def test_class_init(self):
phi = CanonicalDistribution(['x1', ('y', 'z'), 'x3'],
np.array([[1.1, -1, 0], [-1, 4, -2],
[0, -2, 4]]),
np.array([[1], [4.7], [-1]]), -2)
self.assertEqual(phi.variables, ['x1', ('y', 'z'), 'x3'])
np_test.assert_array_equal(
phi.K,
np.array([[1.1, -1, 0], [-1, 4, -2], [0, -2, 4]], dtype=float))
np_test.assert_array_equal(phi.h,
np.array([[1], [4.7], [-1]], dtype=float))
self.assertEqual(phi.g, -2)
phi = CanonicalDistribution(['x1', ('y', 'z'), 'x3'],
np.array([[1.1, -1, 0], [-1, 4, -2],
[0, -2, 4]]),
np.array([1, 4.7, -1]), -2)
self.assertEqual(phi.variables, ['x1', ('y', 'z'), 'x3'])
np_test.assert_array_equal(
phi.K,
np.array([[1.1, -1, 0], [-1, 4, -2], [0, -2, 4]], dtype=float))
np_test.assert_array_equal(phi.h,
np.array([[1], [4.7], [-1]], dtype=float))
self.assertEqual(phi.g, -2)
phi = CanonicalDistribution(['x'], [[1]], [0], 1)
self.assertEqual(phi.variables, ['x'])
np_test.assert_array_equal(phi.K, np.array([[1]], dtype=float))
np_test.assert_array_equal(phi.h, np.array([[0]], dtype=float))
self.assertEqual(phi.g, 1)
def setUp(self):
self.phi1 = CanonicalDistribution(['x1', 'x2', 'x3'],
np.array([[1.1, -1, 0], [-1, 4, -2], [0, -2, 4]]),
np.array([[1], [4.7], [-1]]), -2)
self.phi2 = CanonicalDistribution(['x'], [[1]], [0], 1)
self.phi3 = self.phi1.copy()
self.gauss_phi1 = JGD(['x1', 'x2', 'x3'],
np.array([[3.13043478], [2.44347826], [0.97173913]]),
np.array([[1.30434783, 0.43478261, 0.2173913],
[0.43478261, 0.47826087, 0.23913043],
[0.2173913, 0.23913043, 0.36956522]], dtype=float))
self.gauss_phi2 = JGD(['x'], np.array([0]), np.array([[1]]))
def setUp(self):
self.phi1 = CanonicalDistribution(['x1', 'x2', 'x3'],
np.array([[1.1, -1, 0], [-1, 4, -2],
[0, -2, 4]]),
np.array([[1], [4.7], [-1]]), -2)
self.phi2 = CanonicalDistribution(['x'], [[1]], [0], 1)
self.phi3 = self.phi1.copy()
self.gauss_phi1 = JGD(['x1', 'x2', 'x3'],
np.array([[3.13043478], [2.44347826],
[0.97173913]]),
np.array([[1.30434783, 0.43478261, 0.2173913],
[0.43478261, 0.47826087, 0.23913043],
[0.2173913, 0.23913043, 0.36956522]],
dtype=float))
self.gauss_phi2 = JGD(['x'], np.array([0]), np.array([[1]]))
def to_canonical_factor(self):
u"""
Returns an equivalent CanonicalDistribution object.
The formulas for calculating the cannonical factor parameters
for N(μ; Σ) = C(K; h; g) are as follows -
K = sigma^(-1)
h = sigma^(-1) * mu
g = -(0.5) * mu.T * sigma^(-1) * mu -
log((2*pi)^(n/2) * det(sigma)^(0.5))
where,
K,h,g are the canonical factor parameters
sigma is the covariance_matrix of the distribution,
mu is the mean_vector of the distribution,
mu.T is the transpose of the matrix mu,
and det(sigma) is the determinant of the matrix sigma.
