def test_message_to_parent(self):
"""
Test the message to parents of Concatenate node.
"""
# Two parents without shapes
X1 = GaussianARD(0, 1, plates=(2,), shape=())
X2 = GaussianARD(0, 1, plates=(3,), shape=())
Z = Concatenate(X1, X2)
Y = GaussianARD(Z, 1)
Y.observe(np.random.randn(*Y.get_shape(0)))
m1 = X1._message_from_children()
m2 = X2._message_from_children()
m = Z._message_from_children()
self.assertAllClose((m[0]*np.ones((5,)))[:2],
m1[0]*np.ones((2,)))
self.assertAllClose((m[1]*np.ones((5,)))[:2],
m1[1]*np.ones((2,)))
self.assertAllClose((m[0]*np.ones((5,)))[2:],
m2[0]*np.ones((3,)))
self.assertAllClose((m[1]*np.ones((5,)))[2:],
m2[1]*np.ones((3,)))
# Two parents with shapes
with warnings.catch_warnings():
warnings.simplefilter("ignore", FutureWarning)
X1 = GaussianARD(0, 1, plates=(2,), shape=(4,6))
X2 = GaussianARD(0, 1, plates=(3,), shape=(4,6))
Z = Concatenate(X1, X2)
Y = GaussianARD(Z, 1)
Y.observe(np.random.randn(*Y.get_shape(0)))
m1 = X1._message_from_children()
m2 = X2._message_from_children()
m = Z._message_from_children()
self.assertAllClose((m[0]*np.ones((5,4,6)))[:2],
m1[0]*np.ones((2,4,6)))
self.assertAllClose((m[1]*np.ones((5,4,6,4,6)))[:2],
m1[1]*np.ones((2,4,6,4,6)))
self.assertAllClose((m[0]*np.ones((5,4,6)))[2:],
m2[0]*np.ones((3,4,6)))
self.assertAllClose((m[1]*np.ones((5,4,6,4,6)))[2:],
m2[1]*np.ones((3,4,6,4,6)))
# Two parents with non-default concatenation axis
X1 = GaussianARD(0, 1, plates=(2,4), shape=())
X2 = GaussianARD(0, 1, plates=(3,4), shape=())
Z = Concatenate(X1, X2, axis=-2)
Y = GaussianARD(Z, 1)
Y.observe(np.random.randn(*Y.get_shape(0)))
m1 = X1._message_from_children()
m2 = X2._message_from_children()
m = Z._message_from_children()
self.assertAllClose((m[0]*np.ones((5,4)))[:2],
m1[0]*np.ones((2,4)))
self.assertAllClose((m[1]*np.ones((5,4)))[:2],
m1[1]*np.ones((2,4)))
self.assertAllClose((m[0]*np.ones((5,4)))[2:],
m2[0]*np.ones((3,4)))
self.assertAllClose((m[1]*np.ones((5,4)))[2:],
m2[1]*np.ones((3,4)))
# Constant parent
X1 = np.random.randn(2,4,6)
X2 = GaussianARD(0, 1, plates=(3,), shape=(4,6))
Z = Concatenate(X1, X2)
Y = GaussianARD(Z, 1)
Y.observe(np.random.randn(*Y.get_shape(0)))
m1 = Z._message_to_parent(0)
m2 = X2._message_from_children()
m = Z._message_from_children()
self.assertAllClose((m[0]*np.ones((5,4,6)))[:2],
m1[0]*np.ones((2,4,6)))
self.assertAllClose((m[1]*np.ones((5,4,6,4,6)))[:2],
m1[1]*np.ones((2,4,6,4,6)))
self.assertAllClose((m[0]*np.ones((5,4,6)))[2:],
m2[0]*np.ones((3,4,6)))
self.assertAllClose((m[1]*np.ones((5,4,6,4,6)))[2:],
m2[1]*np.ones((3,4,6,4,6)))
pass
def test_message_to_parent(self):
"""
Test the message to parents of Concatenate node.
