def plot(self):
"""
Plot the joint Gaussian Mixture distribution.
"""
gaussian_components = [nlg.joint_distribution for nlg in self.nlgs]
gaussian_mixture = GaussianMixture(gaussian_components)
gaussian_mixture.plot()
def multiply(self, factor):
"""
Multiply this factor with another factor.
:param factor: the factor to multiply with
:return: the resulting factor
:rtype: NonLinearGaussianMixture
"""
if isinstance(factor, GaussianMixture):
gm_factor = factor
elif isinstance(factor, Gaussian):
gm_factor = GaussianMixture([Gaussian])
else:
raise NotImplementedError()
# TODO: Generalise the Gaussian.split_gaussian function to more than one dimensional cases and remove the
# limitation here
if self.split_singles_before_absorb and len(gm_factor.var_names) == 1:
if len(gm_factor.components) == 1:
gm_factor = gm_factor.components[0]._split_gaussian()
new_nlgs = []
for gauss in gm_factor.components:
for nlg in self.nlgs:
new_nlgs.append(nlg.multiply(gauss))
return NonLinearGaussianMixture(new_nlgs)
def test_moment_match_to_single_gaussian(self):
"""
Test that the moment matching function returns a single Gaussian with the correct parameters.
"""
# TODO: add better test, with different means, here.
gaussian_ab_5 = Gaussian(
cov=[[2, 1], [1, 2]], mean=[0, 0], log_weight=np.log(0.5), var_names=["a", "b"]
)
gaussian_ab_6 = Gaussian(
cov=[[6, 3], [3, 6]], mean=[0, 0], log_weight=np.log(0.5), var_names=["a", "b"]
)
gaussian_mixture = GaussianMixture([gaussian_ab_5, gaussian_ab_6])
actual_gaussian = gaussian_mixture.moment_match_to_single_gaussian()
expected_gaussian = Gaussian(
cov=[[4, 2], [2, 4]], mean=[0, 0], log_weight=np.log(1.0), var_names=["a", "b"]
)
self.assertTrue(actual_gaussian.equals(expected_gaussian))
def test_equals_false_ncomps(self):
"""
Test that the equals function returns false for a GaussianMixture with a different number of components.
"""
gm3 = get_random_gaussian_mixture(num_components=3)
gm4_components = gm3.copy().components + [gm3.components[0].copy()]
gm4 = GaussianMixture(gm4_components)
self.assertFalse(gm3.equals(gm4))
def test_marginalise(self):
"""
Test that the marginalize function results in the correct marginal components.
"""
expected_marginal_components = [
self.gaussian_ab_1.marginalize(vrs="a", keep=False),
self.gaussian_ab_2.marginalize(vrs="a", keep=False),
]
expected_gm = GaussianMixture(expected_marginal_components)
actual_gm = self.gaussian_mixture_ab_12.marginalize(vrs="a", keep=False)
self.assertTrue(actual_gm.equals(expected_gm))
def test_multiply_guassian(self):
"""
Test that the multiply function results in the correct components.
"""
expected_product_components = [
self.gaussian_ab_1.multiply(self.gaussian_ab_3),
self.gaussian_ab_2.multiply(self.gaussian_ab_3),
]
expected_gm = GaussianMixture(expected_product_components)
actual_gm = self.gaussian_mixture_ab_12.multiply(self.gaussian_ab_3)
self.assertTrue(actual_gm.equals(expected_gm))
def get_random_gaussian_mixture(cov_coeff=1.0, mean_coeff=1.0, num_components=3, seed=0):
"""
A test helper function that generates random Gaussian factors.
:param n: the number of components.
:param cov_coeff: The scale coefficient for the uniform distribution that the variance parameter is drawn from.
:param mean_coeff: The scale coefficient for the uniform distribution that the mean parameter is drawn from.
:return: a random Gaussian factor
"""
assert seed >= 0
random_gaussians = []
for i in range(num_components):
comp_seed = (seed + 1) * i
random_gaussians.append(get_random_gaussian(cov_coeff, mean_coeff, seed=comp_seed))
return GaussianMixture(random_gaussians)
def setUp(self):
"""
Run before every test.
