def __initial_parameters(self, S, Sd):
S = numpy.concatenate(S.swapaxes(1, 2), axis=0).T
Sd = numpy.concatenate(Sd.swapaxes(1, 2), axis=0).T
X = numpy.concatenate((S, Sd)).T
gmm = GMM(self.n_components)
gmm.from_samples(X)
if self.verbose:
print("Estimated GMM")
n_task_dims = self.n_task_dims
priors = gmm.priors
means = numpy.ndarray(gmm.means.shape)
means[:, :n_task_dims] = gmm.means[:, :n_task_dims]
# Transform covariances such that they satisfy the optimization
# constraints:
covars = numpy.ndarray(gmm.covariances.shape)
eye = numpy.tile(numpy.eye(n_task_dims), (self.n_components, 1, 1))
covars[:, :n_task_dims, :n_task_dims] = \
eye * numpy.abs(gmm.covariances[:, :n_task_dims, :n_task_dims])
covars[:, n_task_dims:, n_task_dims:] = \
eye * numpy.abs(gmm.covariances[:, n_task_dims:, n_task_dims:])
covars[:, n_task_dims:, :n_task_dims] = \
-eye * numpy.abs(gmm.covariances[:, n_task_dims:, :n_task_dims])
covars[:, :n_task_dims, n_task_dims:] = \
-eye * numpy.abs(gmm.covariances[:, :n_task_dims, n_task_dims:])
# Compute the rest of the means by solving the optimization constraint
for k in range(self.n_components):
means[k, n_task_dims:] = covars[k, n_task_dims:, :n_task_dims].dot(
numpy.linalg.inv(covars[k, :n_task_dims, :n_task_dims]).dot(
means[k, :n_task_dims] - self.attractor))
return priors, means, covars
def test_kmeanspp_initialization():
random_state = check_random_state(1)
n_samples = 300
n_features = 2
X = np.ndarray((n_samples, n_features))
X[:n_samples // 3, :] = random_state.multivariate_normal(
[0.0, 1.0], [[0.5, -1.0], [-1.0, 5.0]], size=(n_samples // 3, ))
X[n_samples // 3:-n_samples // 3, :] = random_state.multivariate_normal(
[-2.0, -2.0], [[3.0, 1.0], [1.0, 1.0]], size=(n_samples // 3, ))
X[-n_samples // 3:, :] = random_state.multivariate_normal(
[3.0, 1.0], [[3.0, -1.0], [-1.0, 1.0]], size=(n_samples // 3, ))
# artificial scaling, makes standard implementation fail
# either the initial covariances have to be adjusted or we have
# to normalize the dataset
X[:, 1] *= 10000.0
gmm = GMM(n_components=3, random_state=random_state)
gmm.from_samples(X, init_params="random")
ellipses = gmm.to_ellipses()
widths = np.array([ellipsis_params[1]
for _, ellipsis_params in ellipses])[:, np.newaxis]
average_widths_random = np.mean(pdist(widths))
gmm = GMM(n_components=3, random_state=random_state)
gmm.from_samples(X, init_params="kmeans++")
ellipses = gmm.to_ellipses()
widths = np.array([ellipsis_params[1]
for _, ellipsis_params in ellipses])[:, np.newaxis]
average_widths_kmeanspp = np.mean(pdist(widths))
# random initialization produces uneven covariance scaling
assert_less(average_widths_kmeanspp, average_widths_random)
def predict(node_info: MixtureGaussianParams,
pvals: List[Union[str, float]]) -> Optional[float]:
"""
Func to get prediction from current node
node_info: nodes info from distributions
pvals: parent values
Return value from MixtureGaussian node
"""
mean = node_info["mean"]
covariance = node_info["covars"]
w = node_info["coef"]
n_comp = len(node_info['coef'])
if n_comp != 0:
if pvals:
indexes = [i for i in range(1, len(pvals) + 1)]
if not np.isnan(np.array(pvals)).all():
gmm = GMM(n_components=n_comp,
priors=w,
means=mean,
covariances=covariance)
sample = gmm.predict(indexes, [pvals])[0][0]
else:
sample = np.nan
else:
# gmm = GMM(n_components=n_comp, priors=w, means=mean, covariances=covariance)
sample = 0
for ind, wi in enumerate(w):
sample += wi * mean[ind][0]
else:
sample = np.nan
return sample
def test_numerically_robust_responsibilities():
random_state = check_random_state(0)
n_samples = 300
n_features = 2
X = np.ndarray((n_samples, n_features))
mean0 = np.array([0.0, 1.0])
X[:n_samples // 3, :] = random_state.multivariate_normal(
mean0, [[0.5, -1.0], [-1.0, 5.0]], size=(n_samples // 3, ))
mean1 = np.array([-2.0, -2.0])
X[n_samples // 3:-n_samples // 3, :] = random_state.multivariate_normal(
mean1, [[3.0, 1.0], [1.0, 1.0]], size=(n_samples // 3, ))
mean2 = np.array([3.0, 1.0])
X[-n_samples // 3:, :] = random_state.multivariate_normal(
mean2, [[3.0, -1.0], [-1.0, 1.0]], size=(n_samples // 3, ))
# artificial scaling, makes naive implementation fail
X[:, 1] *= 10000.0
gmm = GMM(n_components=3, random_state=random_state)
gmm.from_samples(X, init_params="random")
mean_dists = pdist(gmm.means)
assert_true(all(mean_dists > 1))
assert_true(all(1e7 < gmm.covariances[:, 1, 1]))
assert_true(all(gmm.covariances[:, 1, 1] < 1e9))
def test_regression_with_custom_mean_covar_as_lists():
gmm = GMM(n_components=2,
priors=[0.5, 0.5],
means=[[0, 1], [1, 2]],
covariances=[[[1, 0], [0, 1]], [[1, 0], [0, 1]]])
y = gmm.predict([0], [[0]])
assert_array_almost_equal(y, [[1.37754067]])
def test_mvn_to_mvn():
means = 123.0 * np.ones((1, 1))
covs = 4.0 * np.ones((1, 1, 1))
gmm = GMM(n_components=1, priors=np.ones(1), means=means, covariances=covs)
mvn = gmm.to_mvn()
assert_array_almost_equal(mvn.mean, means[0])
assert_array_almost_equal(mvn.covariance, covs[0])
def test_ellipses():
"""Test equiprobable ellipses."""