Example
-------
>>> import numpy as np
>>> from pgmpy.factors.distributions import GaussianDistribution as GD
>>> dis = GD(variables=['x1', 'x2', 'x3'],
... mean=[1, -3, 4],
... cov=[[4, 2, -2],
... [2, 5, -5],
... [-2, -5, 8]])
>>> phi = dis.to_canonical_factor()
>>> phi.variables
['x1', 'x2', 'x3']
>>> phi.K
array([[0.3125, -0.125, 0.],
[-0.125, 0.5833, 0.333],
[ 0., 0.333, 0.333]])
>>> phi.h
array([[ 0.6875],
[-0.54166],
[ 0.33333]]))
>>> phi.g
-6.51533
"""
from pgmpy.factors.continuous import CanonicalDistribution
mu = self.mean
sigma = self.covariance
K = self.precision_matrix
h = np.dot(K, mu)
g = -(0.5) * np.dot(mu.T, h)[0, 0] - np.log(
np.power(2 * np.pi,
len(self.variables) / 2) *
np.power(abs(np.linalg.det(sigma)), 0.5))
return CanonicalDistribution(self.variables, K, h, g)
def test_operate(self):
phi1 = self.phi1 * CanonicalDistribution(
['x2', 'x4'], [[1, 2], [3, 4]], [0, 4.56], -6.78)
phi2 = self.phi1 / CanonicalDistribution(
['x2', 'x3'], [[1, 2], [3, 4]], [0, 4.56], -6.78)
self.assertEqual(phi1.variables, ['x1', 'x2', 'x3', 'x4'])
np_test.assert_almost_equal(
phi1.K,
np.array([[1.1, -1.0, 0.0, 0.0], [-1.0, 5.0, -2.0, 2.0],
[0.0, -2.0, 4.0, 0.0], [0.0, 3.0, 0.0, 4.0]]))
np_test.assert_almost_equal(phi1.h,
np.array([[1.0], [4.7], [-1.0], [4.56]]))
np_test.assert_almost_equal(phi1.g, -8.78)
self.assertEqual(phi2.variables, ['x1', 'x2', 'x3'])
np_test.assert_almost_equal(
phi2.K,
np.array([[1.1, -1.0, 0.0], [-1.0, 3.0, -4.0], [0.0, -5.0, 0.0]]))
np_test.assert_almost_equal(phi2.h, np.array([[1.0], [4.7], [-5.56]]))
np_test.assert_almost_equal(phi2.g, 4.78)
class TestJGDMethods(unittest.TestCase):
def setUp(self):
self.phi1 = CanonicalDistribution(['x1', 'x2', 'x3'],
np.array([[1.1, -1, 0], [-1, 4, -2], [0, -2, 4]]),
np.array([[1], [4.7], [-1]]), -2)
self.phi2 = CanonicalDistribution(['x'], [[1]], [0], 1)
self.phi3 = self.phi1.copy()
self.gauss_phi1 = JGD(['x1', 'x2', 'x3'],
np.array([[3.13043478], [2.44347826], [0.97173913]]),
np.array([[1.30434783, 0.43478261, 0.2173913],
[0.43478261, 0.47826087, 0.23913043],
[0.2173913, 0.23913043, 0.36956522]], dtype=float))
self.gauss_phi2 = JGD(['x'], np.array([0]), np.array([[1]]))
def test_assignment(self):
np_test.assert_almost_equal(self.phi1.assignment(1, 2, 3), 0.0007848640)
np_test.assert_almost_equal(self.phi2.assignment(1.2), 1.323129812337)
def test_to_joint_gaussian(self):
jgd1 = self.phi1.to_joint_gaussian()
jgd2 = self.phi2.to_joint_gaussian()
self.assertEqual(jgd1.variables, self.gauss_phi1.variables)
np_test.assert_almost_equal(jgd1.covariance, self.gauss_phi1.covariance)
np_test.assert_almost_equal(jgd1.mean, self.gauss_phi1.mean)
self.assertEqual(jgd2.variables, self.gauss_phi2.variables)
