def test_initialization(self):
"""
Test initialization methods of GaussianARD
"""
X = GaussianARD(1, 2, shape=(2,), plates=(3,))
# Prior initialization
mu = 1 * np.ones((3, 2))
alpha = 2 * np.ones((3, 2))
X.initialize_from_prior()
u = X._message_to_child()
self.assertAllClose(u[0]*np.ones((3,2)),
mu)
self.assertAllClose(u[1]*np.ones((3,2,2)),
linalg.outer(mu, mu, ndim=1) +
misc.diag(1/alpha, ndim=1))
# Parameter initialization
mu = np.random.randn(3, 2)
alpha = np.random.rand(3, 2)
X.initialize_from_parameters(mu, alpha)
u = X._message_to_child()
self.assertAllClose(u[0], mu)
self.assertAllClose(u[1], linalg.outer(mu, mu, ndim=1) +
misc.diag(1/alpha, ndim=1))
# Value initialization
x = np.random.randn(3, 2)
X.initialize_from_value(x)
u = X._message_to_child()
self.assertAllClose(u[0], x)
self.assertAllClose(u[1], linalg.outer(x, x, ndim=1))
# Random initialization
X.initialize_from_random()
pass
def test_initialization(self):
"""
Test initialization methods of GaussianARD
"""
X = GaussianARD(1, 2, shape=(2, ), plates=(3, ))
# Prior initialization
mu = 1 * np.ones((3, 2))
alpha = 2 * np.ones((3, 2))
X.initialize_from_prior()
u = X._message_to_child()
self.assertAllClose(u[0] * np.ones((3, 2)), mu)
self.assertAllClose(
u[1] * np.ones((3, 2, 2)),
linalg.outer(mu, mu, ndim=1) + misc.diag(1 / alpha, ndim=1))
# Parameter initialization
mu = np.random.randn(3, 2)
alpha = np.random.rand(3, 2)
X.initialize_from_parameters(mu, alpha)
u = X._message_to_child()
self.assertAllClose(u[0], mu)
self.assertAllClose(
u[1],
linalg.outer(mu, mu, ndim=1) + misc.diag(1 / alpha, ndim=1))
# Value initialization
x = np.random.randn(3, 2)
X.initialize_from_value(x)
u = X._message_to_child()
self.assertAllClose(u[0], x)
self.assertAllClose(u[1], linalg.outer(x, x, ndim=1))
# Random initialization
X.initialize_from_random()
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_child(self):
"""
Test moments of GaussianARD.
"""
# Check that moments have full shape when broadcasting
X = GaussianARD(np.zeros((2, )), np.ones((3, 2)), shape=(4, 3, 2))
(u0, u1) = X._message_to_child()
self.assertEqual(np.shape(u0), (4, 3, 2))
self.assertEqual(np.shape(u1), (4, 3, 2, 4, 3, 2))
# Check the formula
X = GaussianARD(2, 3)
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 2)
self.assertAllClose(u1, 2**2 + 1 / 3)
# Check the formula for multidimensional arrays
X = GaussianARD(2 * np.ones((2, 1, 4)), 3 * np.ones((2, 3, 1)), ndim=3)
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 2 * np.ones((2, 3, 4)))
self.assertAllClose(
u1, 2**2 * np.ones(
(2, 3, 4, 2, 3, 4)) + 1 / 3 * misc.identity(2, 3, 4))
# Check the formula for dim-broadcasted mu
X = GaussianARD(2 * np.ones((3, 1)), 3 * np.ones((2, 3, 4)), ndim=3)
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 2 * np.ones((2, 3, 4)))
self.assertAllClose(
u1, 2**2 * np.ones(
(2, 3, 4, 2, 3, 4)) + 1 / 3 * misc.identity(2, 3, 4))
# Check the formula for dim-broadcasted alpha
X = GaussianARD(2 * np.ones((2, 3, 4)), 3 * np.ones((3, 1)), ndim=3)
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 2 * np.ones((2, 3, 4)))
self.assertAllClose(
u1, 2**2 * np.ones(
(2, 3, 4, 2, 3, 4)) + 1 / 3 * misc.identity(2, 3, 4))
# Check the formula for dim-broadcasted mu and alpha
X = GaussianARD(2 * np.ones((3, 1)),
3 * np.ones((3, 1)),
shape=(2, 3, 4))
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 2 * np.ones((2, 3, 4)))
self.assertAllClose(
u1, 2**2 * np.ones(
(2, 3, 4, 2, 3, 4)) + 1 / 3 * misc.identity(2, 3, 4))
# Check the formula for dim-broadcasted mu with plates
mu = GaussianARD(2 * np.ones((5, 1, 3, 4)),
np.ones((5, 1, 3, 4)),
shape=(3, 4),
plates=(5, 1))
X = GaussianARD(mu,
3 * np.ones((5, 2, 3, 4)),
shape=(2, 3, 4),
plates=(5, ))
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 2 * np.ones((5, 2, 3, 4)))
self.assertAllClose(
u1, 2**2 * np.ones(
(5, 2, 3, 4, 2, 3, 4)) + 1 / 3 * misc.identity(2, 3, 4))
# Check posterior
X = GaussianARD(2, 3)
Y = GaussianARD(X, 1)
Y.observe(10)
X.update()
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 1 / (3 + 1) * (3 * 2 + 1 * 10))
self.assertAllClose(u1,
(1 / (3 + 1) * (3 * 2 + 1 * 10))**2 + 1 / (3 + 1))
pass
def test_message_to_child(self):
"""
Test moments of GaussianARD.