"""
# Two parents without shapes
X1 = GaussianARD(0, 1, plates=(2, ), shape=())
X2 = GaussianARD(0, 1, plates=(3, ), shape=())
Z = Concatenate(X1, X2)
Y = GaussianARD(Z, 1)
Y.observe(np.random.randn(*Y.get_shape(0)))
m1 = X1._message_from_children()
m2 = X2._message_from_children()
m = Z._message_from_children()
self.assertAllClose((m[0] * np.ones((5, )))[:2], m1[0] * np.ones(
(2, )))
self.assertAllClose((m[1] * np.ones((5, )))[:2], m1[1] * np.ones(
(2, )))
self.assertAllClose((m[0] * np.ones((5, )))[2:], m2[0] * np.ones(
(3, )))
self.assertAllClose((m[1] * np.ones((5, )))[2:], m2[1] * np.ones(
(3, )))
# Two parents with shapes
with warnings.catch_warnings():
warnings.simplefilter("ignore", FutureWarning)
X1 = GaussianARD(0, 1, plates=(2, ), shape=(4, 6))
X2 = GaussianARD(0, 1, plates=(3, ), shape=(4, 6))
Z = Concatenate(X1, X2)
Y = GaussianARD(Z, 1)
Y.observe(np.random.randn(*Y.get_shape(0)))
m1 = X1._message_from_children()
m2 = X2._message_from_children()
m = Z._message_from_children()
self.assertAllClose((m[0] * np.ones((5, 4, 6)))[:2],
m1[0] * np.ones((2, 4, 6)))
self.assertAllClose((m[1] * np.ones((5, 4, 6, 4, 6)))[:2],
m1[1] * np.ones((2, 4, 6, 4, 6)))
self.assertAllClose((m[0] * np.ones((5, 4, 6)))[2:],
m2[0] * np.ones((3, 4, 6)))
self.assertAllClose((m[1] * np.ones((5, 4, 6, 4, 6)))[2:],
m2[1] * np.ones((3, 4, 6, 4, 6)))
# Two parents with non-default concatenation axis
X1 = GaussianARD(0, 1, plates=(2, 4), shape=())
X2 = GaussianARD(0, 1, plates=(3, 4), shape=())
Z = Concatenate(X1, X2, axis=-2)
Y = GaussianARD(Z, 1)
Y.observe(np.random.randn(*Y.get_shape(0)))
m1 = X1._message_from_children()
m2 = X2._message_from_children()
m = Z._message_from_children()
self.assertAllClose((m[0] * np.ones((5, 4)))[:2], m1[0] * np.ones(
(2, 4)))
self.assertAllClose((m[1] * np.ones((5, 4)))[:2], m1[1] * np.ones(
(2, 4)))
self.assertAllClose((m[0] * np.ones((5, 4)))[2:], m2[0] * np.ones(
(3, 4)))
self.assertAllClose((m[1] * np.ones((5, 4)))[2:], m2[1] * np.ones(
(3, 4)))
# Constant parent
X1 = np.random.randn(2, 4, 6)
X2 = GaussianARD(0, 1, plates=(3, ), shape=(4, 6))
Z = Concatenate(X1, X2)
Y = GaussianARD(Z, 1)
Y.observe(np.random.randn(*Y.get_shape(0)))
m1 = Z._message_to_parent(0)
m2 = X2._message_from_children()
m = Z._message_from_children()
self.assertAllClose((m[0] * np.ones((5, 4, 6)))[:2],
m1[0] * np.ones((2, 4, 6)))
self.assertAllClose((m[1] * np.ones((5, 4, 6, 4, 6)))[:2],
m1[1] * np.ones((2, 4, 6, 4, 6)))
self.assertAllClose((m[0] * np.ones((5, 4, 6)))[2:],
m2[0] * np.ones((3, 4, 6)))
self.assertAllClose((m[1] * np.ones((5, 4, 6, 4, 6)))[2:],
m2[1] * np.ones((3, 4, 6, 4, 6)))
pass
def test_message_to_parent(self):
"""
Test the message to parents of Mixture node.