random_state = check_random_state(0)
means = np.array([[0.0, 1.0], [2.0, -1.0]])
covariances = np.array([[[0.5, 0.0], [0.0, 5.0]], [[5.0, 0.0], [0.0,
0.5]]])
gmm = GMM(n_components=2,
priors=np.array([0.5, 0.5]),
means=means,
covariances=covariances,
random_state=random_state)
ellipses = gmm.to_ellipses()
mean, (angle, width, height) = ellipses[0]
assert_array_almost_equal(means[0], mean)
assert_equal(angle, 0.5 * np.pi)
assert_equal(width, np.sqrt(5.0))
assert_equal(height, np.sqrt(0.5))
mean, (angle, width, height) = ellipses[1]
assert_array_almost_equal(means[1], mean)
assert_equal(angle, -np.pi)
assert_equal(width, np.sqrt(5.0))
assert_equal(height, np.sqrt(0.5))
def test_extract_mvns():
gmm = GMM(n_components=2,
priors=0.5 * np.ones(2),
means=np.array([[1, 2], [3, 4]]),
covariances=[np.eye(2)] * 2)
mvn0 = gmm.extract_mvn(0)
assert_array_almost_equal(mvn0.mean, np.array([1, 2]))
mvn1 = gmm.extract_mvn(1)
assert_array_almost_equal(mvn1.mean, np.array([3, 4]))
def test_float_precision_error():
try:
from sklearn.datasets import load_boston
except ImportError:
raise SkipTest("sklearn is not available")
boston = load_boston()
X, y = boston.data, boston.target
gmm = GMM(n_components=10, random_state=2016)
gmm.from_samples(X)
def test_float_precision_error():
try:
from sklearn.datasets import load_boston
except ImportError:
raise SkipTest("sklearn is not available")
boston = load_boston()
X, y = boston.data, boston.target
gmm = GMM(n_components=10, random_state=2016)
gmm.from_samples(X)
def test_2_components_to_mvn():
priors = np.array([0.25, 0.75])
means = np.array([[1.0, 2.0], [3.0, 4.0]])
covs = np.array([
[[1.0, 0.0], [0.0, 1.0]],
[[1.0, 0.0], [0.0, 1.0]],
])
gmm = GMM(n_components=1, priors=priors, means=means, covariances=covs)
mvn = gmm.to_mvn()
assert_array_almost_equal(mvn.mean, np.array([2.5, 3.5]))
def test_gmm_to_mvn_vs_mvn():
random_state = check_random_state(0)
gmm = GMM(n_components=2, random_state=random_state)
gmm.from_samples(X)
mvn_from_gmm = gmm.to_mvn()
mvn = MVN(random_state=random_state)
mvn.from_samples(X)
assert_array_almost_equal(mvn_from_gmm.mean, mvn.mean)
assert_array_almost_equal(mvn_from_gmm.covariance,
mvn.covariance,
decimal=3)
def test_probability_density():
"""Test PDF of GMM."""
global X
global random_state
gmm = GMM(n_components=2, random_state=random_state)
gmm.from_samples(X)
x = np.linspace(-100, 100, 201)
X_grid = np.vstack(map(np.ravel, np.meshgrid(x, x))).T
p = gmm.to_probability_density(X_grid)
approx_int = np.sum(p) * ((x[-1] - x[0]) / 201) ** 2
assert_less(np.abs(1.0 - approx_int), 0.01)
def test_probability_density():
"""Test PDF of GMM."""
global X
global random_state
gmm = GMM(n_components=2, random_state=random_state)
gmm.from_samples(X)
x = np.linspace(-100, 100, 201)
X_grid = np.vstack(list(map(np.ravel, np.meshgrid(x, x)))).T
p = gmm.to_probability_density(X_grid)
approx_int = np.sum(p) * ((x[-1] - x[0]) / 201)**2
assert_less(np.abs(1.0 - approx_int), 0.01)
def test_conditional_distribution():
"""Test moments from conditional GMM."""
