_z
def log_prob_X_given_z(self):
"""Return the log probability of data in each component p(X|z)."""
return self.components.log_marg()
def log_marg(self):
"""Return log marginal of data and component assignments: p(X, z)"""
log_prob_z = self.log_prob_z()
log_prob_X_given_z = self.log_prob_X_given_z()
# # Log probability of component assignment, (24.24) in Murphy, p. 842
# log_prob_z = (
# gammaln(self.alpha)
# - gammaln(self.alpha + np.sum(self.components.counts))
# + np.sum(
# gammaln(
# self.components.counts
# + float(self.alpha)/self.components.K_max
# )
# - gammaln(self.alpha/self.components.K_max)
# )
# )
# # Log probability of data in each component
# log_prob_X_given_z = self.components.log_marg()
return log_prob_z + log_prob_X_given_z
# @profile
def log_marg_i(self, i, log_prob_z=[], log_prob_z_given_y=[], scale=False):
"""
Return the log marginal of the i'th data vector: p(x_i)
Here it is assumed that x_i is not currently in the acoustic model,
so the -1 term used in the denominator in (24.26) in Murphy, p. 843
is dropped (since x_i is already not included in the counts).
"""
assert i != -1
if not len(log_prob_z):
# Compute log probability of `X[i]` belonging to each component
# (24.26) in Murphy, p. 843
log_prob_z = self.lms * (
np.log(float(self.alpha)/self.components.K_max + self.components.counts)
# - np.log(_cython_utils.sum_ints(self.components.counts) + self.alpha - 1.)
- np.log(_cython_utils.sum_ints(self.components.counts) + self.alpha)
)
if len(log_prob_z_given_y):
log_prob_z += log_prob_z_given_y
log_prob_z -= logsumexp(log_prob_z)
# print('In fbgmm log_marg_i %d, prior: ' % (i) + str(np.min(log_prob_z)) + ' ' + str(np.max(log_prob_z)))
# log_prob_z = lms * (
# np.ones(self.components.K_max)*(
# np.log(float(self.alpha)/self.components.K_max + self.components.counts)
# - np.log(np.sum(self.components.counts) + self.alpha - 1.)
# )
# )
# logger.info("log_prob_z: " + str(log_prob_z))
if scale:
log_likelihood_z = np.nan * np.ones(log_prob_z.shape)
log_likelihood_z[:self.components.K] = self.components.log_post_pred(i)
log_likelihood_z[self.components.K:] = self.components.log_prior(i)
log_prob_z += log_likelihood_z - _cython_utils.logsumexp(log_likelihood_z)
else:
# (24.23) in Murphy, p. 842
log_prob_z[:self.components.K] += self.components.log_post_pred(i)
# Empty (unactive) components
log_prob_z[self.components.K:] += self.components.log_prior(i)
# print('In fbgmm log_marg_i %d, posterior: ' % (i) + str(np.min(log_prob_z)) + ' ' + str(np.max(log_prob_z)))
return _cython_utils.logsumexp(log_prob_z)
def gibbs_sample(self, n_iter, consider_unassigned=True,
anneal_schedule=None, anneal_start_temp_inv=0.1,
anneal_end_temp_inv=1, n_anneal_steps=-1, log_prob_zs=[], log_prob_z_given_ys=[]): #, lms=1.0):
"""
Perform `n_iter` iterations Gibbs sampling on the FBGMM.
Parameters
----------
consider_unassigned : bool
Whether unassigned vectors (-1 in `assignments`) should be
considered during sampling.
anneal_schedule : str
Can be one of the following:
- None: A constant temperature of `anneal_end_temp_inv` is used
throughout; if `anneal_end_temp_inv` is left at default (1), then
this is equivalent to not performing annealing.
- "linear": Linearly take the inverse temperature from
`anneal_start_temp_inv` to `anneal_end_temp_inv` in
`n_anneal_steps`. If `n_anneal_steps` is -1 for this schedule,
annealing is performed over all `n_iter` iterations.
- "step": Piecewise schedule in which the inverse temperature is
taken from `anneal_start_temp_inv` to `anneal_end_temp_inv` in
`n_anneal_steps` steps (annealing will be performed over all
`n_iter` iterations; it might be worth adding an additional
variable for this case to allow the step schedule to stop early).
Return
------
record_dict : dict
Contains several fields describing the sampling process. Each field
is described by its key and statistics are given in a list which
covers the Gibbs sampling iterations.