np_test.assert_almost_equal(jgd2.covariance, self.gauss_phi2.covariance)
np_test.assert_almost_equal(jgd2.mean, self.gauss_phi2.mean)
def test_reduce(self):
phi = self.phi1.reduce([('x1', 7)], inplace=False)
self.assertEqual(phi.variables, ['x2', 'x3'])
np_test.assert_almost_equal(phi.K, np.array([[4.0, -2.0], [-2.0, 4.0]]))
np_test.assert_almost_equal(phi.h, np.array([[11.7], [-1.0]]))
np_test.assert_almost_equal(phi.g, -21.95)
phi = self.phi1.reduce([('x1', 4), ('x2', 1.23)], inplace=False)
self.assertEqual(phi.variables, ['x3'])
np_test.assert_almost_equal(phi.K, np.array([[4.0]]))
np_test.assert_almost_equal(phi.h, np.array([[1.46]]))
np_test.assert_almost_equal(phi.g, 0.8752)
self.phi1.reduce([('x1', 7)])
self.assertEqual(self.phi1.variables, ['x2', 'x3'])
np_test.assert_almost_equal(self.phi1.K, np.array([[4.0, -2.0], [-2.0, 4.0]]))
np_test.assert_almost_equal(self.phi1.h, np.array([[11.7], [-1.0]]))
np_test.assert_almost_equal(self.phi1.g, -21.95)
self.phi1 = self.phi3.copy()
self.phi1.reduce([('x1', 4), ('x2', 1.23)])
self.assertEqual(self.phi1.variables, ['x3'])
np_test.assert_almost_equal(self.phi1.K, np.array([[4.0]]))
np_test.assert_almost_equal(self.phi1.h, np.array([[1.46]]))
np_test.assert_almost_equal(self.phi1.g, 0.8752)
self.phi1 = self.phi3.copy()
self.phi1.reduce([('x2', 1.23), ('x1', 4)])
self.assertEqual(self.phi1.variables, ['x3'])
np_test.assert_almost_equal(self.phi1.K, np.array([[4.0]]))
np_test.assert_almost_equal(self.phi1.h, np.array([[1.46]]))
np_test.assert_almost_equal(self.phi1.g, 0.8752)
def test_marginalize(self):
phi = self.phi1.marginalize(['x1'], inplace=False)
self.assertEqual(phi.variables, ['x2', 'x3'])
np_test.assert_almost_equal(phi.K, np.array([[3.090909, -2.0], [-2.0, 4.0]]))
np_test.assert_almost_equal(phi.h, np.array([[5.6090909], [-1.0]]))
np_test.assert_almost_equal(phi.g, -0.5787165566)
phi = self.phi1.marginalize(['x1', 'x2'], inplace=False)
self.assertEqual(phi.variables, ['x3'])
np_test.assert_almost_equal(phi.K, np.array([[2.70588235]]))
np_test.assert_almost_equal(phi.h, np.array([[2.62941176]]))
np_test.assert_almost_equal(phi.g, 39.25598935059)
self.phi1.marginalize(['x1'])
self.assertEqual(self.phi1.variables, ['x2', 'x3'])
np_test.assert_almost_equal(self.phi1.K, np.array([[3.090909, -2.0], [-2.0, 4.0]]))
np_test.assert_almost_equal(self.phi1.h, np.array([[5.6090909], [-1.0]]))
np_test.assert_almost_equal(self.phi1.g, -0.5787165566)
self.phi1 = self.phi3
self.phi1.marginalize(['x1', 'x2'])
self.assertEqual(self.phi1.variables, ['x3'])
np_test.assert_almost_equal(self.phi1.K, np.array([[2.70588235]]))
np_test.assert_almost_equal(self.phi1.h, np.array([[2.62941176]]))
np_test.assert_almost_equal(self.phi1.g, 39.25598935059)
self.phi1 = self.phi3
def test_operate(self):
