def fit_gmm(self, samples):
"""
Runs a couple of em instances on random starting points and returns
internal GMM representation of best instance
"""
features = RealFeatures(samples.T)
gmms = []
log_likelihoods = zeros(self.num_runs_em)
for i in range(self.num_runs_em):
# set up Shogun's GMM class and run em (corresponds to random
# initialisation)
gmm = GMM(self.num_components)
gmm.set_features(features)
log_likelihoods[i] = gmm.train_em()
gmms.append(gmm)
max_idx = log_likelihoods.argmax()
# construct Gaussian mixture components in internal representation
components = []
for i in range(self.num_components):
mu = gmms[max_idx].get_nth_mean(i)
Sigma = gmms[max_idx].get_nth_cov(i)
components.append(Gaussian(mu, Sigma))
# construct a Gaussian mixture model based on the best EM run
pie = gmms[max_idx].get_coef()
proposal = MixtureDistribution(components[0].dimension,
self.num_components, components,
Discrete(pie))
return proposal
def construct_proposal(self, y):
assert(len(shape(y)) == 1)
m = MixtureDistribution(self.distribution.dimension, self.num_eigen)
m.mixing_proportion = Discrete((self.eigvalues + 1) / (sum(self.eigvalues) + self.num_eigen))
# print "current mixing proportion: ", m.mixing_proportion.omega
for ii in range(self.num_eigen):
L = sqrt(self.dwscale[ii] * self.eigvalues[ii]) * reshape(self.eigvectors[:, ii], (self.distribution.dimension, 1))
m.components[ii] = Gaussian(y, L, is_cholesky=True, ell=1)
# Z=m.sample(1000).samples
# Visualise.plot_data(Z)
return m
def __init__(self,
dimension=2,
num_components=2,
components=None,
mixing_proportion=None):
Distribution.__init__(self, dimension)
self.num_components = num_components
if (components == None):
self.components = [
Gaussian(mu=zeros(self.dimension), Sigma=eye(self.dimension))
for _ in range(self.num_components)
]
else:
assert (len(components) == self.num_components)
self.components = components
if (mixing_proportion == None):
self.mixing_proportion = Discrete(
(1.0 / num_components) * ones([num_components]))
else:
assert (num_components == mixing_proportion.num_objects)
self.mixing_proportion = mixing_proportion
class MixtureDistribution(Distribution):
"""
mixing_proportion is of class Distribution->Discrete
components is a list of Distributions
"""
def __init__(self, dimension=2, num_components=2, components=None, mixing_proportion=None):
Distribution.__init__(self, dimension)
self.num_components = num_components
if (components == None):
self.components = [Gaussian(mu=zeros(self.dimension),Sigma=eye(self.dimension)) for _ in range(self.num_components)]
else:
assert(len(components)==self.num_components)
self.components=components
if (mixing_proportion == None):
self.mixing_proportion=Discrete((1.0/num_components)*ones([num_components]))
else:
assert(num_components==mixing_proportion.num_objects)
self.mixing_proportion = mixing_proportion
def __str__(self):
s=self.__class__.__name__+ "=["
s += "components="+ str(self.components)
s += ", mixing_proportion="+ str(self.mixing_proportion)
s += ", " + Distribution.__str__(self)
s += "]"
return s
def log_pdf(self, X, component_index_given=None):
"""
If component_index_given is given, then just condition on it,
otherwise, should compute the overall log_pdf
"""
if component_index_given == None:
rez = zeros([len(X)])
for ii in range(len(X)):
logpdfs = zeros([self.num_components])
for jj in range(self.num_components):
logpdfs[jj] = self.components[jj].log_pdf([X[ii]])
lmax = max(logpdfs)
rez[ii] = lmax + log(sum(self.mixing_proportion.omega * exp(logpdfs - lmax)))
return rez
else:
assert(component_index_given < self.num_components)
return self.components[component_index_given].log_pdf(X)
def sample(self, n=1):
rez = zeros([n, self.dimension])
for ii in range(n):
which_component = self.mixing_proportion.sample().samples
rez[ii, :] = self.components[which_component].sample().samples
return SampleFromMixture(rez,which_component)
def __init__(self, dimension=2, num_components=2, components=None, mixing_proportion=None):
Distribution.__init__(self, dimension)
self.num_components = num_components
if (components == None):
self.components = [Gaussian(mu=zeros(self.dimension),Sigma=eye(self.dimension)) for _ in range(self.num_components)]
else:
assert(len(components)==self.num_components)
self.components=components
if (mixing_proportion == None):
self.mixing_proportion=Discrete((1.0/num_components)*ones([num_components]))
else:
assert(num_components==mixing_proportion.num_objects)
self.mixing_proportion = mixing_proportion
def construct_proposal(self, y):
"""
proposal is a mixture of normals,
centred at y and with covariance gamma^2 I + nu^2 MHaa'HM',
where a are the eigenvectors of centred kernel matrix Kc=HKH
"""
assert (len(shape(y)) == 1)
m = MixtureDistribution(self.distribution.dimension, self.num_eigen)
m.mixing_proportion = Discrete(
(self.eigvalues + 1) / (sum(self.eigvalues) + self.num_eigen))
# print "current mixing proportion: ", m.mixing_proportion.omega
M = 2 * self.kernel.gradient(y, self.Z)
H = Kernel.centring_matrix(len(self.Z))
for ii in range(self.num_eigen):
Sigma = self.gamma ** 2 * eye(len(y)) + \
self.nu2 * (M.T).dot(H.dot(outer(self.eigvectors[:, ii], self.eigvectors[:, ii]).dot(H.dot(M))))
m.components[ii] = Gaussian(y, Sigma)
return m
class MixtureDistribution(Distribution):
"""
mixing_proportion is of class Distribution->Discrete
components is a list of Distributions
"""
def __init__(self,
dimension=2,
num_components=2,
components=None,
mixing_proportion=None):
Distribution.__init__(self, dimension)
self.num_components = num_components
if (components == None):
self.components = [
Gaussian(mu=zeros(self.dimension), Sigma=eye(self.dimension))
for _ in range(self.num_components)
]
else:
assert (len(components) == self.num_components)
self.components = components
if (mixing_proportion == None):
self.mixing_proportion = Discrete(
(1.0 / num_components) * ones([num_components]))
else:
assert (num_components == mixing_proportion.num_objects)
self.mixing_proportion = mixing_proportion
def __str__(self):
s = self.__class__.__name__ + "=["
s += "components=" + str(self.components)
s += ", mixing_proportion=" + str(self.mixing_proportion)
s += ", " + Distribution.__str__(self)
s += "]"
return s
def log_pdf(self, X, component_index_given=None):
"""
If component_index_given is given, then just condition on it,
otherwise, should compute the overall log_pdf
"""
if component_index_given == None:
rez = zeros([len(X)])
for ii in range(len(X)):
logpdfs = zeros([self.num_components])
for jj in range(self.num_components):
logpdfs[jj] = self.components[jj].log_pdf([X[ii]])
lmax = max(logpdfs)
rez[ii] = lmax + log(
sum(self.mixing_proportion.omega * exp(logpdfs - lmax)))
return rez
else:
assert (component_index_given < self.num_components)
return self.components[component_index_given].log_pdf(X)
def sample(self, n=1):
rez = zeros([n, self.dimension])
for ii in range(n):
which_component = self.mixing_proportion.sample().samples
rez[ii, :] = self.components[which_component].sample().samples
return SampleFromMixture(rez, which_component)