"""
# Setup record dictionary
record_dict = {}
record_dict["sample_time"] = []
start_time = time.time()
record_dict["log_marg"] = []
record_dict["log_prob_z"] = []
record_dict["log_prob_X_given_z"] = []
record_dict["anneal_temp"] = []
record_dict["components"] = []
# Setup annealing iterator
if anneal_schedule is None:
get_anneal_temp = iter([])
elif anneal_schedule == "linear":
if n_anneal_steps == -1:
n_anneal_steps = n_iter
anneal_list = 1./np.linspace(anneal_start_temp_inv, anneal_end_temp_inv, n_anneal_steps)
get_anneal_temp = iter(anneal_list)
elif anneal_schedule == "step":
assert not n_anneal_steps == -1, (
"`n_anneal_steps` of -1 not allowed for step annealing schedule"
)
n_iter_per_step = int(round(float(n_iter)/n_anneal_steps))
anneal_list = np.linspace(anneal_start_temp_inv, anneal_end_temp_inv, n_anneal_steps)
anneal_list = 1./anneal_list
anneal_list = np.repeat(anneal_list, n_iter_per_step)
get_anneal_temp = iter(anneal_list)
if len(log_prob_zs):
log_prob_zs = np.concatenate(log_prob_zs, axis=0)
if len(log_prob_z_given_ys):
log_prob_z_given_ys = np.concatenate(log_prob_z_given_ys, axis=0)
# Loop over iterations
for i_iter in range(n_iter):
# Get anneal temperature
anneal_temp = next(get_anneal_temp, anneal_end_temp_inv)
# Loop over data items
count = 0
for i in xrange(self.components.N):
# Cache some old values for possible future use
k_old = self.components.assignments[i]
if not consider_unassigned and k_old == -1:
continue
K_old = self.components.K
stats_old = self.components.cache_component_stats(k_old)
# Remove data vector `X[i]` from its current component
# TODO Handle this
self.components.del_item(i)
# Compute log probability of `X[i]` belonging to each component
# (24.26) in Murphy, p. 843
if not len(log_prob_zs):
log_prob_z = self.lms * (
np.ones(self.components.K_max)*np.log(
float(self.alpha)/self.components.K_max + self.components.counts
)
)
if len(log_prob_z_given_ys):
log_prob_z += log_prob_z_given_ys[count]
log_prob_z -= logsumexp(log_prob_z)
else:
log_prob_z = deepcopy(log_prob_zs[count])
count += 1
# (24.23) in Murphy, p. 842
log_prob_z[:self.components.K] += self.components.log_post_pred(i)
# Empty (unactive) components
log_prob_z[self.components.K:] += self.components.log_prior(i)
if anneal_temp != 1:
log_prob_z = log_prob_z - logsumexp(log_prob_z)
log_prob_z_anneal = 1./anneal_temp * log_prob_z - logsumexp(1./anneal_temp * log_prob_z)
prob_z = np.exp(log_prob_z_anneal)
else:
prob_z = np.exp(log_prob_z - logsumexp(log_prob_z))
# prob_z = np.exp(log_prob_z - logsumexp(log_prob_z))
# Sample the new component assignment for `X[i]`
k = utils.draw(prob_z)
# There could be several empty, unactive components at the end
if k > self.components.K:
k = self.components.K
# print prob_z, k, prob_z[k]
# Add data item X[i] into its component `k`
if k == k_old and self.components.K == K_old:
# Assignment same and no components have been removed
self.components.restore_component_from_stats(k_old, *stats_old)
self.components.assignments[i] = k_old
else:
# Add data item X[i] into its new component `k`
self.components.add_item(i, k)
# Update record
record_dict["sample_time"].append(time.time() - start_time)
start_time = time.time()
record_dict["log_marg"].append(self.log_marg())
record_dict["log_prob_z"].append(self.log_prob_z())
record_dict["log_prob_X_given_z"].append(self.log_prob_X_given_z())
record_dict["anneal_temp"].append(anneal_temp)
record_dict["components"].append(self.components.K)
# Log info
info = "iteration: " + str(i_iter)
for key in sorted(record_dict):
info += ", " + key + ": " + str(record_dict[key][-1])
logger.info(info)
return record_dict
def gibbs_sample_inside_loop_i(self, i, anneal_temp=1, log_prob_z=[], log_prob_z_given_y=[]): #, lms=1.):
"""
Perform the inside loop of Gibbs sampling for data vector `i`.
This is the inside of `gibbs_sample` and can be used by outside objects
to perform only the inside loop part of the Gibbs sampling operation.
The step in the loop is sample a new assignment for data vector `i`.
The reason for not replacing the actual inner part of `gibbs_sample` by
a call to this function is because this won't allow for caching the old
component stats.