random_state = check_random_state(0)
gmm = GMM(n_components=2, priors=np.array([0.5, 0.5]), means=means,
covariances=covariances, random_state=random_state)
conditional = gmm.condition(np.array([1]), np.array([1.0]))
assert_array_almost_equal(conditional.means[0], np.array([0.0]))
assert_array_almost_equal(conditional.covariances[0], np.array([[0.3]]))
conditional = gmm.condition(np.array([0]), np.array([2.0]))
assert_array_almost_equal(conditional.means[1], np.array([-1.0]))
assert_array_almost_equal(conditional.covariances[1], np.array([[0.3]]))
def test_sample_confidence_region():
"""Test sampling from confidence region."""
random_state = check_random_state(0)
means = np.array([[0.0, 1.0], [2.0, -1.0]])
covariances = np.array([[[0.5, 0.0], [0.0, 5.0]], [[5.0, 0.0], [0.0,
0.5]]])
gmm = GMM(n_components=2,
priors=np.array([0.5, 0.5]),
means=means,
covariances=covariances,
random_state=random_state)
samples = gmm.sample_confidence_region(100, 0.7)
for sample in samples:
assert_true(gmm.is_in_confidence_region(sample, 0.7))
def test_conditional_distribution():
"""Test moments from conditional GMM."""
random_state = check_random_state(0)
gmm = GMM(n_components=2,
priors=np.array([0.5, 0.5]),
means=means,
covariances=covariances,
random_state=random_state)
conditional = gmm.condition(np.array([1]), np.array([1.0]))
assert_array_almost_equal(conditional.means[0], np.array([0.0]))
assert_array_almost_equal(conditional.covariances[0], np.array([[0.3]]))
conditional = gmm.condition(np.array([0]), np.array([2.0]))
assert_array_almost_equal(conditional.means[1], np.array([-1.0]))
assert_array_almost_equal(conditional.covariances[1], np.array([[0.3]]))
def test_estimation_from_previous_initialization():
global X
global random_state
global means
global covariances
gmm = GMM(n_components=2,
priors=0.5 * np.ones(2),
means=np.copy(means),
covariances=np.copy(covariances),
random_state=check_random_state(2))
gmm.from_samples(X, n_iter=2)
assert_less(np.linalg.norm(gmm.means[0] - means[0]), 0.01)
assert_less(np.linalg.norm(gmm.covariances[0] - covariances[0]), 0.03)
assert_less(np.linalg.norm(gmm.means[1] - means[1]), 0.01)
assert_less(np.linalg.norm(gmm.covariances[1] - covariances[1]), 0.04)
def test_verbose_from_samples():
"""Test verbose output."""
global X
random_state = check_random_state(0)
old_stdout = sys.stdout
sys.stdout = StringIO()
try:
gmm = GMM(n_components=2, verbose=True, random_state=random_state)
gmm.from_samples(X)
finally:
out = sys.stdout.getvalue()
sys.stdout.close()
sys.stdout = old_stdout
assert ("converged" in out)
def test_verbose_from_samples():
"""Test verbose output."""
global X
random_state = check_random_state(0)
old_stdout = sys.stdout
sys.stdout = StringIO()
try:
gmm = GMM(n_components=2, verbose=True, random_state=random_state)
gmm.from_samples(X)
finally:
out = sys.stdout.getvalue()
sys.stdout.close()
sys.stdout = old_stdout
assert("converged" in out)
def test_regression_with_2d_input():
"""Test regression with GMM and two-dimensional input."""
random_state = check_random_state(0)
n_samples = 200
x = np.linspace(0, 2, n_samples)[:, np.newaxis]
y1 = 3 * x[:n_samples / 2] + 1
y2 = -3 * x[n_samples / 2:] + 7
noise = random_state.randn(n_samples, 1) * 0.01
y = np.vstack((y1, y2)) + noise
samples = np.hstack((x, x[::-1], y))
gmm = GMM(n_components=2, random_state=random_state)
gmm.from_samples(samples)
pred = gmm.predict(np.array([0, 1]), np.hstack((x, x[::-1])))
mse = np.sum((y - pred) ** 2) / n_samples
def test_regression_with_2d_input():
"""Test regression with GMM and two-dimensional input."""
random_state = check_random_state(0)
n_samples = 200
x = np.linspace(0, 2, n_samples)[:, np.newaxis]
y1 = 3 * x[:n_samples // 2] + 1
y2 = -3 * x[n_samples // 2:] + 7
noise = random_state.randn(n_samples, 1) * 0.01
y = np.vstack((y1, y2)) + noise
samples = np.hstack((x, x[::-1], y))
gmm = GMM(n_components=2, random_state=random_state)
gmm.from_samples(samples)
pred = gmm.predict(np.array([0, 1]), np.hstack((x, x[::-1])))
mse = np.sum((y - pred)**2) / n_samples
def test_from_samples_with_oas():
n_samples = 9
n_features = 2
X = np.ndarray((n_samples, n_features))
X[:n_samples // 3, :] = random_state.multivariate_normal(
[0.0, 1.0], [[0.5, -1.0], [-1.0, 5.0]], size=(n_samples // 3, ))
X[n_samples // 3:-n_samples // 3, :] = random_state.multivariate_normal(
[-2.0, -2.0], [[3.0, 1.0], [1.0, 1.0]], size=(n_samples // 3, ))
X[-n_samples // 3:, :] = random_state.multivariate_normal(
[3.0, 3.0], [[3.0, -1.0], [-1.0, 1.0]], size=(n_samples // 3, ))
gmm = GMM(n_components=3, random_state=random_state)
gmm.from_samples(X,
init_params="kmeans++",
oracle_approximating_shrinkage=True)
cond = gmm.condition(np.array([0]), np.array([1.0]))
for i in range(cond.n_components):
eigvals = np.linalg.eigvals(cond.covariances[i])
assert_true(all(eigvals >= 0))
def test_regression_without_noise():
"""Test regression without noise."""