"""
K = 3
# Broadcasting the moments on the cluster axis
Mu = GaussianARD(2, 1, ndim=0, plates=(K, ))
(mu, mumu) = Mu._message_to_child()
Alpha = Gamma(3, 1, plates=(K, ))
(alpha, logalpha) = Alpha._message_to_child()
z = Categorical(np.ones(K) / K)
X = Mixture(z, GaussianARD, Mu, Alpha)
tau = 4
Y = GaussianARD(X, tau)
y = 5
Y.observe(y)
(x, xx) = X._message_to_child()
m = z._message_from_children()
self.assertAllClose(
m[0] * np.ones(K),
random.gaussian_logpdf(xx * alpha, x * alpha * mu, mumu * alpha,
logalpha, 0) * np.ones(K))
m = Mu._message_from_children()
self.assertAllClose(m[0], 1 / K * (alpha * x) * np.ones(3))
self.assertAllClose(m[1], -0.5 * 1 / K * alpha * np.ones(3))
# Some parameters do not have cluster plate axis
Mu = GaussianARD(2, 1, ndim=0, plates=(K, ))
(mu, mumu) = Mu._message_to_child()
Alpha = Gamma(3, 1) # Note: no cluster plate axis!
(alpha, logalpha) = Alpha._message_to_child()
z = Categorical(np.ones(K) / K)
X = Mixture(z, GaussianARD, Mu, Alpha)
tau = 4
Y = GaussianARD(X, tau)
y = 5
Y.observe(y)
(x, xx) = X._message_to_child()
m = z._message_from_children()
self.assertAllClose(
m[0] * np.ones(K),
random.gaussian_logpdf(xx * alpha, x * alpha * mu, mumu * alpha,
logalpha, 0) * np.ones(K))
m = Mu._message_from_children()
self.assertAllClose(m[0], 1 / K * (alpha * x) * np.ones(3))
self.assertAllClose(m[1], -0.5 * 1 / K * alpha * np.ones(3))
# Cluster assignments do not have as many plate axes as parameters.
M = 2
Mu = GaussianARD(2, 1, ndim=0, plates=(K, M))
(mu, mumu) = Mu._message_to_child()
Alpha = Gamma(3, 1, plates=(K, M))
(alpha, logalpha) = Alpha._message_to_child()
z = Categorical(np.ones(K) / K)
X = Mixture(z, GaussianARD, Mu, Alpha, cluster_plate=-2)
tau = 4
Y = GaussianARD(X, tau)
y = 5 * np.ones(M)
Y.observe(y)
(x, xx) = X._message_to_child()
m = z._message_from_children()
self.assertAllClose(
m[0] * np.ones(K),
np.sum(random.gaussian_logpdf(xx * alpha, x * alpha * mu,
mumu * alpha, logalpha, 0) * np.ones(
(K, M)),
axis=-1))
m = Mu._message_from_children()
self.assertAllClose(m[0] * np.ones((K, M)),
1 / K * (alpha * x) * np.ones((K, M)))
self.assertAllClose(m[1] * np.ones((K, M)),
-0.5 * 1 / K * alpha * np.ones((K, M)))
# Mixed distribution broadcasts g
# This tests for a found bug. The bug caused an error.
Z = Categorical([0.3, 0.5, 0.2])
X = Mixture(Z, Categorical, [[0.2, 0.8], [0.1, 0.9], [0.3, 0.7]])
m = Z._message_from_children()
pass
def test_message_to_parent_mu(self):
"""
Test that GaussianARD computes the message to the 1st parent correctly.
