def _train_simple_em_log(self, data, model, maxiter, thresh):
# Likelihood is kept
like = N.zeros(maxiter)
# Em computation, with computation of the likelihood
g, tgd = model.compute_log_responsabilities(data)
like[0] = N.sum(densities.logsumexp(tgd), axis = 0)
model.update_em(data, N.exp(g))
for i in range(1, maxiter):
g, tgd = model.compute_log_responsabilities(data)
like[i] = N.sum(densities.logsumexp(tgd), axis = 0)
model.update_em(data, N.exp(g))
if has_em_converged(like[i], like[i-1], thresh):
return like[0:i]
def _train_simple_em_log(self, data, model, maxiter, thresh):
# Likelihood is kept
like = N.zeros(maxiter)
# Em computation, with computation of the likelihood
g, tgd = model.compute_log_responsabilities(data)
like[0] = N.sum(densities.logsumexp(tgd), axis=0)
model.update_em(data, N.exp(g))
for i in range(1, maxiter):
g, tgd = model.compute_log_responsabilities(data)
like[i] = N.sum(densities.logsumexp(tgd), axis=0)
model.update_em(data, N.exp(g))
if has_em_converged(like[i], like[i - 1], thresh):
return like[0:i]
def pdf(self, x, log=False):
"""Computes the pdf of the model at given points.
:Parameters:
x : ndarray
points where to estimate the pdf. One row for one
multi-dimensional sample (eg to estimate the pdf at 100
different points in 10 dimension, data's shape should be (100,
20)).
log : bool
If true, returns the log pdf instead of the pdf.
:Returns:
y : ndarray
the pdf at points x."""
if log:
return D.logsumexp(D.multiple_gauss_den(x, self.mu, self.va, log=True) + N.log(self.w))
else:
return N.sum(D.multiple_gauss_den(x, self.mu, self.va) * self.w, 1)
def pdf(self, x, log=False):
"""Computes the pdf of the model at given points.
:Parameters:
x : ndarray
points where to estimate the pdf. One row for one
multi-dimensional sample (eg to estimate the pdf at 100
different points in 10 dimension, data's shape should be (100,
20)).
log : bool
If true, returns the log pdf instead of the pdf.
:Returns:
y : ndarray
the pdf at points x."""
if log:
return D.logsumexp(
D.multiple_gauss_den(x, self.mu, self.va, log=True) +
N.log(self.w))
else:
return N.sum(D.multiple_gauss_den(x, self.mu, self.va) * self.w, 1)
def compute_log_responsabilities(self, data):
"""Compute log responsabilities.
Return normalized and non-normalized responsabilities for the model (in
the log domain)
Note
----
Computes the latent variable distribution (a posteriori probability)
knowing the explicit data for the Gaussian model (w, mu, var): gamma(t,
i) = P[state = i | observation = data(t); w, mu, va]
This is basically the E step of EM for finite mixtures."""
# compute the gaussian pdf
tgd = densities.multiple_gauss_den(data, self.gm.mu,
self.gm.va, log = True)
# multiply by the weight
tgd += N.log(self.gm.w)
# Normalize to get a (log) pdf
gd = tgd - densities.logsumexp(tgd)[:, N.newaxis]
return gd, tgd
def compute_log_responsabilities(self, data):
"""Compute log responsabilities.
Return normalized and non-normalized responsabilities for the model (in
the log domain)
Note
----
Computes the latent variable distribution (a posteriori probability)
knowing the explicit data for the Gaussian model (w, mu, var): gamma(t,
i) = P[state = i | observation = data(t); w, mu, va]
This is basically the E step of EM for finite mixtures."""
# compute the gaussian pdf
tgd = densities.multiple_gauss_den(data,
self.gm.mu,
self.gm.va,
log=True)
# multiply by the weight
tgd += N.log(self.gm.w)
# Normalize to get a (log) pdf
gd = tgd - densities.logsumexp(tgd)[:, N.newaxis]
return gd, tgd
def train(self, data, model, maxiter=20, thresh=1e-5):
"""Train a model using EM.
Train a model using data, and stops when the likelihood increase
between two consecutive iteration fails behind a threshold, or when the
number of iterations > niter, whichever comes first
:Parameters:
data : ndarray
contains the observed features, one row is one frame, ie one
observation of dimension d
model : GMM
GMM instance.
maxiter : int
maximum number of iterations
thresh : threshold
if the slope of the likelihood falls below this value, the
algorithm stops.
:Returns:
likelihood : ndarray
one value per iteration.
Note
----
The model is trained, and its parameters updated accordingly, eg the
results are put in the GMM instance.
"""
mode = model.gm.mode
# Build regularizer
if mode == 'diag':
regularize = curry(regularize_diag,
np=self.pcnt,
prior=self.pval * N.ones(model.gm.d))
elif mode == 'full':
regularize = curry(regularize_full,
np=self.pcnt,
prior=self.pval * N.eye(model.gm.d))
else:
raise ValueError("unknown variance mode")
model.init(data)
regularize(model.gm.va)
# Likelihood is kept
like = N.empty(maxiter, N.float)
# Em computation, with computation of the likelihood
g, tgd = model.compute_log_responsabilities(data)
g = N.exp(g)
model.update_em(data, g)
regularize(model.gm.va)
like[0] = N.sum(densities.logsumexp(tgd), axis=0)
for i in range(1, maxiter):
g, tgd = model.compute_log_responsabilities(data)
g = N.exp(g)
model.update_em(data, g)
regularize(model.gm.va)
like[i] = N.sum(densities.logsumexp(tgd), axis=0)
if has_em_converged(like[i], like[i - 1], thresh):
return like[0:i]
return like
def train(self, data, model, maxiter = 20, thresh = 1e-5):
"""Train a model using EM.
Train a model using data, and stops when the likelihood increase
between two consecutive iteration fails behind a threshold, or when the
number of iterations > niter, whichever comes first
:Parameters:
data : ndarray
contains the observed features, one row is one frame, ie one
observation of dimension d
model : GMM
GMM instance.
maxiter : int
maximum number of iterations
thresh : threshold
if the slope of the likelihood falls below this value, the
algorithm stops.
:Returns:
likelihood : ndarray
one value per iteration.
Note
----
The model is trained, and its parameters updated accordingly, eg the
results are put in the GMM instance.
"""
mode = model.gm.mode
# Build regularizer
if mode == 'diag':
regularize = curry(regularize_diag, np = self.pcnt, prior =
self.pval * N.ones(model.gm.d))
elif mode == 'full':
regularize = curry(regularize_full, np = self.pcnt, prior =
self.pval * N.eye(model.gm.d))
else:
raise ValueError("unknown variance mode")
model.init(data)
regularize(model.gm.va)
# Likelihood is kept
like = N.empty(maxiter, N.float)
# Em computation, with computation of the likelihood
g, tgd = model.compute_log_responsabilities(data)
g = N.exp(g)
model.update_em(data, g)
regularize(model.gm.va)
like[0] = N.sum(densities.logsumexp(tgd), axis = 0)
for i in range(1, maxiter):
g, tgd = model.compute_log_responsabilities(data)
g = N.exp(g)
model.update_em(data, g)
regularize(model.gm.va)
like[i] = N.sum(densities.logsumexp(tgd), axis = 0)
if has_em_converged(like[i], like[i-1], thresh):
return like[0:i]