random_state = check_random_state(0)
n_samples = 200
x = np.linspace(0, 2, n_samples)[:, np.newaxis]
y1 = 3 * x[:n_samples / 2] + 1
y2 = -3 * x[n_samples / 2:] + 7
y = np.vstack((y1, y2))
samples = np.hstack((x, y))
gmm = GMM(n_components=2, random_state=random_state)
gmm.from_samples(samples)
assert_array_almost_equal(gmm.priors, 0.5 * np.ones(2), decimal=2)
assert_array_almost_equal(gmm.means[0], np.array([1.5, 2.5]), decimal=2)
assert_array_almost_equal(gmm.means[1], np.array([0.5, 2.5]), decimal=1)
pred = gmm.predict(np.array([0]), x)
mse = np.sum((y - pred) ** 2) / n_samples
assert_less(mse, 0.01)
def test_regression_without_noise():
"""Test regression without noise."""
random_state = check_random_state(0)
n_samples = 200
x = np.linspace(0, 2, n_samples)[:, np.newaxis]
y1 = 3 * x[:n_samples // 2] + 1
y2 = -3 * x[n_samples // 2:] + 7
y = np.vstack((y1, y2))
samples = np.hstack((x, y))
gmm = GMM(n_components=2, random_state=random_state)
gmm.from_samples(samples)
assert_array_almost_equal(gmm.priors, 0.5 * np.ones(2), decimal=2)
assert_array_almost_equal(gmm.means[0], np.array([1.5, 2.5]), decimal=2)
assert_array_almost_equal(gmm.means[1], np.array([0.5, 2.5]), decimal=1)
pred = gmm.predict(np.array([0]), x)
mse = np.sum((y - pred)**2) / n_samples
assert_less(mse, 0.01)
def predict(node_info: Dict[str, Dict[str, CondMixtureGaussParams]],
pvals: List[Union[str, float]]) -> Optional[float]:
"""
Function to get prediction from ConditionalMixtureGaussian node
params:
node_info: nodes info from distributions
pvals: parent values
"""
dispvals = []
lgpvals = []
for pval in pvals:
if ((isinstance(pval, str)) | ((isinstance(pval, int)))):
dispvals.append(pval)
else:
lgpvals.append(pval)
lgdistribution = node_info["hybcprob"][str(dispvals)]
mean = lgdistribution["mean"]
covariance = lgdistribution["covars"]
w = lgdistribution["coef"]
if len(w) != 0:
if len(lgpvals) != 0:
indexes = [i for i in range(1, (len(lgpvals) + 1), 1)]
if not np.isnan(np.array(lgpvals)).all():
n_comp = len(w)
gmm = GMM(n_components=n_comp,
priors=w,
means=mean,
covariances=covariance)
sample = gmm.predict(indexes, [lgpvals])[0][0]
else:
sample = np.nan
else:
# n_comp = len(w)
# gmm = GMM(n_components=n_comp, priors=w, means=mean, covariances=covariance)
sample = 0
for ind, wi in enumerate(w):
sample += wi * mean[ind][0]
else:
sample = np.nan
return sample
def fit_parameters(self, data: DataFrame) -> MixtureGaussianParams:
"""
Train params for Mixture Gaussian Node
"""
parents = self.disc_parents + self.cont_parents
if not parents:
n_comp = int((component(data, [self.name], 'aic') +
component(data, [self.name], 'bic')) /
2) # component(data, [node], 'LRTS')#
# n_comp = 3
gmm = GMM(n_components=n_comp).from_samples(np.transpose(
[data[self.name].values]),
n_iter=500,
init_params='kmeans++')
means = gmm.means.tolist()
cov = gmm.covariances.tolist()
# weigts = np.transpose(gmm.to_responsibilities(np.transpose([data[node].values])))
w = gmm.priors.tolist() # []
# for row in weigts:
# w.append(np.mean(row))
return {"mean": means, "coef": w, "covars": cov}
if parents:
if not self.disc_parents and self.cont_parents:
nodes = [self.name] + self.cont_parents
new_data = data[nodes]
new_data.reset_index(inplace=True, drop=True)
n_comp = int((component(new_data, nodes, 'aic') +
component(new_data, nodes, 'bic')) /
2) # component(new_data, nodes, 'LRTS')#
# n_comp = 3
gmm = GMM(n_components=n_comp).from_samples(
new_data[nodes].values, n_iter=500, init_params='kmeans++')
means = gmm.means.tolist()
cov = gmm.covariances.tolist()
# weigts = np.transpose(gmm.to_responsibilities(new_data[nodes].values))
w = gmm.priors.tolist() # []
# for row in weigts:
# w.append(np.mean(row))
return {"mean": means, "coef": w, "covars": cov}
def test_estimate_moments():
"""Test moments estimated from samples and sampling from GMM."""