"""
# Check formula with uncertain parent alpha
mu = GaussianARD(0, 1)
alpha = Gamma(2, 1)
X = GaussianARD(mu, alpha)
X.observe(3)
(m0, m1) = mu._message_from_children()
#(m0, m1) = X._message_to_parent(0)
self.assertAllClose(m0, 2 * 3)
self.assertAllClose(m1, -0.5 * 2)
# Check formula with uncertain node
mu = GaussianARD(1, 1e10)
X = GaussianARD(mu, 2)
Y = GaussianARD(X, 1)
Y.observe(5)
X.update()
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0, 2 * 1 / (2 + 1) * (2 * 1 + 1 * 5))
self.assertAllClose(m1, -0.5 * 2)
# Check alpha larger than mu
mu = GaussianARD(np.zeros((2, 3)), 1e10, shape=(2, 3))
X = GaussianARD(mu, 2 * np.ones((3, 2, 3)))
X.observe(3 * np.ones((3, 2, 3)))
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0, 2 * 3 * 3 * np.ones((2, 3)))
self.assertAllClose(m1, -0.5 * 3 * 2 * misc.identity(2, 3))
# Check mu larger than alpha
mu = GaussianARD(np.zeros((3, 2, 3)), 1e10, shape=(3, 2, 3))
X = GaussianARD(mu, 2 * np.ones((2, 3)))
X.observe(3 * np.ones((3, 2, 3)))
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0, 2 * 3 * np.ones((3, 2, 3)))
self.assertAllClose(m1, -0.5 * 2 * misc.identity(3, 2, 3))
# Check node larger than mu and alpha
mu = GaussianARD(np.zeros((2, 3)), 1e10, shape=(2, 3))
X = GaussianARD(mu, 2 * np.ones((3, )), shape=(3, 2, 3))
X.observe(3 * np.ones((3, 2, 3)))
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0, 2 * 3 * 3 * np.ones((2, 3)))
self.assertAllClose(m1, -0.5 * 2 * 3 * misc.identity(2, 3))
# Check broadcasting of dimensions
mu = GaussianARD(np.zeros((2, 1)), 1e10, shape=(2, 1))
X = GaussianARD(mu, 2 * np.ones((2, 3)), shape=(2, 3))
X.observe(3 * np.ones((2, 3)))
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0, 2 * 3 * 3 * np.ones((2, 1)))
self.assertAllClose(m1, -0.5 * 2 * 3 * misc.identity(2, 1))
# Check plates for smaller mu than node
mu = GaussianARD(0, 1, shape=(3, ), plates=(4, 1, 1))
X = GaussianARD(mu, 2 * np.ones((3, )), shape=(2, 3), plates=(4, 5))
X.observe(3 * np.ones((4, 5, 2, 3)))
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0 * np.ones((4, 1, 1, 3)),
2 * 3 * 5 * 2 * np.ones((4, 1, 1, 3)))
self.assertAllClose(
m1 * np.ones((4, 1, 1, 3, 3)),
-0.5 * 2 * 5 * 2 * misc.identity(3) * np.ones((4, 1, 1, 3, 3)))
# Check mask
mu = GaussianARD(np.zeros((2, 1, 3)), 1e10, shape=(3, ))
X = GaussianARD(mu,
2 * np.ones((2, 4, 3)),
shape=(3, ),
plates=(
2,
4,
))
X.observe(3 * np.ones((2, 4, 3)),
mask=[[True, True, True, False], [False, True, False, True]])
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0, (2 * 3 * np.ones(
(2, 1, 3)) * np.array([[[3]], [[2]]])))
self.assertAllClose(m1, (-0.5 * 2 * misc.identity(3) * np.ones(
(2, 1, 1, 1)) * np.array([[[[3]]], [[[2]]]])))
# Check mask with different shapes
mu = GaussianARD(np.zeros((2, 1, 3)), 1e10, shape=())
X = GaussianARD(mu,
2 * np.ones((2, 4, 3)),
shape=(3, ),
plates=(
2,
4,
))
mask = np.array([[True, True, True, False], [False, True, False,
True]])
X.observe(3 * np.ones((2, 4, 3)), mask=mask)
