def setUp(self):
"""
Set up each test with a new XDGMM object and some data.
"""
self.xdgmm = XDGMM(n_components=3)
self.files = []
"""
Use scikit-learn GaussianMixture for sampling some data points
"""
self.gmm = skl_GMM(n_components=3,
max_iter=10,
covariance_type='full',
random_state=None)
self.gmm.weights_ = np.array([0.3, 0.5, 0.2])
self.gmm.means_ = np.array(
[np.array([0, 1]),
np.array([5, 4]),
np.array([2, 4])])
self.gmm.covariances_ = np.array([
np.diag((2, 1)),
np.array([[1, 0.2], [0.2, 1]]),
np.diag((0.3, 0.5))
])
self.gmm.precisions_ = np.linalg.inv(self.gmm.covariances_)
self.gmm.precisions_cholesky_ = np.linalg.cholesky(
self.gmm.precisions_)
self.X = self.gmm.sample(1000)[0]
errs = 0.2 * np.random.random_sample((1000, 2))
self.Xerr = np.zeros(self.X.shape + self.X.shape[-1:])
diag = np.arange(self.X.shape[-1])
self.Xerr[:, diag, diag] = np.vstack([errs[:, 0]**2, errs[:, 1]**2]).T
def fit(self, X, Xerr):
"""Fit the XD model to data
Whichever method is specified in self.method will be used.
Results are saved in self.mu/V/weights and in the self.GMM
object
Parameters
----------
X: array_like, shape = (n_samples, n_features)
Input data.
Xerr: array_like, shape = (n_samples, n_features, n_features)
Error on input data.
"""
if type(X) == pd.core.frame.DataFrame:
if type(X.columns) == pd.indexes.base.Index:
self.labels = np.array(X.columns)
X = X.values
if self.method=='astroML':
self.GMM.n_components=self.n_components
self.GMM.n_iter=self.n_iter
self.GMM.fit(X, Xerr)
self.V=self.GMM.V
self.mu=self.GMM.mu
self.weights=self.GMM.alpha
if self.method=='Bovy':
"""
Bovy extreme_deconvolution only imports if the method is
'Bovy' (this is because installation is somewhat more
complicated than astroML, and we don't want it to be
required)
As with the astroML method, initialize with a few steps of
the scikit-learn GMM
"""
from extreme_deconvolution import extreme_deconvolution\
as bovyXD
tmp_gmm = skl_GMM(self.n_components, max_iter=1,
covariance_type='full',
random_state=self.random_state)
tmp_gmm._initialize_parameters(X, self.random_state)
#tmp_gmm.fit(X)
self.mu = tmp_gmm.means_
self.weights = tmp_gmm.weights_
self.V = tmp_gmm.covariances_
logl=bovyXD.extreme_deconvolution(X,Xerr,self.weights,self.mu,self.V,
splitnmerge=self.splitnmerge,tol=self.tol,maxiter=self.n_iter,w=self.w)
self.GMM.V = self.V
self.GMM.mu = self.mu
self.GMM.alpha = self.weights
return self
def plot_cond_model(xdgmm, cond_xdgmm, y):
plt.clf()
setup_text_plots(fontsize=16, usetex=True)
fig = plt.figure(figsize=(12, 9))
ax1 = fig.add_subplot(111)
for i in range(xdgmm.n_components):
draw_ellipse(xdgmm.mu[i],
xdgmm.V[i],
scales=[2],
ax=ax1,
ec='None',
fc='gray',
alpha=0.2)
ax1.plot([-2, 15], [y, y], color='blue', linewidth=2)
ax1.set_xlim(-1, 13)
ax1.set_ylim(-6, 16)
ax1.set_xlabel('$x$', fontsize=18)
ax1.set_ylabel('$y$', fontsize=18)
ax2 = ax1.twinx()
x = np.array([np.linspace(-2, 14, 1000)]).T
gmm = skl_GMM(n_components=cond_xdgmm.n_components, covariance_type='full')
gmm.means_ = cond_xdgmm.mu
gmm.weights_ = cond_xdgmm.weights
gmm.covars_ = cond_xdgmm.V
logprob, responsibilities = gmm.score_samples(x)
pdf = np.exp(logprob)
ax2.plot(x,
pdf,
color='red',
linewidth=2,
label='Cond. dist. of $x$ given $y=' + str(y) + '\pm 0.05$')
ax2.legend()
ax2.set_ylabel('Probability', fontsize=18)
ax2.set_ylim(0, 0.52)
ax1.set_xlim(-1, 13)
plt.show()
def score_samples(self, X, Xerr):
"""Return per-sample liklihood of the data under the model
Uses the scikit-learn GMM.score_samples method to compute the
log probability of X under the model and return the
posterior probabilites of each mixture component for each
element of X
Scores each data point in X separately so that each
corresponding Xerr array can be folded into the covariance
matrices and be included in the calculation (since the
scikit-learn GMM implementation does not include errors)
Parameters
----------
X: array_like, shape = (n_samples, n_features)
Input data.
Xerr: array_like, shape = (n_samples, n_features, n_features)
Error on input data.
Returns
-------
logprob : array_like, shape = (n_samples, n_features)
Log probabilities of each data point in X.
responsibilities: array_like, shape = (n_samples, n_components)
Posterior probabilities of each mixture component for each
data point in X.
"""
if self.V is None or self.mu is None or self.weights is None:
raise StandardError("Model parameters not set.")
if type(X) == pd.core.frame.DataFrame: X = X.values
tmp_GMM = skl_GMM(self.n_components, max_iter=self.n_iter,
covariance_type='full',
random_state=self.random_state)
tmp_GMM.weights_ = self.weights
tmp_GMM.means_ = self.mu
X = X[:, np.newaxis, :]
Xerr = Xerr[:, np.newaxis, :, :]
T = Xerr + self.V
logprob = []
responsibilities = []
for i in range(X.shape[0]):
tmp_GMM.covariances_ = T[i]
tmp_GMM.precisions_ = np.linalg.inv(T[i])
chol = np.linalg.cholesky(np.linalg.inv(T[i]))
tmp_GMM.precisions_cholesky_ = chol
lp = tmp_GMM.score_samples(X[i].reshape(1,-1))
logprob.append(lp)
resp = tmp_GMM.predict_proba(X[i].reshape(1,-1))
responsibilities.append(resp)
logprob=np.array(logprob)[:,0]
responsibilities=np.array(responsibilities)[:,0]
return logprob,responsibilities