global X
global random_state
gmm = GMM(n_components=2, random_state=random_state)
gmm.from_samples(X)
assert_less(np.linalg.norm(gmm.means[0] - means[0]), 0.005)
assert_less(np.linalg.norm(gmm.covariances[0] - covariances[0]), 0.01)
assert_less(np.linalg.norm(gmm.means[1] - means[1]), 0.01)
assert_less(np.linalg.norm(gmm.covariances[1] - covariances[1]), 0.03)
X = gmm.sample(n_samples=100000)
gmm = GMM(n_components=2, random_state=random_state)
gmm.from_samples(X)
assert_less(np.linalg.norm(gmm.means[0] - means[0]), 0.01)
assert_less(np.linalg.norm(gmm.covariances[0] - covariances[0]), 0.03)
assert_less(np.linalg.norm(gmm.means[1] - means[1]), 0.01)
assert_less(np.linalg.norm(gmm.covariances[1] - covariances[1]), 0.04)
def choose(self, pvalues, method, outcome):
'''
Randomly choose state of node from probability distribution conditioned on *pvalues*.
This method has two parts: (1) determining the proper probability
distribution, and (2) using that probability distribution to determine
an outcome.
Arguments:
1. *pvalues* -- An array containing the assigned states of the node's parents. This must be in the same order as the parents appear in ``self.Vdataentry['parents']``.
The function creates a Gaussian distribution in the manner described in :doc:`lgbayesiannetwork`, and samples from that distribution, returning its outcome.
'''
random.seed()
sample = 0
if method == 'simple':
# calculate Bayesian parameters (mean and variance)
mean = self.Vdataentry["mean_base"]
if (self.Vdataentry["parents"] != None):
for x in range(len(self.Vdataentry["parents"])):
if (pvalues[x] != "default"):
mean += pvalues[x] * self.Vdataentry["mean_scal"][x]
else:
print(
"Attempted to sample node with unassigned parents."
)
variance = self.Vdataentry["variance"]
sample = random.gauss(mean, math.sqrt(variance))
else:
mean = self.Vdataentry["mean_base"]
variance = self.Vdataentry["variance"]
w = self.Vdataentry["mean_scal"]
n_comp = len(self.Vdataentry["mean_scal"])
if n_comp != 0:
if (self.Vdataentry["parents"] != None):
indexes = [
i for i in range(1, (len(self.Vdataentry["parents"]) +
1), 1)
]
if not np.isnan(np.array(pvalues)).all():
gmm = GMM(n_components=n_comp,
priors=w,
means=mean,
covariances=variance)
sample = gmm.predict(indexes, [pvalues])[0][0]
else:
sample = np.nan
else:
gmm = GMM(n_components=n_comp,
priors=w,
means=mean,
covariances=variance)
sample = gmm.sample(1)[0][0]
else:
sample = np.nan
return sample
def test_plot():
"""Test plot of GMM."""
gmm = GMM(n_components=2,
priors=np.array([0.5, 0.5]),
means=means,
covariances=covariances,
random_state=0)
ax = AxisStub()
plot_error_ellipses(ax, gmm)
assert_equal(ax.count, 16)
ax = AxisStub()
plot_error_ellipses(ax, gmm, colors=["r", "g"])
assert_equal(ax.count, 16)
def test_uninitialized():
"""Test behavior of uninitialized GMM."""
random_state = check_random_state(0)
gmm = GMM(n_components=2, random_state=random_state)
assert_raises(ValueError, gmm.sample, 10)
assert_raises(ValueError, gmm.to_probability_density, np.ones((1, 1)))
assert_raises(ValueError, gmm.condition, np.zeros(0), np.zeros(0))
assert_raises(ValueError, gmm.predict, np.zeros(0), np.zeros(0))
assert_raises(ValueError, gmm.to_ellipses)
gmm = GMM(n_components=2, priors=np.ones(2), random_state=random_state)
assert_raises(ValueError, gmm.sample, 10)
assert_raises(ValueError, gmm.to_probability_density, np.ones((1, 1)))
assert_raises(ValueError, gmm.condition, np.zeros(0), np.zeros(0))
assert_raises(ValueError, gmm.predict, np.zeros(0), np.zeros(0))
assert_raises(ValueError, gmm.to_ellipses)
gmm = GMM(n_components=2,
priors=np.ones(2),
means=np.zeros((2, 2)),
random_state=random_state)
assert_raises(ValueError, gmm.sample, 10)
assert_raises(ValueError, gmm.to_probability_density, np.ones((1, 1)))
assert_raises(ValueError, gmm.condition, np.zeros(0), np.zeros(0))
assert_raises(ValueError, gmm.predict, np.zeros(0), np.zeros(0))
assert_raises(ValueError, gmm.to_ellipses)
def test_ellipses():
"""Test equiprobable ellipses."""