(m0, m1) = mu._message_from_children()
self.assertAllClose(
m0, 2 * 3 * np.sum(
np.ones((2, 4, 3)) * mask[..., None], axis=-2, keepdims=True))
self.assertAllClose(m1, (-0.5 * 2 * np.sum(
np.ones((2, 4, 3)) * mask[..., None], axis=-2, keepdims=True)))
# Check non-ARD Gaussian child
mu = np.array([1, 2])
Mu = GaussianARD(mu, 1e10, shape=(2, ))
alpha = np.array([3, 4])
Lambda = np.array([[1, 0.5], [0.5, 1]])
X = GaussianARD(Mu, alpha)
Y = Gaussian(X, Lambda)
y = np.array([5, 6])
Y.observe(y)
X.update()
(m0, m1) = Mu._message_from_children()
mean = np.dot(np.linalg.inv(np.diag(alpha) + Lambda),
np.dot(np.diag(alpha), mu) + np.dot(Lambda, y))
self.assertAllClose(m0, np.dot(np.diag(alpha), mean))
self.assertAllClose(m1, -0.5 * np.diag(alpha))
# Check broadcasted variable axes
mu = GaussianARD(np.zeros(1), 1e10, shape=(1, ))
X = GaussianARD(mu, 2, shape=(3, ))
X.observe(3 * np.ones(3))
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0,
2 * 3 * np.sum(np.ones(3), axis=-1, keepdims=True))
self.assertAllClose(
m1,
-0.5 * 2 * np.sum(np.identity(3), axis=(-1, -2), keepdims=True))
pass
def test_message_to_parent_mu(self):
"""
Test that GaussianARD computes the message to the 1st parent correctly.
"""
# Check formula with uncertain parent alpha
mu = GaussianARD(0, 1)
alpha = Gamma(2,1)
X = GaussianARD(mu,
alpha)
X.observe(3)
(m0, m1) = mu._message_from_children()
#(m0, m1) = X._message_to_parent(0)
self.assertAllClose(m0,
2*3)
self.assertAllClose(m1,
-0.5*2)
# Check formula with uncertain node
mu = GaussianARD(1, 1e10)
X = GaussianARD(mu, 2)
Y = GaussianARD(X, 1)
Y.observe(5)
X.update()
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0,
2 * 1/(2+1)*(2*1+1*5))
self.assertAllClose(m1,
-0.5*2)
# Check alpha larger than mu
mu = GaussianARD(np.zeros((2,3)), 1e10, shape=(2,3))
X = GaussianARD(mu,
2*np.ones((3,2,3)))
X.observe(3*np.ones((3,2,3)))
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0,
2*3 * 3 * np.ones((2,3)))
self.assertAllClose(m1,
-0.5 * 3 * 2*misc.identity(2,3))
# Check mu larger than alpha
mu = GaussianARD(np.zeros((3,2,3)), 1e10, shape=(3,2,3))
X = GaussianARD(mu,
2*np.ones((2,3)))
X.observe(3*np.ones((3,2,3)))
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0,
2 * 3 * np.ones((3,2,3)))
self.assertAllClose(m1,
-0.5 * 2*misc.identity(3,2,3))
# Check node larger than mu and alpha
mu = GaussianARD(np.zeros((2,3)), 1e10, shape=(2,3))
X = GaussianARD(mu,
2*np.ones((3,)),
shape=(3,2,3))
X.observe(3*np.ones((3,2,3)))
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0,
2*3 * 3*np.ones((2,3)))
self.assertAllClose(m1,
-0.5 * 2 * 3*misc.identity(2,3))
# Check broadcasting of dimensions
mu = GaussianARD(np.zeros((2,1)), 1e10, shape=(2,1))
X = GaussianARD(mu,
2*np.ones((2,3)),
shape=(2,3))
X.observe(3*np.ones((2,3)))
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0,
2*3 * 3*np.ones((2,1)))
self.assertAllClose(m1,
-0.5 * 2 * 3*misc.identity(2,1))
# Check plates for smaller mu than node
mu = GaussianARD(0,1,
shape=(3,),
plates=(4,1,1))
X = GaussianARD(mu,