"""
self.gaussian_ab_1 = Gaussian(cov=np.eye(2), mean=[1, 1], log_weight=1.0, var_names=["a", "b"])
self.gaussian_ab_2 = Gaussian(cov=np.eye(2), mean=[2, 2], log_weight=2.0, var_names=["a", "b"])
self.gaussian_ab_3 = Gaussian(cov=np.eye(2), mean=[3, 3], log_weight=3.0, var_names=["a", "b"])
self.gaussian_ab_4 = Gaussian(cov=np.eye(2), mean=[3, 3], log_weight=3.0, var_names=["a", "b"])
self.gaussian_cd_1 = Gaussian(cov=np.eye(2), mean=[1, 1], log_weight=1.0, var_names=["c", "d"])
self.gaussian_mixture_ab_34 = GaussianMixture(factors=[self.gaussian_ab_3, self.gaussian_ab_4])
self.gaussian_mixture_ab_12 = GaussianMixture(factors=[self.gaussian_ab_1, self.gaussian_ab_2])
self.gaussian_mixture_ab_123 = GaussianMixture(
factors=[self.gaussian_ab_1, self.gaussian_ab_2, self.gaussian_ab_3]
)
self.gaussian_mixture_ab_1_copy = GaussianMixture(factors=[self.gaussian_ab_1, self.gaussian_ab_2])
def joint_distribution(self):
gaussian_joints = []
for nlg in self.nlgs:
gaussian_joints.append(nlg.joint_distribution)
return GaussianMixture(gaussian_joints)
def test_invalid_construction(self):
"""
Test that constructor fails with inconsistent scope Gaussian.
"""
with self.assertRaises(ValueError):
GaussianMixture([self.gaussian_ab_1, self.gaussian_cd_1])
class TestGaussianMixture(unittest.TestCase):
"""
Tests for the GaussianMixture class
"""
def setUp(self):
"""
Run before every test.
"""
self.gaussian_ab_1 = Gaussian(cov=np.eye(2), mean=[1, 1], log_weight=1.0, var_names=["a", "b"])
self.gaussian_ab_2 = Gaussian(cov=np.eye(2), mean=[2, 2], log_weight=2.0, var_names=["a", "b"])
self.gaussian_ab_3 = Gaussian(cov=np.eye(2), mean=[3, 3], log_weight=3.0, var_names=["a", "b"])
self.gaussian_ab_4 = Gaussian(cov=np.eye(2), mean=[3, 3], log_weight=3.0, var_names=["a", "b"])
self.gaussian_cd_1 = Gaussian(cov=np.eye(2), mean=[1, 1], log_weight=1.0, var_names=["c", "d"])
self.gaussian_mixture_ab_34 = GaussianMixture(factors=[self.gaussian_ab_3, self.gaussian_ab_4])
self.gaussian_mixture_ab_12 = GaussianMixture(factors=[self.gaussian_ab_1, self.gaussian_ab_2])
self.gaussian_mixture_ab_123 = GaussianMixture(
factors=[self.gaussian_ab_1, self.gaussian_ab_2, self.gaussian_ab_3]
)
self.gaussian_mixture_ab_1_copy = GaussianMixture(factors=[self.gaussian_ab_1, self.gaussian_ab_2])
def test_invalid_construction(self):
"""
Test that constructor fails with inconsistent scope Gaussian.
"""
with self.assertRaises(ValueError):
GaussianMixture([self.gaussian_ab_1, self.gaussian_cd_1])
def test_equals_not_gm_fails(self):
"""
Test that the equals function returns false when the factor comparing with is not a GaussianMixture.
"""
not_a_gm_factor = mockito.mock()
gmix = get_random_gaussian_mixture()
with self.assertRaises(TypeError):
gmix.equals(not_a_gm_factor)
def test_equals_true(self):
"""
Test that the equals function returns true for identical Gaussian mixtures.
"""
self.assertTrue(self.gaussian_mixture_ab_12.equals(self.gaussian_mixture_ab_1_copy))
def test_equals_false(self):
"""
Test that the equals function returns false for different Gaussian mixtures.
"""
self.assertFalse(self.gaussian_mixture_ab_12.equals(self.gaussian_mixture_ab_34))
def test_equals_false_ncomps(self):
"""
Test that the equals function returns false for a GaussianMixture with a different number of components.
"""
gm3 = get_random_gaussian_mixture(num_components=3)
gm4_components = gm3.copy().components + [gm3.components[0].copy()]
gm4 = GaussianMixture(gm4_components)
self.assertFalse(gm3.equals(gm4))
def test_multiply_gm(self):
"""
Test that the multiply function results in the correct components.
"""
expected_product_components = [
self.gaussian_ab_1.multiply(self.gaussian_ab_3),
self.gaussian_ab_1.multiply(self.gaussian_ab_4),
self.gaussian_ab_2.multiply(self.gaussian_ab_3),
self.gaussian_ab_2.multiply(self.gaussian_ab_4),
]
expected_gm = GaussianMixture(expected_product_components)
actual_gm = self.gaussian_mixture_ab_12.multiply(self.gaussian_mixture_ab_34)
self.assertTrue(actual_gm.equals(expected_gm))
def test_multiply_guassian(self):
"""
Test that the multiply function results in the correct components.
"""
expected_product_components = [
self.gaussian_ab_1.multiply(self.gaussian_ab_3),
self.gaussian_ab_2.multiply(self.gaussian_ab_3),
]
expected_gm = GaussianMixture(expected_product_components)
actual_gm = self.gaussian_mixture_ab_12.multiply(self.gaussian_ab_3)
self.assertTrue(actual_gm.equals(expected_gm))
def test_multiply_invalid_type_fails(self):
"""
Test that the multiply function fails with invalid type.
"""
not_a_gm = mockito.mock()
gma = get_random_gaussian_mixture()
with self.assertRaises(TypeError):
gma.multiply(not_a_gm)
def test_marginalise(self):
"""
Test that the marginalize function results in the correct marginal components.
"""
expected_marginal_components = [
self.gaussian_ab_1.marginalize(vrs="a", keep=False),
self.gaussian_ab_2.marginalize(vrs="a", keep=False),
]
expected_gm = GaussianMixture(expected_marginal_components)
actual_gm = self.gaussian_mixture_ab_12.marginalize(vrs="a", keep=False)
self.assertTrue(actual_gm.equals(expected_gm))
def test_normalize(self):
"""
Test that the normalize function results in a a mixture with a weight of 1.0.
"""
normed_gm = self.gaussian_mixture_ab_123.normalize()
log_weight = normed_gm.get_log_weight()
actual_weight = np.exp(log_weight)
self.assertAlmostEqual(actual_weight, 1.0)
def test_moment_match_to_single_gaussian(self):
"""
Test that the moment matching function returns a single Gaussian with the correct parameters.
"""
# TODO: add better test, with different means, here.
gaussian_ab_5 = Gaussian(
cov=[[2, 1], [1, 2]], mean=[0, 0], log_weight=np.log(0.5), var_names=["a", "b"]
)
gaussian_ab_6 = Gaussian(
cov=[[6, 3], [3, 6]], mean=[0, 0], log_weight=np.log(0.5), var_names=["a", "b"]
)
gaussian_mixture = GaussianMixture([gaussian_ab_5, gaussian_ab_6])
actual_gaussian = gaussian_mixture.moment_match_to_single_gaussian()
expected_gaussian = Gaussian(
cov=[[4, 2], [2, 4]], mean=[0, 0], log_weight=np.log(1.0), var_names=["a", "b"]
)
self.assertTrue(actual_gaussian.equals(expected_gaussian))
def test_cancel_method_1(self):
"""
Test that the _gm_division_m2 function returns
"""
# TODO: improve this test.
gaussian_mixture_1 = get_random_gaussian_mixture(cov_coeff=10, seed=1)
gaussian_mixture_2 = get_random_gaussian_mixture(cov_coeff=10, seed=2)
gaussian_mixture_12 = gaussian_mixture_1.multiply(gaussian_mixture_2)
gaussian_mixture_12.cancel_method = 1
gaussian_mixture_quotient_approximation = gaussian_mixture_12.divide(gaussian_mixture_2)
self.assertEqual(gaussian_mixture_quotient_approximation.num_components, 1)
def test_cancel_method_2(self):
"""
Test that the _gm_division_m2 function returns.
"""
# TODO: improve this test.
gaussian_mixture_1 = get_random_gaussian_mixture(cov_coeff=10, seed=1)
gaussian_mixture_2 = get_random_gaussian_mixture(cov_coeff=10, seed=2)
gaussian_mixture_12 = gaussian_mixture_1.multiply(gaussian_mixture_2)
gaussian_mixture_12.cancel_method = 2
gaussian_mixture_quotient_approximation = gaussian_mixture_12.divide(gaussian_mixture_2)
self.assertEqual(gaussian_mixture_quotient_approximation.num_components, 9)