random_state = check_random_state(0)
means = np.array([[0.0, 1.0],
[2.0, -1.0]])
covariances = np.array([[[0.5, 0.0], [0.0, 5.0]],
[[5.0, 0.0], [0.0, 0.5]]])
gmm = GMM(n_components=2, priors=np.array([0.5, 0.5]), means=means,
covariances=covariances, random_state=random_state)
ellipses = gmm.to_ellipses()
mean, (angle, width, height) = ellipses[0]
assert_array_almost_equal(means[0], mean)
assert_equal(angle, 0.5 * np.pi)
assert_equal(width, np.sqrt(5.0))
assert_equal(height, np.sqrt(0.5))
mean, (angle, width, height) = ellipses[1]
assert_array_almost_equal(means[1], mean)
assert_equal(angle, -np.pi)
assert_equal(width, np.sqrt(5.0))
assert_equal(height, np.sqrt(0.5))
def test_plot():
"""Test plot of GMM."""
gmm = GMM(n_components=2,
priors=np.array([0.5, 0.5]),
means=means,
covariances=covariances,
random_state=0)
ax = AxisStub()
try:
plot_error_ellipses(ax, gmm)
except ImportError:
raise SkipTest("matplotlib is required for this test")
assert_equal(ax.count, 16)
ax = AxisStub()
plot_error_ellipses(ax, gmm, colors=["r", "g"])
assert_equal(ax.count, 16)
def choose_gmm(self, pvalues, outcome):
'''
Randomly choose state of node from probability distribution conditioned on *pvalues*.
This method has two parts: (1) determining the proper probability
distribution, and (2) using that probability distribution to determine
an outcome.
Arguments:
1. *pvalues* -- An array containing the assigned states of the node's parents. This must be in the same order as the parents appear in ``self.Vdataentry['parents']``.
The function creates a Gaussian distribution in the manner described in :doc:`lgbayesiannetwork`, and samples from that distribution, returning its outcome.
'''
random.seed()
# calculate Bayesian parameters (mean and variance)
s = 0
mean = self.Vdataentry["mean_base"]
variance = self.Vdataentry["variance"]
w = self.Vdataentry["mean_scal"]
n_comp = len(self.Vdataentry["mean_scal"])
indexes = [
i for i in range(1, (len(self.Vdataentry["parents"]) + 1), 1)
]
if (self.Vdataentry["parents"] != None):
# for x in range(len(self.Vdataentry["parents"])):
# if (pvalues[x] != "default"):
# X.append(pvalues[x])
# else:
# print ("Attempted to sample node with unassigned parents.")
if not np.isnan(np.array(pvalues)).any():
gmm = GMM(n_components=n_comp,
priors=w,
means=mean,
covariances=variance)
s = gmm.predict(indexes, [pvalues])[0][0]
else:
s = np.nan
else:
gmm = GMM(n_components=n_comp,
priors=w,
means=mean,
covariances=variance)
s = gmm.sample(1)[0][0]
# draw random outcome from Gaussian
# note that this built in function takes the standard deviation, not the
# variance, thus requiring a square root
return s
def test_kmeanspp_initialization():
random_state = check_random_state(0)
n_samples = 300
n_features = 2
X = np.ndarray((n_samples, n_features))
mean0 = np.array([0.0, 1.0])
X[:n_samples // 3, :] = random_state.multivariate_normal(
mean0, [[0.5, -1.0], [-1.0, 5.0]], size=(n_samples // 3, ))
mean1 = np.array([-2.0, -2.0])
X[n_samples // 3:-n_samples // 3, :] = random_state.multivariate_normal(
mean1, [[3.0, 1.0], [1.0, 1.0]], size=(n_samples // 3, ))
mean2 = np.array([3.0, 1.0])
X[-n_samples // 3:, :] = random_state.multivariate_normal(
mean2, [[3.0, -1.0], [-1.0, 1.0]], size=(n_samples // 3, ))
# artificial scaling, makes standard implementation fail
# either the initial covariances have to be adjusted or we have
# to normalize the dataset
X[:, 1] *= 10000.0
gmm = GMM(n_components=3, random_state=random_state)
gmm.from_samples(X, init_params="random")
# random initialization fails
assert_less(gmm.covariances[0, 0, 0], np.finfo(float).eps)
assert_less(gmm.covariances[1, 0, 0], np.finfo(float).eps)
assert_less(gmm.covariances[2, 0, 0], np.finfo(float).eps)
assert_less(gmm.covariances[0, 1, 1], np.finfo(float).eps)
assert_less(gmm.covariances[1, 1, 1], np.finfo(float).eps)
assert_less(gmm.covariances[2, 1, 1], np.finfo(float).eps)
gmm = GMM(n_components=3, random_state=random_state)
gmm.from_samples(X, init_params="kmeans++")
mean_dists = pdist(gmm.means)
assert_true(all(mean_dists > 1))
assert_true(all(1e7 < gmm.covariances[:, 1, 1]))
assert_true(all(gmm.covariances[:, 1, 1] < 1e9))
def test_estimate_moments():
"""Test moments estimated from samples and sampling from GMM."""