"""
# Check that moments have full shape when broadcasting
X = GaussianARD(np.zeros((2,)),
np.ones((3,2)),
shape=(4,3,2))
(u0, u1) = X._message_to_child()
self.assertEqual(np.shape(u0),
(4,3,2))
self.assertEqual(np.shape(u1),
(4,3,2,4,3,2))
# Check the formula
X = GaussianARD(2, 3)
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 2)
self.assertAllClose(u1, 2**2 + 1/3)
# Check the formula for multidimensional arrays
X = GaussianARD(2*np.ones((2,1,4)),
3*np.ones((2,3,1)),
ndim=3)
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 2*np.ones((2,3,4)))
self.assertAllClose(u1,
2**2 * np.ones((2,3,4,2,3,4))
+ 1/3 * misc.identity(2,3,4))
# Check the formula for dim-broadcasted mu
X = GaussianARD(2*np.ones((3,1)),
3*np.ones((2,3,4)),
ndim=3)
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 2*np.ones((2,3,4)))
self.assertAllClose(u1,
2**2 * np.ones((2,3,4,2,3,4))
+ 1/3 * misc.identity(2,3,4))
# Check the formula for dim-broadcasted alpha
X = GaussianARD(2*np.ones((2,3,4)),
3*np.ones((3,1)),
ndim=3)
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 2*np.ones((2,3,4)))
self.assertAllClose(u1,
2**2 * np.ones((2,3,4,2,3,4))
+ 1/3 * misc.identity(2,3,4))
# Check the formula for dim-broadcasted mu and alpha
X = GaussianARD(2*np.ones((3,1)),
3*np.ones((3,1)),
shape=(2,3,4))
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 2*np.ones((2,3,4)))
self.assertAllClose(u1,
2**2 * np.ones((2,3,4,2,3,4))
+ 1/3 * misc.identity(2,3,4))
# Check the formula for dim-broadcasted mu with plates
mu = GaussianARD(2*np.ones((5,1,3,4)),
np.ones((5,1,3,4)),
shape=(3,4),
plates=(5,1))
X = GaussianARD(mu,
3*np.ones((5,2,3,4)),
shape=(2,3,4),
plates=(5,))
(u0, u1) = X._message_to_child()
self.assertAllClose(u0, 2*np.ones((5,2,3,4)))
self.assertAllClose(u1,
2**2 * np.ones((5,2,3,4,2,3,4))
+ 1/3 * misc.identity(2,3,4))
# Check posterior
X = GaussianARD(2, 3)
Y = GaussianARD(X, 1)
Y.observe(10)
X.update()
(u0, u1) = X._message_to_child()
self.assertAllClose(u0,
1/(3+1) * (3*2 + 1*10))
self.assertAllClose(u1,
(1/(3+1) * (3*2 + 1*10))**2 + 1/(3+1))
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
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 = X._message_to_parent(0)
self.assertAllClose(m[0],
random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0))
m = X._message_to_parent(1)
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 = X._message_to_parent(0)
self.assertAllClose(m[0],
random.gaussian_logpdf(xx*alpha,
x*alpha*mu,
mumu*alpha,
logalpha,
0))
m = X._message_to_parent(1)
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 = X._message_to_parent(0)
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 = X._message_to_parent(1)
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)))
pass