"""
if not len(log_prob_z):
# Compute log probability of `X[i]` belonging to each component
# (24.26) in Murphy, p. 843
log_prob_z = self.lms * (
np.ones(self.components.K_max)*np.log(
float(self.alpha)/self.components.K_max + self.components.counts
)
)
if len(log_prob_z_given_y):
log_prob_z += log_prob_z_given_y
log_prob_z -= logsumexp(log_prob_z)
# print('Maximum indices according to prior: ' + str(np.argsort(-log_prob_z)[:5]))
# (24.23) in Murphy, p. 842
log_prob_z[:self.components.K] += self.components.log_post_pred(i)
# Empty (unactive) components
log_prob_z[self.components.K:] += self.components.log_prior(i)
if anneal_temp != 1:
log_prob_z = log_prob_z - logsumexp(log_prob_z)
log_prob_z_anneal = 1./anneal_temp * log_prob_z - logsumexp(1./anneal_temp * log_prob_z)
prob_z = np.exp(log_prob_z_anneal)
# print('Maximum indices according to posterior: ' + str(np.argsort(-prob_z)[:5]))
# print('Maximum probs: ' + str(sorted(prob_z, reverse=True)[:5]))
else:
prob_z = np.exp(log_prob_z - logsumexp(log_prob_z))
# prob_z = np.exp(log_prob_z - logsumexp(log_prob_z))
assert not np.isnan(np.sum(prob_z))
# TODO Try using the viterbi path
# Sample the new component assignment for `X[i]`
k = utils.draw(prob_z)
# There could be several empty, unactive components at the end
if k > self.components.K:
k = self.components.K
logger.debug("Adding item " + str(i) + " to acoustic model component " + str(k))
self.components.add_item(i, k)
def map_assign_i(self, i):
"""
Assign data vector `i` to the component giving the maximum posterior.
This function is very similar to `gibbs_sample_inside_loop_i`, but
instead of sampling the assignment, the MAP estimate is used.
"""
# Compute log probability of `X[i]` belonging to each component
# (24.26) in Murphy, p. 843
log_prob_z = (
np.ones(self.components.K_max)*np.log(
float(self.alpha)/self.components.K_max + self.components.counts
)
)
# (24.23) in Murphy, p. 842
log_prob_z[:self.components.K] += self.components.log_post_pred(i)
# Empty (unactive) components
log_prob_z[self.components.K:] += self.components.log_prior(i)
prob_z = np.exp(log_prob_z - logsumexp(log_prob_z))
# Take the MAP assignment for `X[i]`
k = np.argmax(prob_z)
# There could be several empty, unactive components at the end
if k > self.components.K:
k = self.components.K
logger.debug("Adding item " + str(i) + " to acoustic model component " + str(k))
self.components.add_item(i, k)
def get_n_assigned(self):
"""Return the number of assigned data vectors."""
return len(np.where(self.components.assignments != -1)[0])
class FBGMM(object):
"""
A finite Bayesian Gaussian mixture model (FBGMM).
See `GaussianComponents` or `GaussianComponentsDiag` for an overview of the
parameters not mentioned below.
Parameters
----------
alpha : float
Concentration parameter for the symmetric Dirichlet prior over the
mixture weights.
K : int
The number of mixture components. This is actually a maximum number,
and it is possible to empty out some of these components.
assignments : vector of int or str
If vector of int, this gives the initial component assignments. The
vector should therefore have N entries between 0 and `K`. Values of
-1 is also allowed, indicating that the data vector does not belong to
any component. Alternatively, `assignments` can take one of the
following values:
- "rand": Vectors are assigned randomly to one of `K` components.
- "each-in-own": Each vector is assigned to a component of its own.
covariance_type : str
String describing the type of covariance parameters to use. Must be
one of "full", "diag" or "fixed".
lms : float
Language model scaling factor.
"""
def __init__(self, X, prior, alpha, K, assignments="rand",
covariance_type="full", lms=1.0):
self.alpha = alpha
self.prior = prior
self.covariance_type = covariance_type
self.lms = lms
self.setup_components(K, assignments, X)
# N, D = X.shape
# # Initial component assignments
# if assignments == "rand":
# assignments = np.random.randint(0, K, N)
# # Make sure we have consequetive values
# for k in xrange(assignments.max()):
# while len(np.nonzero(assignments == k)[0]) == 0:
# assignments[np.where(assignments > k)] -= 1
# if assignments.max() == k:
# break
# elif assignments == "each-in-own":
# assignments = np.arange(N)
# else:
# # `assignments` is a vector
# pass
# if covariance_type == "full":
# self.components = GaussianComponents(X, prior, assignments, K_max=K)
# elif covariance_type == "diag":
# self.components = GaussianComponentsDiag(X, prior, assignments, K_max=K)
# elif covariance_type == "fixed":
# self.components = GaussianComponentsFixedVar(X, prior, assignments, K_max=K)
# else:
# assert False, "Invalid covariance type."
def setup_components(self, K, assignments="rand", X=None):
"""
Setup the `components` attribute.