global X
global random_state
gmm = GMM(n_components=2, random_state=random_state)
gmm.from_samples(X)
assert_less(np.linalg.norm(gmm.means[0] - means[0]), 0.005)
assert_less(np.linalg.norm(gmm.covariances[0] - covariances[0]), 0.01)
assert_less(np.linalg.norm(gmm.means[1] - means[1]), 0.01)
assert_less(np.linalg.norm(gmm.covariances[1] - covariances[1]), 0.03)
X = gmm.sample(n_samples=100000)
gmm = GMM(n_components=2, random_state=random_state)
gmm.from_samples(X)
assert_less(np.linalg.norm(gmm.means[0] - means[0]), 0.01)
assert_less(np.linalg.norm(gmm.covariances[0] - covariances[0]), 0.03)
assert_less(np.linalg.norm(gmm.means[1] - means[1]), 0.01)
assert_less(np.linalg.norm(gmm.covariances[1] - covariances[1]), 0.04)
We will cluster the Iris dataset but we will use sklearn to initialize
our GMM. sklearn allows restricted covariances such as diagonal covariances.
This is just for demonstration purposes and does not represent an example
of a particularly good fit. Take a look at `plot_iris.py` for a fit with
full covariances.
"""
print(__doc__)
import numpy as np
from sklearn.datasets import load_iris
from sklearn.decomposition import PCA
from sklearn.mixture import GaussianMixture
import matplotlib.pyplot as plt
from gmr import GMM, plot_error_ellipses
X, y = load_iris(return_X_y=True)
X_pca = PCA(n_components=2, whiten=True, random_state=1).fit_transform(X)
gmm_sklearn = GaussianMixture(n_components=3, covariance_type="diag",
random_state=3)
gmm_sklearn.fit(X_pca)
gmm = GMM(
n_components=3, priors=gmm_sklearn.weights_, means=gmm_sklearn.means_,
covariances=np.array([np.diag(c) for c in gmm_sklearn.covariances_]))
plt.figure()
ax = plt.subplot(111)
ax.scatter(X_pca[:, 0], X_pca[:, 1], c=y)
plot_error_ellipses(ax, gmm, alpha=0.1, colors=["r", "g", "b"])
plt.show()
# Drop some features:
df = df.drop([name + ' s1' for name in features_to_drop], axis=1)
df = df.drop([name + ' s2' for name in features_to_drop], axis=1)
data = df.to_numpy()
print('Number of transitions in the data: %d' % data.shape[0])
if sys.argv[1] == 'train':
#######################
# Train the GMM model #
#######################
n_components = 500
gmm = GMM(n_components=n_components)
print('Training the model with %d gaussian units' % n_components)
gmm.from_samples(data,
init='',
plot_title=gmm_id,
n_iter=100,
savefig=True)
print('Model ready')
plt.show()
# Save the model:
with open(gmm_file, 'wb') as f:
pickle.dump(gmm, f)
elif sys.argv[1] == 'score':
if isinstance(seed, np.random.RandomState):
return seed
raise ValueError('%r cannot be used to seed a numpy.random.RandomState'
' instance' % seed)
random_state = check_random_state(0)
x_axes = np.array([0]) #x-axis
y_axes = np.array([1]) #y-axis
n_samples = 100
X = np.ndarray((n_samples, 2))
X[:, 1] = np.linspace(0, 2 * np.pi, n_samples)
X[:, 0] = np.sin(X[:, 1]) + random_state.randn(n_samples) * 0.1
gmm = GMM(n_components=3, random_state=0)
gmm.from_samples(X)
X_test = np.linspace(-1.5, 1.5)
X_test = X_test[:, np.newaxis]
Y = gmm.predict(x_axes, X_test)
gmm2 = mixture.GMM(n_components=3, covariance_type='full')
gmm2.fit(X)
color_iter = itertools.cycle(['r', 'g', 'b', 'c', 'm'])
for i, (clf, title) in enumerate([(gmm2, 'GMM')]):
splot = plt.subplot(2, 1, i + 1)
Y_ = clf.predict(X)
if isinstance(seed, (numbers.Integral, np.integer)):
return np.random.RandomState(seed)
if isinstance(seed, np.random.RandomState):
return seed
raise ValueError('%r cannot be used to seed a numpy.random.RandomState'
' instance' % seed)
random_state = check_random_state(0)
x_axes = np.array([0]) #x-axis
y_axes = np.array([1]) #y-axis
X = np.loadtxt("samples", unpack=True)
gmm = GMM(n_components=4, random_state=0)
gmm.from_samples(X)
gmm2 = mixture.GMM(n_components=4, covariance_type='full')
gmm2.fit(X)
color_iter = itertools.cycle(['r', 'g', 'b', 'c', 'm'])
