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_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)
from gmr import MVN, GMM, plot_error_ellipses
if __name__ == "__main__":
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
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
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
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