See parameters of `FBGMM` for parameters not described below. This
function is also useful for resetting the `components`, e.g. if you
want to change the maximum number of possible components.
Parameters
----------
X : NxD matrix or None
The data matrix. If None, then it is assumed that the `components`
attribute has already been initialized and that this function is
called to reset the `components`; in this case the data is taken
from the previous initialization.
"""
if X is None:
assert hasattr(self, "components")
X = self.components.X
N, D = X.shape
# Initial component assignments
if isinstance(assignments, basestring) and assignments == "rand":
assignments = np.random.randint(0, K, N)
elif isinstance(assignments, basestring) and assignments == "each-in-own":
assignments = np.arange(N)
else:
# `assignments` is a vector
pass
# Make sure we have consequetive values
for k in xrange(assignments.max()):
while len(np.nonzero(assignments == k)[0]) == 0:
assignments[np.where(assignments > k)] -= 1
if assignments.max() == k:
break
if self.covariance_type == "full":
self.components = GaussianComponents(X, self.prior, assignments, K_max=K)
elif self.covariance_type == "diag":
self.components = GaussianComponentsDiag(X, self.prior, assignments, K_max=K)
elif self.covariance_type == "fixed":
self.components = GaussianComponentsFixedVar(X, self.prior, assignments, K_max=K)
else:
assert False, "Invalid covariance type."
def set_K(self, K, reassign=True):
"""
Set the number of components `K`.
The `K` largest existing components are kept, and the rest of the data
vectors are re-assigned to one of these (if `reassign` is True).
"""
if self.components.K <= K:
# The active components are already less than the new K
self.components.K_max = K
return
sizes = self.components.counts
old_assignments = self.components.assignments
# Keep only the `K` biggest assignments
assignments_to_keep = list(np.argsort(sizes)[-K:])
new_assignments = [
i if i in assignments_to_keep else -1 for i in old_assignments
]
mapping = dict([(assignments_to_keep[i], i) for i in range(K)])
mapping[-1] = -1
new_assignments = np.array([mapping[i] for i in new_assignments])
# Make sure we have consequetive assignment values
for k in xrange(new_assignments.max()):
while len(np.nonzero(new_assignments == k)[0]) == 0:
new_assignments[np.where(new_assignments > k)] -= 1
if new_assignments.max() == k:
break
# Create new `components` attribute
self.setup_components(K, list(new_assignments))
# Now add back those vectors which were assigned before but are unassigned now
if reassign:
for i, old_assignment in enumerate(old_assignments):
new_assignment = new_assignments[i]
if old_assignment == -1 or new_assignment != -1:
continue
self.gibbs_sample_inside_loop_i(i)
# sizes = self.components.counts
# cur_assignments = self.components.assignments
# print cur_assignments[:100]
# # Keep only the `K` biggest assignments
# assignments_to_keep = list(np.argsort(sizes)[-K:])
# print assignments_to_keep
# new_assignments = [
# i if i in assignments_to_keep else -1 if i == -1 else
# random.choice(assignments_to_keep) for i in cur_assignments
# ]
# mapping = dict([(assignments_to_keep[i], i) for i in range(K)])
# print mapping
# mapping[-1] = -1
# new_assignments = np.array([mapping[i] for i in new_assignments])
# print new_assignments[:100]
# # Make sure we have consequetive assignment values
# for k in xrange(new_assignments.max()):
# while len(np.nonzero(new_assignments == k)[0]) == 0:
# new_assignments[np.where(new_assignments > k)] -= 1
# if new_assignments.max() == k:
# break
# self.setup_components(K, list(new_assignments))
def log_prob_z(self):
"""
Return the log marginal probability of component assignment P(z).
See (24.24) in Murphy, p. 842.
"""
log_prob_z = (
gammaln(self.alpha)
- gammaln(self.alpha + np.sum(self.components.counts))
+ np.sum(
gammaln(
self.components.counts
+ float(self.alpha)/self.components.K_max
)
- gammaln(self.alpha/self.components.K_max)
)
)
return log_prob_z
def log_prob_X_given_z(self):
"""Return the log probability of data in each component p(X|z)."""
return self.components.log_marg()
def log_marg(self):
"""Return log marginal of data and component assignments: p(X, z)"""
log_prob_z = self.log_prob_z()
log_prob_X_given_z = self.log_prob_X_given_z()
# # Log probability of component assignment, (24.24) in Murphy, p. 842
# log_prob_z = (
# gammaln(self.alpha)
# - gammaln(self.alpha + np.sum(self.components.counts))
# + np.sum(
# gammaln(
# self.components.counts
# + float(self.alpha)/self.components.K_max
# )
# - gammaln(self.alpha/self.components.K_max)
# )
# )
# # Log probability of data in each component
# log_prob_X_given_z = self.components.log_marg()
return log_prob_z + log_prob_X_given_z
# @profile
def log_marg_i(self, i): #, lms=1.):
"""
Return the log marginal of the i'th data vector: p(x_i)
Here it is assumed that x_i is not currently in the acoustic model,
so the -1 term used in the denominator in (24.26) in Murphy, p. 843
is dropped (since x_i is already not included in the counts).