for i, (clf, title) in enumerate([(gmm2, 'GMM')]):
splot = plt.subplot(2, 1, 1 + i)
Y_ = clf.predict(X)
for i, (mean, covar, color) in enumerate(zip(
clf.means_, clf._get_covars(), color_iter)):
v, w = linalg.eigh(covar)
u = w[0] / linalg.norm(w[0])
' instance' % seed)
random_state = check_random_state(0)
X_test = np.linspace(0, 2 * np.pi, 100)
Y_test = np.linspace(-1.5, 1.5)
plt.figure(figsize=(10, 5))
n_samples = 100
X = np.ndarray((n_samples, 2))
X[:, 0] = np.linspace(0, 2 * np.pi, n_samples)
X[:, 1] = np.sin(X[:, 0]) + random_state.randn(n_samples) * 0.1
gmm = GMM(n_components=3, random_state=0)
gmm.from_samples(X)
Y_x = gmm.predict(np.array([0]), X_test[:, np.newaxis])
Y_y = gmm.predict(np.array([1]), Y_test[:, np.newaxis])
plt.subplot(1, 2, 1)
plt.title("Mixture of Experts: $p(Y | X) = \Sigma_k \pi_{k, Y|X} "
"\mathcal{N}_{k, Y|X}$")
plt.scatter(X[:, 0], X[:, 1])
plot_error_ellipses(plt.gca(), gmm, colors=["r", "g", "b"])
plt.plot(X_test, Y_x.ravel(), c="k", lw=2)
plt.plot(Y_y.ravel(), Y_test, c="k", lw=2)
X2 = np.loadtxt("samples", unpack=True)
X2_test = np.linspace(-7.0, 4.0)#X2[:, 0]
X_test = np.linspace(0, 2 * np.pi, 100)
mean, covariance = mvn.predict(np.array([0]), X_test[:, np.newaxis])
plt.figure(figsize=(10, 5))
plt.subplot(1, 2, 1)
plt.title("Linear: $p(Y | X) = \mathcal{N}(\mu_{Y|X}, \Sigma_{Y|X})$")
plt.scatter(X[:, 0], X[:, 1])
y = mean.ravel()
s = covariance.ravel()
plt.fill_between(X_test, y - s, y + s, alpha=0.2)
plt.plot(X_test, y, lw=2)
n_samples = 100
X = np.ndarray((n_samples, 2))
X[:, 0] = np.linspace(0, 2 * np.pi, n_samples)
X[:, 1] = np.sin(X[:, 0]) + random_state.randn(n_samples) * 0.1
gmm = GMM(n_components=3, random_state=0)
gmm.from_samples(X)
Y = gmm.predict(np.array([0]), X_test[:, np.newaxis])
plt.subplot(1, 2, 2)
plt.title("Mixture of Experts: $p(Y | X) = \Sigma_k \pi_{k, Y|X} "
"\mathcal{N}_{k, Y|X}$")
plt.scatter(X[:, 0], X[:, 1])
plot_error_ellipses(plt.gca(), gmm, colors=["r", "g", "b"])
plt.plot(X_test, Y.ravel(), c="k", lw=2)
plt.show()
X_test = np.linspace(0, 2 * np.pi, 100)
mean, covariance = mvn.predict(np.array([0]), X_test[:, np.newaxis])
plt.figure(figsize=(10, 5))
plt.subplot(1, 2, 1)
plt.title("Linear: $p(Y | X) = \mathcal{N}(\mu_{Y|X}, \Sigma_{Y|X})$")
plt.scatter(X[:, 0], X[:, 1])
y = mean.ravel()
s = covariance.ravel()
plt.fill_between(X_test, y - s, y + s, alpha=0.2)
plt.plot(X_test, y, lw=2)
n_samples = 100
X = np.ndarray((n_samples, 2))
X[:, 0] = np.linspace(0, 2 * np.pi, n_samples)
X[:, 1] = np.sin(X[:, 0]) + random_state.randn(n_samples) * 0.1
gmm = GMM(n_components=3, random_state=0)
gmm.from_samples(X)
Y = gmm.predict(np.array([0]), X_test[:, np.newaxis])
plt.subplot(1, 2, 2)
plt.title("Mixture of Experts: $p(Y | X) = \Sigma_k \pi_{k, Y|X} "
"\mathcal{N}_{k, Y|X}$")
plt.scatter(X[:, 0], X[:, 1])
plot_error_ellipses(plt.gca(), gmm, colors=["r", "g", "b"])
plt.plot(X_test, Y.ravel(), c="k", lw=2)
plt.show()
if __name__ == "__main__":
random_state = check_random_state(0)
n_samples = 300
n_features = 2
X = np.ndarray((n_samples, n_features))
X[:n_samples / 3, :] = random_state.multivariate_normal(
[0.0, 1.0], [[0.5, -2.0], [-2.0, 5.0]], size=(n_samples / 3,))
X[n_samples / 3:-n_samples / 3, :] = random_state.multivariate_normal(
[-2.0, -2.0], [[3.0, 2.0], [2.0, 1.0]], size=(n_samples / 3,))
X[-n_samples / 3:, :] = random_state.multivariate_normal(
[3.0, 1.0], [[3.0, -1.0], [-1.0, 1.0]], size=(n_samples / 3,))
gmm = GMM(n_components=3, random_state=random_state)
gmm.from_samples(X)
cond = gmm.condition(np.array([0]), np.array([1.0]))
plt.figure(figsize=(15, 5))
plt.subplot(1, 3, 1)
plt.title("Gaussian Mixture Model")
plt.xlim((-10, 10))
plt.ylim((-10, 10))
plot_error_ellipses(plt.gca(), gmm, colors=["r", "g", "b"])
plt.scatter(X[:, 0], X[:, 1])
plt.subplot(1, 3, 2)
plt.title("Probability Density and Samples")
plt.xlim((-10, 10))