2*np.ones((3,)),
shape=(2,3),
plates=(4,5))
X.observe(3*np.ones((4,5,2,3)))
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0 * np.ones((4,1,1,3)),
2*3 * 5*2*np.ones((4,1,1,3)))
self.assertAllClose(m1 * np.ones((4,1,1,3,3)),
-0.5*2 * 5*2*misc.identity(3) * np.ones((4,1,1,3,3)))
# Check mask
mu = GaussianARD(np.zeros((2,1,3)), 1e10, shape=(3,))
X = GaussianARD(mu,
2*np.ones((2,4,3)),
shape=(3,),
plates=(2,4,))
X.observe(3*np.ones((2,4,3)), mask=[[True, True, True, False],
[False, True, False, True]])
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0,
(2*3 * np.ones((2,1,3))
* np.array([[[3]], [[2]]])))
self.assertAllClose(m1,
(-0.5*2 * misc.identity(3)
* np.ones((2,1,1,1))
* np.array([[[[3]]], [[[2]]]])))
# Check mask with different shapes
mu = GaussianARD(np.zeros((2,1,3)), 1e10, shape=())
X = GaussianARD(mu,
2*np.ones((2,4,3)),
shape=(3,),
plates=(2,4,))
mask = np.array([[True, True, True, False],
[False, True, False, True]])
X.observe(3*np.ones((2,4,3)), mask=mask)
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0,
2*3 * np.sum(np.ones((2,4,3))*mask[...,None],
axis=-2,
keepdims=True))
self.assertAllClose(m1,
(-0.5*2 * np.sum(np.ones((2,4,3))*mask[...,None],
axis=-2,
keepdims=True)))
# Check non-ARD Gaussian child
mu = np.array([1,2])
Mu = GaussianARD(mu, 1e10, shape=(2,))
alpha = np.array([3,4])
Lambda = np.array([[1, 0.5],
[0.5, 1]])
X = GaussianARD(Mu, alpha, ndim=1)
Y = Gaussian(X, Lambda)
y = np.array([5,6])
Y.observe(y)
X.update()
(m0, m1) = Mu._message_from_children()
mean = np.dot(np.linalg.inv(np.diag(alpha)+Lambda),
np.dot(np.diag(alpha), mu)
+ np.dot(Lambda, y))
self.assertAllClose(m0,
np.dot(np.diag(alpha), mean))
self.assertAllClose(m1,
-0.5*np.diag(alpha))
# Check broadcasted variable axes
mu = GaussianARD(np.zeros(1), 1e10, shape=(1,))
X = GaussianARD(mu,
2,
shape=(3,))
X.observe(3*np.ones(3))
(m0, m1) = mu._message_from_children()
self.assertAllClose(m0,
2*3 * np.sum(np.ones(3), axis=-1, keepdims=True))
self.assertAllClose(m1,
-0.5*2 * np.sum(np.identity(3),
axis=(-1,-2),
keepdims=True))
pass
def test_message_to_parent(self):
"""
Test the message to parents of Mixture node.
"""
K = 3
# Broadcasting the moments on the cluster axis
Mu = GaussianARD(2, 1,
ndim=0,
plates=(K,))
(mu, mumu) = Mu._message_to_child()
Alpha = Gamma(3, 1,
plates=(K,))
(alpha, logalpha) = Alpha._message_to_child()
z = Categorical(np.ones(K)/K)
X = Mixture(z, GaussianARD, Mu, Alpha)
tau = 4
Y = GaussianARD(X, tau)
y = 5
Y.observe(y)
(x, xx) = X._message_to_child()
m = z._message_from_children()
self.assertAllClose(m[0] * np.ones(K),
random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0)
* np.ones(K))
m = Mu._message_from_children()
self.assertAllClose(m[0],
1/K * (alpha*x) * np.ones(3))
self.assertAllClose(m[1],
-0.5 * 1/K * alpha * np.ones(3))
# Some parameters do not have cluster plate axis
Mu = GaussianARD(2, 1,
ndim=0,
plates=(K,))
(mu, mumu) = Mu._message_to_child()
Alpha = Gamma(3, 1) # Note: no cluster plate axis!
