def XDGMM(X, Xcov, n_components, n_iter=100, tol=1E-5, Nthreads=1, R=None,
init_n_iter=10, w=None, model=None, fixed_means=None,
aligned_covs=None, verbose=False):
"""
Extreme Deconvolution
Fit an extreme deconvolution (XD) model to the data
Parameters
----------
n_components: integer
number of gaussian components to fit to the data
n_iter: integer (optional)
number of EM iterations to perform (default=100)
tol: float (optional)
stopping criterion for EM iterations (default=1E-5)
X: array_like
Input data. shape = (n_samples, n_features)
Xcov: array_like
Covariance of input data. shape = (n_samples, n_features,
n_features)
R: array_like
(TODO: not implemented)
Transformation matrix from underlying to observed data. If
unspecified, then it is assumed to be the identity matrix.
w: float or array_like
if float - w * np.eye is added to V
if vector - np.diag(w) is added to V
if array - w is added to V
Notes
-----
This implementation follows Bovy et al. arXiv 0905.2979
"""
if model is None:
model = xd_model(X.shape, n_components, n_iter, tol, w, Nthreads,
fixed_means, aligned_covs, verbose)
if R is not None:
raise NotImplementedError("mixing matrix R is not yet implemented")
X = np.asarray(X)
Xcov = np.asarray(Xcov)
# assume full covariances of data
assert Xcov.shape == (model.n_samples, model.n_features, model.n_features)
# initialize components via a few steps of GMM
# this doesn't take into account errors, but is a fast first-guess
if model.V is None:
t0 = time()
if (fixed_means is None) & (aligned_covs is None):
gmm = GMM(model.n_components, n_iter=init_n_iter,
covariance_type='full').fit(X)
else:
gmm = constrained_GMM(X, model.n_components, init_n_iter,
fixed_means, aligned_covs)
model.mu = gmm.means_
model.alpha = gmm.weights_
model.V = gmm.covars_
model.initial_logL = model.logLikelihood(X, Xcov)
if model.verbose:
print 'Initalization done in %.2g sec' % (time() - t0)
print 'Initial Log Likelihood: ', model.initial_logL
logL = -np.inf
for i in range(model.n_iter):
t0 = time()
model = _EMstep(model, X, Xcov)
logL_next = model.logLikelihood(X, Xcov)
t1 = time()
if model.verbose:
print "%i: log(L) = %.5g" % (i + 1, logL_next)
print " (%.2g sec)" % (t1 - t0)
model.prev_logL = logL
model.logL = logL_next
if logL_next < logL + model.tol:
break
logL = logL_next
return model
def XDGMM(X,
Xcov,
n_components,
n_iter=100,
tol=1E-5,
Nthreads=1,
R=None,
init_n_iter=10,
w=None,
model=None,
fixed_means=None,
aligned_covs=None,
verbose=False):
"""
Extreme Deconvolution
Fit an extreme deconvolution (XD) model to the data
Parameters
----------
n_components: integer
number of gaussian components to fit to the data
n_iter: integer (optional)
number of EM iterations to perform (default=100)
tol: float (optional)
stopping criterion for EM iterations (default=1E-5)
X: array_like
Input data. shape = (n_samples, n_features)
Xcov: array_like
Covariance of input data. shape = (n_samples, n_features,
n_features)
R: array_like
(TODO: not implemented)
Transformation matrix from underlying to observed data. If
unspecified, then it is assumed to be the identity matrix.
w: float or array_like
if float - w * np.eye is added to V
if vector - np.diag(w) is added to V
if array - w is added to V
Notes
-----
This implementation follows Bovy et al. arXiv 0905.2979
"""
if model is None:
model = xd_model(X.shape, n_components, n_iter, tol, w, Nthreads,
fixed_means, aligned_covs, verbose)
if R is not None:
raise NotImplementedError("mixing matrix R is not yet implemented")
X = np.asarray(X)
Xcov = np.asarray(Xcov)
# assume full covariances of data
assert Xcov.shape == (model.n_samples, model.n_features, model.n_features)
# initialize components via a few steps of GMM
# this doesn't take into account errors, but is a fast first-guess
if model.V is None:
t0 = time()
if (fixed_means is None) & (aligned_covs is None):
gmm = GMM(model.n_components,
n_iter=init_n_iter,
covariance_type='full').fit(X)
else:
gmm = constrained_GMM(X, model.n_components, init_n_iter,
fixed_means, aligned_covs)
model.mu = gmm.means_
model.alpha = gmm.weights_
model.V = gmm.covars_
model.initial_logL = model.logLikelihood(X, Xcov)
if model.verbose:
print 'Initalization done in %.2g sec' % (time() - t0)
print 'Initial Log Likelihood: ', model.initial_logL
logL = -np.inf
for i in range(model.n_iter):
t0 = time()
model = _EMstep(model, X, Xcov)
logL_next = model.logLikelihood(X, Xcov)
t1 = time()
if model.verbose:
print "%i: log(L) = %.5g" % (i + 1, logL_next)
print " (%.2g sec)" % (t1 - t0)
model.prev_logL = logL
model.logL = logL_next
if logL_next < logL + model.tol:
break
logL = logL_next
return model
