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_without_noise():
"""Test probability density of MVN with not invertible covariance."""
random_state = check_random_state(0)
n_samples = 10
x = np.linspace(0, 1, n_samples)[:, np.newaxis]
y = np.ones((n_samples, 1))
samples = np.hstack((x, y))
mvn = MVN(random_state=random_state)
mvn.from_samples(samples)
assert_array_almost_equal(mvn.mean, np.array([0.5, 1.0]), decimal=2)
assert_equal(mvn.covariance[1, 1], 0.0)
p_training = mvn.to_probability_density(samples)
p_test = mvn.to_probability_density(samples + 1)
assert_true(np.all(p_training > p_test))
def test_probability_density_without_noise():
"""Test probability density of MVN with not invertible covariance."""
random_state = check_random_state(0)
n_samples = 10
x = np.linspace(0, 1, n_samples)[:, np.newaxis]
y = np.ones((n_samples, 1))
samples = np.hstack((x, y))
mvn = MVN(random_state=random_state)
mvn.from_samples(samples)
assert_array_almost_equal(mvn.mean, np.array([0.5, 1.0]), decimal=2)
assert_equal(mvn.covariance[1, 1], 0.0)
p_training = mvn.to_probability_density(samples)
p_test = mvn.to_probability_density(samples + 1)
assert_true(np.all(p_training > p_test))
def test_regression_without_noise():
"""Test regression without noise with MVN."""
random_state = check_random_state(0)
n_samples = 10
x = np.linspace(0, 1, n_samples)[:, np.newaxis]
y = 3 * x + 1
samples = np.hstack((x, y))
mvn = MVN(random_state=random_state)
mvn.from_samples(samples)
assert_array_almost_equal(mvn.mean, np.array([0.5, 2.5]), decimal=2)
pred, cov = mvn.predict(np.array([0]), x)
mse = np.sum((y - pred) ** 2) / n_samples
assert_less(mse, 1e-10)
assert_less(cov[0, 0], 1e-10)
def test_regression_without_noise():
"""Test regression without noise with MVN."""
random_state = check_random_state(0)
n_samples = 10
x = np.linspace(0, 1, n_samples)[:, np.newaxis]
y = 3 * x + 1
samples = np.hstack((x, y))
mvn = MVN(random_state=random_state)
mvn.from_samples(samples)
assert_array_almost_equal(mvn.mean, np.array([0.5, 2.5]), decimal=2)
pred, cov = mvn.predict(np.array([0]), x)
mse = np.sum((y - pred)**2) / n_samples
assert_less(mse, 1e-10)
assert_less(cov[0, 0], 1e-10)
def test_estimate_moments():
"""Test moments estimated from samples and sampling from MVN."""
random_state = check_random_state(0)
actual_mean = np.array([0.0, 1.0])
actual_covariance = np.array([[0.5, -1.0], [-1.0, 5.0]])
X = random_state.multivariate_normal(actual_mean, actual_covariance,
size=(100000,))
mvn = MVN(random_state=random_state)
mvn.from_samples(X)
assert_less(np.linalg.norm(mvn.mean - actual_mean), 0.02)
assert_less(np.linalg.norm(mvn.covariance - actual_covariance), 0.02)
X2 = mvn.sample(n_samples=100000)
mvn2 = MVN(random_state=random_state)
mvn2.from_samples(X2)
assert_less(np.linalg.norm(mvn2.mean - actual_mean), 0.03)
assert_less(np.linalg.norm(mvn2.covariance - actual_covariance), 0.03)
def test_estimate_moments():
"""Test moments estimated from samples and sampling from MVN."""
random_state = check_random_state(0)
actual_mean = np.array([0.0, 1.0])
actual_covariance = np.array([[0.5, -1.0], [-1.0, 5.0]])
X = random_state.multivariate_normal(actual_mean, actual_covariance,
size=(100000,))
mvn = MVN(random_state=random_state)
mvn.from_samples(X)
assert_less(np.linalg.norm(mvn.mean - actual_mean), 0.02)
assert_less(np.linalg.norm(mvn.covariance - actual_covariance), 0.02)
X2 = mvn.sample(n_samples=100000)
mvn2 = MVN(random_state=random_state)
mvn2.from_samples(X2)
assert_less(np.linalg.norm(mvn2.mean - actual_mean), 0.03)
assert_less(np.linalg.norm(mvn2.covariance - actual_covariance), 0.03)
def test_regression_with_2d_input():
"""Test regression with MVN and two-dimensional input."""
random_state = check_random_state(0)
n_samples = 100
x = np.linspace(0, 1, n_samples)[:, np.newaxis]
y = 3 * x + 1
noise = random_state.randn(n_samples, 1) * 0.01
y += noise
samples = np.hstack((x, x[::-1], y))
mvn = MVN(random_state=random_state)
mvn.from_samples(samples)
assert_array_almost_equal(mvn.mean, np.array([0.5, 0.5, 2.5]), decimal=2)
x_test = np.hstack((x, x[::-1]))
pred, cov = mvn.predict(np.array([0, 1]), x_test)
mse = np.sum((y - pred)**2) / n_samples
assert_less(mse, 1e-3)
assert_less(cov[0, 0], 0.01)
def test_regression_with_2d_input():
"""Test regression with MVN and two-dimensional input."""
random_state = check_random_state(0)
n_samples = 100
x = np.linspace(0, 1, n_samples)[:, np.newaxis]
y = 3 * x + 1
noise = random_state.randn(n_samples, 1) * 0.01
y += noise
samples = np.hstack((x, x[::-1], y))
mvn = MVN(random_state=random_state)
mvn.from_samples(samples)
assert_array_almost_equal(mvn.mean, np.array([0.5, 0.5, 2.5]), decimal=2)
x_test = np.hstack((x, x[::-1]))
pred, cov = mvn.predict(np.array([0, 1]), x_test)
mse = np.sum((y - pred) ** 2) / n_samples
assert_less(mse, 1e-3)
assert_less(cov[0, 0], 0.01)
distributions.
"""
print(__doc__)
import numpy as np
import matplotlib.pyplot as plt
from sklearn.utils import check_random_state
from gmr import MVN, plot_error_ellipse
if __name__ == "__main__":
random_state = check_random_state(0)
mvn = MVN(random_state=random_state)
X = random_state.multivariate_normal([0.0, 1.0], [[0.5, -2.0], [-2.0, 5.0]],
size=(100,))
mvn.from_samples(X)
X_sampled = mvn.sample(n_samples=100)
plt.figure(figsize=(15, 5))
plt.subplot(1, 3, 1)
plt.xlim((-10, 10))
plt.ylim((-10, 10))
plot_error_ellipse(plt.gca(), mvn)
plt.scatter(X[:, 0], X[:, 1], c="g", label="Training data")
plt.scatter(X_sampled[:, 0], X_sampled[:, 1], c="r", label="Samples")
plt.title("Bivariate Gaussian")
plt.legend(loc="best")
x = np.linspace(-10, 10, 100)
plt.subplot(1, 3, 2)
plt.xticks(())
import numpy as np
import matplotlib.pyplot as plt
from gmr.utils import check_random_state
from gmr import MVN, GMM, plot_error_ellipses
random_state = check_random_state(0)
n_samples = 10
X = np.ndarray((n_samples, 2))
X[:, 0] = np.linspace(0, 2 * np.pi, n_samples)
X[:, 1] = 1 - 3 * X[:, 0] + random_state.randn(n_samples)
mvn = MVN(random_state=0)
mvn.from_samples(X)
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