phi1 = self.phi1 * CanonicalDistribution(['x2', 'x4'], [[1, 2], [3, 4]], [0, 4.56], -6.78)
phi2 = self.phi1 / CanonicalDistribution(['x2', 'x3'], [[1, 2], [3, 4]], [0, 4.56], -6.78)
self.assertEqual(phi1.variables, ['x1', 'x2', 'x3', 'x4'])
np_test.assert_almost_equal(phi1.K, np.array([[1.1, -1.0, 0.0, 0.0],
[-1.0, 5.0, -2.0, 2.0],
[0.0, -2.0, 4.0, 0.0],
[0.0, 3.0, 0.0, 4.0]]))
np_test.assert_almost_equal(phi1.h, np.array([[1.0],
[4.7],
[-1.0],
[4.56]]))
np_test.assert_almost_equal(phi1.g, -8.78)
self.assertEqual(phi2.variables, ['x1', 'x2', 'x3'])
np_test.assert_almost_equal(phi2.K, np.array([[1.1, -1.0, 0.0],
[-1.0, 3.0, -4.0],
[0.0, -5.0, 0.0]]))
np_test.assert_almost_equal(phi2.h, np.array([[1.0],
[4.7],
[-5.56]]))
np_test.assert_almost_equal(phi2.g, 4.78)
def test_copy(self):
copy_phi1 = self.phi1.copy()
self.assertEqual(copy_phi1.variables, self.phi1.variables)
np_test.assert_array_equal(copy_phi1.K, self.phi1.K)
np_test.assert_array_equal(copy_phi1.h, self.phi1.h)
np_test.assert_array_equal(copy_phi1.g, self.phi1.g)
copy_phi1.marginalize(['x1'])
self.assertEqual(self.phi1.variables, ['x1', 'x2', 'x3'])
np_test.assert_array_equal(self.phi1.K, np.array([[1.1, -1, 0], [-1, 4, -2], [0, -2, 4]], dtype=float))
np_test.assert_array_equal(self.phi1.h, np.array([[1], [4.7], [-1]], dtype=float))
self.assertEqual(self.phi1.g, -2)
self.phi1.marginalize(['x2'])
self.assertEqual(copy_phi1.variables, ['x2', 'x3'])
np_test.assert_almost_equal(copy_phi1.K, np.array([[3.090909, -2.0], [-2.0, 4.0]]))
np_test.assert_almost_equal(copy_phi1.h, np.array([[5.6090909], [-1.0]]))
np_test.assert_almost_equal(copy_phi1.g, -0.5787165566)
self.phi1 = self.phi3
def tearDown(self):
del self.phi1
del self.phi2
del self.phi3
del self.gauss_phi1
del self.gauss_phi2
class TestJGDMethods(unittest.TestCase):
def setUp(self):
self.phi1 = CanonicalDistribution(['x1', 'x2', 'x3'],
np.array([[1.1, -1, 0], [-1, 4, -2],
[0, -2, 4]]),
np.array([[1], [4.7], [-1]]), -2)
self.phi2 = CanonicalDistribution(['x'], [[1]], [0], 1)
self.phi3 = self.phi1.copy()
self.gauss_phi1 = JGD(['x1', 'x2', 'x3'],
np.array([[3.13043478], [2.44347826],
[0.97173913]]),
np.array([[1.30434783, 0.43478261, 0.2173913],
[0.43478261, 0.47826087, 0.23913043],
[0.2173913, 0.23913043, 0.36956522]],
dtype=float))
self.gauss_phi2 = JGD(['x'], np.array([0]), np.array([[1]]))
def test_assignment(self):
np_test.assert_almost_equal(self.phi1.assignment(1, 2, 3),
0.0007848640)
np_test.assert_almost_equal(self.phi2.assignment(1.2), 1.323129812337)
def test_to_joint_gaussian(self):
jgd1 = self.phi1.to_joint_gaussian()
jgd2 = self.phi2.to_joint_gaussian()
self.assertEqual(jgd1.variables, self.gauss_phi1.variables)
np_test.assert_almost_equal(jgd1.covariance,