(alpha, logalpha) = Alpha._message_to_child()
z = Categorical(np.ones(K)/K)
X = Mixture(z, GaussianARD, Mu, Alpha)
tau = 4
Y = GaussianARD(X, tau)
y = 5
Y.observe(y)
(x, xx) = X._message_to_child()
m = z._message_from_children()
self.assertAllClose(m[0] * np.ones(K),
random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0)
* np.ones(K))
m = Mu._message_from_children()
self.assertAllClose(m[0],
1/K * (alpha*x) * np.ones(3))
self.assertAllClose(m[1],
-0.5 * 1/K * alpha * np.ones(3))
# Cluster assignments do not have as many plate axes as parameters.
M = 2
Mu = GaussianARD(2, 1,
ndim=0,
plates=(K,M))
(mu, mumu) = Mu._message_to_child()
Alpha = Gamma(3, 1,
plates=(K,M))
(alpha, logalpha) = Alpha._message_to_child()
z = Categorical(np.ones(K)/K)
X = Mixture(z, GaussianARD, Mu, Alpha, cluster_plate=-2)
tau = 4
Y = GaussianARD(X, tau)
y = 5 * np.ones(M)
Y.observe(y)
(x, xx) = X._message_to_child()
m = z._message_from_children()
self.assertAllClose(m[0]*np.ones(K),
np.sum(random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0) *
np.ones((K,M)),
axis=-1))
m = Mu._message_from_children()
self.assertAllClose(m[0] * np.ones((K,M)),
1/K * (alpha*x) * np.ones((K,M)))
self.assertAllClose(m[1] * np.ones((K,M)),
-0.5 * 1/K * alpha * np.ones((K,M)))
# Mixed distribution broadcasts g
# This tests for a found bug. The bug caused an error.
Z = Categorical([0.3, 0.5, 0.2])
X = Mixture(Z, Categorical, [[0.2,0.8], [0.1,0.9], [0.3,0.7]])
m = Z._message_from_children()
pass
def test_message_to_parent(self):
"""
Test the message to parents of Mixture node.
"""
K = 3
# Broadcasting the moments on the cluster axis
Mu = GaussianARD(2, 1,
ndim=0,
plates=(K,))
(mu, mumu) = Mu._message_to_child()
Alpha = Gamma(3, 1,
plates=(K,))
(alpha, logalpha) = Alpha._message_to_child()
z = Categorical(np.ones(K)/K)
X = Mixture(z, GaussianARD, Mu, Alpha)
tau = 4
Y = GaussianARD(X, tau)
y = 5
Y.observe(y)
(x, xx) = X._message_to_child()
m = z._message_from_children()
self.assertAllClose(m[0] * np.ones(K),
random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0)
* np.ones(K))
m = Mu._message_from_children()
self.assertAllClose(m[0],
1/K * (alpha*x) * np.ones(3))
self.assertAllClose(m[1],
-0.5 * 1/K * alpha * np.ones(3))
# Some parameters do not have cluster plate axis
Mu = GaussianARD(2, 1,
ndim=0,
plates=(K,))
(mu, mumu) = Mu._message_to_child()
Alpha = Gamma(3, 1) # Note: no cluster plate axis!
(alpha, logalpha) = Alpha._message_to_child()
z = Categorical(np.ones(K)/K)
X = Mixture(z, GaussianARD, Mu, Alpha)
tau = 4
Y = GaussianARD(X, tau)
y = 5
Y.observe(y)
(x, xx) = X._message_to_child()
m = z._message_from_children()
self.assertAllClose(m[0] * np.ones(K),
random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0)
* np.ones(K))
m = Mu._message_from_children()
self.assertAllClose(m[0],
1/K * (alpha*x) * np.ones(3))
self.assertAllClose(m[1],
-0.5 * 1/K * alpha * np.ones(3))
# Cluster assignments do not have as many plate axes as parameters.
M = 2
Mu = GaussianARD(2, 1,
ndim=0,
plates=(K,M))
(mu, mumu) = Mu._message_to_child()
Alpha = Gamma(3, 1,
plates=(K,M))
(alpha, logalpha) = Alpha._message_to_child()
z = Categorical(np.ones(K)/K)
X = Mixture(z, GaussianARD, Mu, Alpha, cluster_plate=-2)
tau = 4
Y = GaussianARD(X, tau)
y = 5 * np.ones(M)
Y.observe(y)
(x, xx) = X._message_to_child()
m = z._message_from_children()
self.assertAllClose(m[0]*np.ones(K),
np.sum(random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0) *
np.ones((K,M)),
axis=-1))
m = Mu._message_from_children()
self.assertAllClose(m[0] * np.ones((K,M)),
1/K * (alpha*x) * np.ones((K,M)))
self.assertAllClose(m[1] * np.ones((K,M)),
-0.5 * 1/K * alpha * np.ones((K,M)))
# Mixed distribution broadcasts g
# This tests for a found bug. The bug caused an error.
Z = Categorical([0.3, 0.5, 0.2])
X = Mixture(Z, Categorical, [[0.2,0.8], [0.1,0.9], [0.3,0.7]])
m = Z._message_from_children()
#
# Test nested mixtures
#
t1 = [1, 1, 0, 3, 3]
t2 = [2]
p = Dirichlet([1, 1], plates=(4, 3))
X = Mixture(t1, Mixture, t2, Categorical, p)
X.observe([1, 1, 0, 0, 0])
p.update()
self.assertAllClose(
p.phi[0],
[
[[1, 1], [1, 1], [2, 1]],
[[1, 1], [1, 1], [1, 3]],
[[1, 1], [1, 1], [1, 1]],
[[1, 1], [1, 1], [3, 1]],
]
)
# Test sample plates in nested mixtures
t1 = Categorical([0.3, 0.7], plates=(5,))
t2 = [[1], [1], [0], [3], [3]]
t3 = 2
p = Dirichlet([1, 1], plates=(2, 4, 3))
X = Mixture(t1, Mixture, t2, Mixture, t3, Categorical, p)
X.observe([1, 1, 0, 0, 0])
p.update()
self.assertAllClose(
p.phi[0],
[
[
[[1, 1], [1, 1], [1.3, 1]],
[[1, 1], [1, 1], [1, 1.6]],
[[1, 1], [1, 1], [1, 1]],
[[1, 1], [1, 1], [1.6, 1]],
],
[
[[1, 1], [1, 1], [1.7, 1]],
[[1, 1], [1, 1], [1, 2.4]],
[[1, 1], [1, 1], [1, 1]],
[[1, 1], [1, 1], [2.4, 1]],
]
]
)
# Check that Gate and nested Mixture are equal
t1 = Categorical([0.3, 0.7], plates=(5,))
t2 = Categorical([0.1, 0.3, 0.6], plates=(5, 1))
p = Dirichlet([1, 2, 3, 4], plates=(2, 3))
X = Mixture(t1, Mixture, t2, Categorical, p)
X.observe([3, 3, 1, 2, 2])
t1_msg = t1._message_from_children()
t2_msg = t2._message_from_children()
p_msg = p._message_from_children()
t1 = Categorical([0.3, 0.7], plates=(5,))
t2 = Categorical([0.1, 0.3, 0.6], plates=(5, 1))
p = Dirichlet([1, 2, 3, 4], plates=(2, 3))
X = Categorical(Gate(t1, Gate(t2, p)))
X.observe([3, 3, 1, 2, 2])
t1_msg2 = t1._message_from_children()
t2_msg2 = t2._message_from_children()
p_msg2 = p._message_from_children()
self.assertAllClose(t1_msg[0], t1_msg2[0])
self.assertAllClose(t2_msg[0], t2_msg2[0])
self.assertAllClose(p_msg[0], p_msg2[0])
pass