"""
assert i != -1
# Compute log probability of `X[i]` belonging to each component
# (24.26) in Murphy, p. 843
log_prob_z = self.lms * (
np.log(float(self.alpha)/self.components.K_max + self.components.counts)
# - np.log(_cython_utils.sum_ints(self.components.counts) + self.alpha - 1.)
- np.log(_cython_utils.sum_ints(self.components.counts) + self.alpha)
)
# log_prob_z = lms * (
# np.ones(self.components.K_max)*(
# np.log(float(self.alpha)/self.components.K_max + self.components.counts)
# - np.log(np.sum(self.components.counts) + self.alpha - 1.)
# )
# )
# logger.info("log_prob_z: " + str(log_prob_z))
# (24.23) in Murphy, p. 842
log_prob_z[:self.components.K] += self.components.log_post_pred(i)
# Empty (unactive) components
log_prob_z[self.components.K:] += self.components.log_prior(i)
return _cython_utils.logsumexp(log_prob_z)
# return logsumexp(log_prob_z)
def gibbs_sample(self, n_iter, consider_unassigned=True,
anneal_schedule=None, anneal_start_temp_inv=0.1,
anneal_end_temp_inv=1, n_anneal_steps=-1): #, lms=1.0):
"""
Perform `n_iter` iterations Gibbs sampling on the FBGMM.
Parameters
----------
consider_unassigned : bool
Whether unassigned vectors (-1 in `assignments`) should be
considered during sampling.
anneal_schedule : str
Can be one of the following:
- None: A constant temperature of `anneal_end_temp_inv` is used
throughout; if `anneal_end_temp_inv` is left at default (1), then
this is equivalent to not performing annealing.
- "linear": Linearly take the inverse temperature from
`anneal_start_temp_inv` to `anneal_end_temp_inv` in
`n_anneal_steps`. If `n_anneal_steps` is -1 for this schedule,
annealing is performed over all `n_iter` iterations.
- "step": Piecewise schedule in which the inverse temperature is
taken from `anneal_start_temp_inv` to `anneal_end_temp_inv` in
`n_anneal_steps` steps (annealing will be performed over all
`n_iter` iterations; it might be worth adding an additional
variable for this case to allow the step schedule to stop early).
Return
------
record_dict : dict
Contains several fields describing the sampling process. Each field
is described by its key and statistics are given in a list which
covers the Gibbs sampling iterations.
"""
# Setup record dictionary
record_dict = {}
record_dict["sample_time"] = []
start_time = time.time()
record_dict["log_marg"] = []
record_dict["log_prob_z"] = []
record_dict["log_prob_X_given_z"] = []
record_dict["anneal_temp"] = []
record_dict["components"] = []
# Setup annealing iterator
if anneal_schedule is None:
get_anneal_temp = iter([])
elif anneal_schedule == "linear":
if n_anneal_steps == -1:
n_anneal_steps = n_iter
anneal_list = 1./np.linspace(anneal_start_temp_inv, anneal_end_temp_inv, n_anneal_steps)
get_anneal_temp = iter(anneal_list)
elif anneal_schedule == "step":
assert not n_anneal_steps == -1, (
"`n_anneal_steps` of -1 not allowed for step annealing schedule"
)
n_iter_per_step = int(round(float(n_iter)/n_anneal_steps))
anneal_list = np.linspace(anneal_start_temp_inv, anneal_end_temp_inv, n_anneal_steps)
anneal_list = 1./anneal_list
anneal_list = np.repeat(anneal_list, n_iter_per_step)
get_anneal_temp = iter(anneal_list)
# Loop over iterations
for i_iter in range(n_iter):
# Get anneal temperature
anneal_temp = next(get_anneal_temp, anneal_end_temp_inv)
# Loop over data items
for i in xrange(self.components.N):
# Cache some old values for possible future use
k_old = self.components.assignments[i]
if not consider_unassigned and k_old == -1:
continue
K_old = self.components.K
stats_old = self.components.cache_component_stats(k_old)
# Remove data vector `X[i]` from its current component
self.components.del_item(i)
# Compute log probability of `X[i]` belonging to each component
# (24.26) in Murphy, p. 843
log_prob_z = self.lms * (
np.ones(self.components.K_max)*np.log(
float(self.alpha)/self.components.K_max + self.components.counts
)
)
# (24.23) in Murphy, p. 842
log_prob_z[:self.components.K] += self.components.log_post_pred(i)
# Empty (unactive) components
log_prob_z[self.components.K:] += self.components.log_prior(i)
if anneal_temp != 1:
log_prob_z = log_prob_z - logsumexp(log_prob_z)
log_prob_z_anneal = 1./anneal_temp * log_prob_z - logsumexp(1./anneal_temp * log_prob_z)
prob_z = np.exp(log_prob_z_anneal)
else:
prob_z = np.exp(log_prob_z - logsumexp(log_prob_z))
# prob_z = np.exp(log_prob_z - logsumexp(log_prob_z))
# Sample the new component assignment for `X[i]`
k = utils.draw(prob_z)
# There could be several empty, unactive components at the end
if k > self.components.K:
k = self.components.K
# print prob_z, k, prob_z[k]
# Add data item X[i] into its component `k`
if k == k_old and self.components.K == K_old:
# Assignment same and no components have been removed
self.components.restore_component_from_stats(k_old, *stats_old)
self.components.assignments[i] = k_old
else:
# Add data item X[i] into its new component `k`
self.components.add_item(i, k)
# Update record
record_dict["sample_time"].append(time.time() - start_time)
start_time = time.time()
record_dict["log_marg"].append(self.log_marg())
record_dict["log_prob_z"].append(self.log_prob_z())
record_dict["log_prob_X_given_z"].append(self.log_prob_X_given_z())
record_dict["anneal_temp"].append(anneal_temp)
record_dict["components"].append(self.components.K)
# Log info
info = "iteration: " + str(i_iter)
for key in sorted(record_dict):
info += ", " + key + ": " + str(record_dict[key][-1])
logger.info(info)
return record_dict
def gibbs_sample_inside_loop_i(self, i, anneal_temp=1): #, lms=1.):
"""
Perform the inside loop of Gibbs sampling for data vector `i`.
This is the inside of `gibbs_sample` and can be used by outside objects
to perform only the inside loop part of the Gibbs sampling operation.
The step in the loop is sample a new assignment for data vector `i`.
The reason for not replacing the actual inner part of `gibbs_sample` by
a call to this function is because this won't allow for caching the old
component stats.
"""
# Compute log probability of `X[i]` belonging to each component
# (24.26) in Murphy, p. 843
log_prob_z = self.lms * (
np.ones(self.components.K_max)*np.log(
float(self.alpha)/self.components.K_max + self.components.counts
)
)
# (24.23) in Murphy, p. 842
log_prob_z[:self.components.K] += self.components.log_post_pred(i)
# Empty (unactive) components
log_prob_z[self.components.K:] += self.components.log_prior(i)
if anneal_temp != 1:
log_prob_z = log_prob_z - logsumexp(log_prob_z)
log_prob_z_anneal = 1./anneal_temp * log_prob_z - logsumexp(1./anneal_temp * log_prob_z)
prob_z = np.exp(log_prob_z_anneal)
else:
prob_z = np.exp(log_prob_z - logsumexp(log_prob_z))
# prob_z = np.exp(log_prob_z - logsumexp(log_prob_z))
assert not np.isnan(np.sum(prob_z))
# Sample the new component assignment for `X[i]`
k = utils.draw(prob_z)
# There could be several empty, unactive components at the end
if k > self.components.K:
k = self.components.K
logger.debug("Adding item " + str(i) + " to acoustic model component " + str(k))
self.components.add_item(i, k)
def map_assign_i(self, i):
"""
Assign data vector `i` to the component giving the maximum posterior.
This function is very similar to `gibbs_sample_inside_loop_i`, but
instead of sampling the assignment, the MAP estimate is used.
"""
# Compute log probability of `X[i]` belonging to each component
# (24.26) in Murphy, p. 843
log_prob_z = (
np.ones(self.components.K_max)*np.log(
float(self.alpha)/self.components.K_max + self.components.counts
)
)
# (24.23) in Murphy, p. 842
log_prob_z[:self.components.K] += self.components.log_post_pred(i)
# Empty (unactive) components
log_prob_z[self.components.K:] += self.components.log_prior(i)
prob_z = np.exp(log_prob_z - logsumexp(log_prob_z))
# Take the MAP assignment for `X[i]`
k = np.argmax(prob_z)
# There could be several empty, unactive components at the end
if k > self.components.K:
k = self.components.K
logger.debug("Adding item " + str(i) + " to acoustic model component " + str(k))
self.components.add_item(i, k)
def get_n_assigned(self):
"""Return the number of assigned data vectors."""
return len(np.where(self.components.assignments != -1)[0])
class FBGMM(object):
"""
A finite Bayesian Gaussian mixture model (FBGMM).
See `GaussianComponents` or `GaussianComponentsDiag` for an overview of the
parameters not mentioned below.
Parameters
----------
alpha : float
Concentration parameter for the symmetric Dirichlet prior over the
mixture weights.
K : int
The number of mixture components. This is actually a maximum number,
and it is possible to empty out some of these components.
assignments : vector of int or str
If vector of int, this gives the initial component assignments. The
vector should therefore have N entries between 0 and `K`. Values of
-1 is also allowed, indicating that the data vector does not belong to
any component. Alternatively, `assignments` can take one of the
following values:
- "rand": Vectors are assigned randomly to one of `K` components.
- "each-in-own": Each vector is assigned to a component of its own.
covariance_type : str
String describing the type of covariance parameters to use. Must be
one of "full", "diag" or "fixed".
"""
def __init__(
self, X, prior, alpha, K, assignments="rand",
covariance_type="full"
):
self.alpha = alpha
N, D = X.shape
# Initial component assignments
if assignments == "rand":
assignments = np.random.randint(0, K, N)
# Make sure we have consequetive values
for k in xrange(assignments.max()):
while len(np.nonzero(assignments == k)[0]) == 0:
assignments[np.where(assignments > k)] -= 1
if assignments.max() == k:
break
elif assignments == "each-in-own":
assignments = np.arange(N)
else:
# assignments is a vector
pass
if covariance_type == "full":
self.components = GaussianComponents(X, prior, assignments, K_max=K)
elif covariance_type == "diag":
self.components = GaussianComponentsDiag(X, prior, assignments, K_max=K)
elif covariance_type == "fixed":
self.components = GaussianComponentsFixedVar(X, prior, assignments, K_max=K)
else:
assert False, "Invalid covariance type."
def log_marg(self):
"""Return log marginal of data and component assignments: p(X, z)"""
# Log probability of component assignment, (24.24) in Murphy, p. 842
log_prob_z = (
gammaln(self.alpha)
- gammaln(self.alpha + np.sum(self.components.counts))
+ np.sum(
gammaln(
self.components.counts
+ float(self.alpha)/self.components.K_max
)
- gammaln(self.alpha/self.components.K_max)
)
)
# Log probability of data in each component
log_prob_X_given_z = self.components.log_marg()
return log_prob_z + log_prob_X_given_z
def gibbs_sample(self, n_iter):
"""
Perform `n_iter` iterations Gibbs sampling on the FBGMM.
A record dict is constructed over the iterations, which contains
several fields describing the sampling process. Each field is described
by its key and statistics are given in a list which covers the Gibbs
sampling iterations. This dict is returned.
"""
# Setup record dictionary
record_dict = {}
record_dict["sample_time"] = []
start_time = time.time()
record_dict["log_marg"] = []
record_dict["components"] = []
# Loop over iterations
for i_iter in range(n_iter):
# Loop over data items
for i in xrange(self.components.N):
# Cache some old values for possible future use
k_old = self.components.assignments[i]
K_old = self.components.K
stats_old = self.components.cache_component_stats(k_old)
# Remove data vector `X[i]` from its current component
self.components.del_item(i)
# Compute log probability of `X[i]` belonging to each component
# (24.26) in Murphy, p. 843
log_prob_z = (
np.ones(self.components.K_max)*np.log(
float(self.alpha)/self.components.K_max + self.components.counts
)
)
# (24.23) in Murphy, p. 842
log_prob_z[:self.components.K] += self.components.log_post_pred(i)
# Empty (unactive) components
log_prob_z[self.components.K:] += self.components.log_prior(i)
prob_z = np.exp(log_prob_z - logsumexp(log_prob_z))
# Sample the new component assignment for `X[i]`
k = utils.draw(prob_z)
# There could be several empty, unactive components at the end
if k > self.components.K:
k = self.components.K
# print prob_z, k, prob_z[k]
# Add data item X[i] into its component `k`
if k == k_old and self.components.K == K_old:
# Assignment same and no components have been removed
self.components.restore_component_from_stats(k_old, *stats_old)
self.components.assignments[i] = k_old
else:
# Add data item X[i] into its new component `k`
self.components.add_item(i, k)
# Update record
record_dict["sample_time"].append(time.time() - start_time)
start_time = time.time()
record_dict["log_marg"].append(self.log_marg())
record_dict["components"].append(self.components.K - 1)
# Log info
info = "iteration: " + str(i_iter)
for key in sorted(record_dict):
info += ", " + key + ": " + str(record_dict[key][-1])
info += "."
logger.info(info)
return record_dict
class IGMM(object):
"""
An infinite Gaussian mixture model (IGMM).
See `GaussianComponents` for an overview of the parameters not mentioned
below.
Parameters
----------
alpha : float
Concentration parameter for the Dirichlet process.
assignments : vector of int or str
If vector of int, this gives the initial component assignments. The
vector should therefore have N entries between 0 and `K`. Values of
-1 is also allowed, indicating that the data vector does not belong to
any component. Alternatively, `assignments` can take one of the
following values:
- "rand": Vectors are assigned randomly to one of `K` components.
- "one-by-one": Vectors are assigned one at a time; the value of
`K` becomes irrelevant.
- "each-in-own": Each vector is assigned to a component of its own.
K : int
The initial number of mixture components: this is only used when
`assignments` is "rand".
covariance_type : str
String describing the type of covariance parameters to use. Must be
one of "full", "diag" or "fixed".
"""
def __init__(
self, X, prior, alpha, assignments="rand", K=1, K_max=None,
covariance_type="full"
):
self.alpha = alpha
N, D = X.shape
# Initial component assignments
if assignments == "rand":
assignments = np.random.randint(0, K, N)
# Make sure we have consequetive values
for k in xrange(assignments.max()):
while len(np.nonzero(assignments == k)[0]) == 0:
assignments[np.where(assignments > k)] -= 1
if assignments.max() == k:
break
elif assignments == "one-by-one":
assignments = -1*np.ones(N, dtype="int")
assignments[0] = 0 # first data vector belongs to first component
elif assignments == "each-in-own":
assignments = np.arange(N)
else:
# assignments is a vector
pass
if covariance_type == "full":
self.components = GaussianComponents(X, prior, assignments, K_max)
elif covariance_type == "diag":
self.components = GaussianComponentsDiag(X, prior, assignments, K_max)
elif covariance_type == "fixed":
self.components = GaussianComponentsFixedVar(X, prior, assignments, K_max)
else:
assert False, "Invalid covariance type."
def log_marg(self):
"""Return log marginal of data and component assignments: p(X, z)"""
# Log probability of component assignment P(z|alpha)
# Equation (10) in Wood and Black, 2008
# Use \Gamma(n) = (n - 1)!
facts_ = gammaln(self.components.counts[:self.components.K])
facts_[self.components.counts[:self.components.K] == 0] = 0 # definition of log(0!)
log_prob_z = (
(self.components.K - 1)*math.log(self.alpha) + gammaln(self.alpha)
- gammaln(np.sum(self.components.counts[:self.components.K])
+ self.alpha) + np.sum(facts_)
)
log_prob_X_given_z = self.components.log_marg()
return log_prob_z + log_prob_X_given_z
# @profile
def gibbs_sample(self, n_iter):
"""
Perform `n_iter` iterations Gibbs sampling on the IGMM.
A record dict is constructed over the iterations, which contains
several fields describing the sampling process. Each field is described
by its key and statistics are given in a list which covers the Gibbs
sampling iterations. This dict is returned.
"""
# Setup record dictionary
record_dict = {}
record_dict["sample_time"] = []
start_time = time.time()
record_dict["log_marg"] = []
record_dict["components"] = []
# Loop over iterations
for i_iter in range(n_iter):
# Loop over data items
# import random
# permuted = range(self.components.N)
# random.shuffle(permuted)
# for i in permuted:
for i in xrange(self.components.N):
# Cache some old values for possible future use
k_old = self.components.assignments[i]
K_old = self.components.K
stats_old = self.components.cache_component_stats(k_old)
# Remove data vector `X[i]` from its current component
self.components.del_item(i)
# Compute log probability of `X[i]` belonging to each component
log_prob_z = np.zeros(self.components.K + 1, np.float)
# (25.35) in Murphy, p. 886
log_prob_z[:self.components.K] = np.log(self.components.counts[:self.components.K])
# (25.33) in Murphy, p. 886
log_prob_z[:self.components.K] += self.components.log_post_pred(i)
# Add one component to which nothing has been assigned
log_prob_z[-1] = math.log(self.alpha) + self.components.cached_log_prior[i]
prob_z = np.exp(log_prob_z - logsumexp(log_prob_z))
# Sample the new component assignment for `X[i]`
k = utils.draw(prob_z)
# logger.debug("Sampled k = " + str(k) + " from " + str(prob_z) + ".")
# Add data item X[i] into its component `k`
if k == k_old and self.components.K == K_old:
# Assignment same and no components have been removed
self.components.restore_component_from_stats(k_old, *stats_old)
self.components.assignments[i] = k_old
else:
# Add data item X[i] into its new component `k`
self.components.add_item(i, k)
# Update record
record_dict["sample_time"].append(time.time() - start_time)
start_time = time.time()
record_dict["log_marg"].append(self.log_marg())
record_dict["components"].append(self.components.K - 1)
# Log info
info = "iteration: " + str(i_iter)
for key in sorted(record_dict):
info += ", " + key + ": " + str(record_dict[key][-1])
info += "."
logger.info(info)
return record_dict