self.gauss_phi1.covariance)
np_test.assert_almost_equal(jgd1.mean, self.gauss_phi1.mean)
self.assertEqual(jgd2.variables, self.gauss_phi2.variables)
np_test.assert_almost_equal(jgd2.covariance,
self.gauss_phi2.covariance)
np_test.assert_almost_equal(jgd2.mean, self.gauss_phi2.mean)
def test_reduce(self):
phi = self.phi1.reduce([('x1', 7)], inplace=False)
self.assertEqual(phi.variables, ['x2', 'x3'])
np_test.assert_almost_equal(phi.K, np.array([[4.0, -2.0], [-2.0,
4.0]]))
np_test.assert_almost_equal(phi.h, np.array([[11.7], [-1.0]]))
np_test.assert_almost_equal(phi.g, -21.95)
phi = self.phi1.reduce([('x1', 4), ('x2', 1.23)], inplace=False)
self.assertEqual(phi.variables, ['x3'])
np_test.assert_almost_equal(phi.K, np.array([[4.0]]))
np_test.assert_almost_equal(phi.h, np.array([[1.46]]))
np_test.assert_almost_equal(phi.g, 0.8752)
self.phi1.reduce([('x1', 7)])
self.assertEqual(self.phi1.variables, ['x2', 'x3'])
np_test.assert_almost_equal(self.phi1.K,
np.array([[4.0, -2.0], [-2.0, 4.0]]))
np_test.assert_almost_equal(self.phi1.h, np.array([[11.7], [-1.0]]))
np_test.assert_almost_equal(self.phi1.g, -21.95)
self.phi1 = self.phi3.copy()
self.phi1.reduce([('x1', 4), ('x2', 1.23)])
self.assertEqual(self.phi1.variables, ['x3'])
np_test.assert_almost_equal(self.phi1.K, np.array([[4.0]]))
np_test.assert_almost_equal(self.phi1.h, np.array([[1.46]]))
np_test.assert_almost_equal(self.phi1.g, 0.8752)
self.phi1 = self.phi3.copy()
self.phi1.reduce([('x2', 1.23), ('x1', 4)])
self.assertEqual(self.phi1.variables, ['x3'])
np_test.assert_almost_equal(self.phi1.K, np.array([[4.0]]))
np_test.assert_almost_equal(self.phi1.h, np.array([[1.46]]))
np_test.assert_almost_equal(self.phi1.g, 0.8752)
def test_marginalize(self):
phi = self.phi1.marginalize(['x1'], inplace=False)
self.assertEqual(phi.variables, ['x2', 'x3'])
np_test.assert_almost_equal(phi.K,
np.array([[3.090909, -2.0], [-2.0, 4.0]]))
np_test.assert_almost_equal(phi.h, np.array([[5.6090909], [-1.0]]))
np_test.assert_almost_equal(phi.g, -0.5787165566)
phi = self.phi1.marginalize(['x1', 'x2'], inplace=False)
self.assertEqual(phi.variables, ['x3'])
np_test.assert_almost_equal(phi.K, np.array([[2.70588235]]))
np_test.assert_almost_equal(phi.h, np.array([[2.62941176]]))
np_test.assert_almost_equal(phi.g, 39.25598935059)
self.phi1.marginalize(['x1'])
self.assertEqual(self.phi1.variables, ['x2', 'x3'])
np_test.assert_almost_equal(self.phi1.K,
np.array([[3.090909, -2.0], [-2.0, 4.0]]))
np_test.assert_almost_equal(self.phi1.h, np.array([[5.6090909],
[-1.0]]))
np_test.assert_almost_equal(self.phi1.g, -0.5787165566)
self.phi1 = self.phi3
self.phi1.marginalize(['x1', 'x2'])
self.assertEqual(self.phi1.variables, ['x3'])
np_test.assert_almost_equal(self.phi1.K, np.array([[2.70588235]]))
np_test.assert_almost_equal(self.phi1.h, np.array([[2.62941176]]))
np_test.assert_almost_equal(self.phi1.g, 39.25598935059)
self.phi1 = self.phi3
def test_operate(self):
phi1 = self.phi1 * CanonicalDistribution(
['x2', 'x4'], [[1, 2], [3, 4]], [0, 4.56], -6.78)
phi2 = self.phi1 / CanonicalDistribution(
['x2', 'x3'], [[1, 2], [3, 4]], [0, 4.56], -6.78)
self.assertEqual(phi1.variables, ['x1', 'x2', 'x3', 'x4'])
np_test.assert_almost_equal(
phi1.K,
np.array([[1.1, -1.0, 0.0, 0.0], [-1.0, 5.0, -2.0, 2.0],
[0.0, -2.0, 4.0, 0.0], [0.0, 3.0, 0.0, 4.0]]))
np_test.assert_almost_equal(phi1.h,
np.array([[1.0], [4.7], [-1.0], [4.56]]))
np_test.assert_almost_equal(phi1.g, -8.78)
self.assertEqual(phi2.variables, ['x1', 'x2', 'x3'])
np_test.assert_almost_equal(
phi2.K,
np.array([[1.1, -1.0, 0.0], [-1.0, 3.0, -4.0], [0.0, -5.0, 0.0]]))
np_test.assert_almost_equal(phi2.h, np.array([[1.0], [4.7], [-5.56]]))
np_test.assert_almost_equal(phi2.g, 4.78)
def test_copy(self):
copy_phi1 = self.phi1.copy()
self.assertEqual(copy_phi1.variables, self.phi1.variables)
np_test.assert_array_equal(copy_phi1.K, self.phi1.K)
np_test.assert_array_equal(copy_phi1.h, self.phi1.h)
np_test.assert_array_equal(copy_phi1.g, self.phi1.g)
copy_phi1.marginalize(['x1'])
self.assertEqual(self.phi1.variables, ['x1', 'x2', 'x3'])
np_test.assert_array_equal(
self.phi1.K,
np.array([[1.1, -1, 0], [-1, 4, -2], [0, -2, 4]], dtype=float))
np_test.assert_array_equal(self.phi1.h,
np.array([[1], [4.7], [-1]], dtype=float))
self.assertEqual(self.phi1.g, -2)
self.phi1.marginalize(['x2'])
self.assertEqual(copy_phi1.variables, ['x2', 'x3'])
np_test.assert_almost_equal(copy_phi1.K,
np.array([[3.090909, -2.0], [-2.0, 4.0]]))
np_test.assert_almost_equal(copy_phi1.h, np.array([[5.6090909],
[-1.0]]))
np_test.assert_almost_equal(copy_phi1.g, -0.5787165566)
self.phi1 = self.phi3
def tearDown(self):
del self.phi1
del self.phi2
del self.phi3
del self.gauss_phi1
del self.gauss_phi2
# $$
# h = Σ^{-1}μ
# $$
# $$
# g = -0.5μ^TΣ^{-1}μ - log((2π)^{n/2}|Σ|^{1/2}
# $$
# Similar to the JointGaussainDistribution class, the CanonicalFactor class is also derived from the ContinuousFactor class but with its own implementations of the methods required for the sum-product algorithms that are much more efficient than its parent class methods. Let us have a look at the API of a few methods in this class.
# In[18]:
from pgmpy.factors.continuous import CanonicalDistribution
phi1 = CanonicalDistribution(['x1', 'x2', 'x3'],
np.array([[1, -1, 0], [-1, 4, -2], [0, -2, 4]]),
np.array([[1], [4], [-1]]), -2)
phi2 = CanonicalDistribution(['x1', 'x2'], np.array([[3, -2], [-2, 4]]),
np.array([[5], [-1]]), 1)
phi3 = phi1 * phi2
phi3.variables
# In[19]:
phi3.h
# In[20]: