def test_moments(self):
"""
Test the moments of Poisson nodes.
"""
# Simple test
X = Poisson(12.8)
u = X._message_to_child()
self.assertEqual(len(u),
1)
self.assertAllClose(u[0],
12.8)
# Test plates in rate
X = Poisson(12.8*np.ones((2,3)))
u = X._message_to_child()
self.assertAllClose(u[0],
12.8*np.ones((2,3)))
# Test with gamma prior
alpha = Gamma(5, 2)
r = np.exp(alpha._message_to_child()[1])
X = Poisson(alpha)
u = X._message_to_child()
self.assertAllClose(u[0],
r)
# Test with broadcasted plates in parents
X = Poisson(Gamma(5, 2, plates=(2,3)))
u = X._message_to_child()
self.assertAllClose(u[0]*np.ones((2,3)),
r*np.ones((2,3)))
pass
def test_moments(self):
"""
Test the moments of Poisson nodes.
"""
# Simple test
X = Poisson(12.8)
u = X._message_to_child()
self.assertEqual(len(u), 1)
self.assertAllClose(u[0], 12.8)
# Test plates in rate
X = Poisson(12.8 * np.ones((2, 3)))
u = X._message_to_child()
self.assertAllClose(u[0], 12.8 * np.ones((2, 3)))
# Test with gamma prior
alpha = Gamma(5, 2)
r = np.exp(alpha._message_to_child()[1])
X = Poisson(alpha)
u = X._message_to_child()
self.assertAllClose(u[0], r)
# Test with broadcasted plates in parents
X = Poisson(Gamma(5, 2, plates=(2, 3)))
u = X._message_to_child()
self.assertAllClose(u[0] * np.ones((2, 3)), r * np.ones((2, 3)))
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 the message to child of GaussianGammaISO node.
"""
# Simple test
mu = np.array([1, 2, 3])
Lambda = np.identity(3)
a = 2
b = 10
X_alpha = GaussianGammaISO(mu, Lambda, a, b)
u = X_alpha._message_to_child()
self.assertEqual(len(u), 4)
tau = np.array(a / b)
self.assertAllClose(u[0], tau[..., None] * mu)
self.assertAllClose(
u[1],
(linalg.inv(Lambda) + tau[..., None, None] * linalg.outer(mu, mu)))
self.assertAllClose(u[2], tau)
self.assertAllClose(u[3], -np.log(b) + special.psi(a))
# Test with unknown parents
mu = Gaussian(np.arange(3), 10 * np.identity(3))
Lambda = Wishart(10, np.identity(3))
a = 2
b = Gamma(3, 15)
X_alpha = GaussianGammaISO(mu, Lambda, a, b)
u = X_alpha._message_to_child()
(mu, mumu) = mu._message_to_child()
Cov_mu = mumu - linalg.outer(mu, mu)
(Lambda, _) = Lambda._message_to_child()
(b, _) = b._message_to_child()
(tau, logtau) = Gamma(
a, b + 0.5 * np.sum(Lambda * Cov_mu))._message_to_child()
self.assertAllClose(u[0], tau[..., None] * mu)
self.assertAllClose(
u[1],
(linalg.inv(Lambda) + tau[..., None, None] * linalg.outer(mu, mu)))
self.assertAllClose(u[2], tau)
self.assertAllClose(u[3], logtau)
# Test with plates
mu = Gaussian(np.reshape(np.arange(3 * 4), (4, 3)),
10 * np.identity(3),
plates=(4, ))
Lambda = Wishart(10, np.identity(3))
a = 2
b = Gamma(3, 15)
X_alpha = GaussianGammaISO(mu, Lambda, a, b, plates=(4, ))
u = X_alpha._message_to_child()
(mu, mumu) = mu._message_to_child()
Cov_mu = mumu - linalg.outer(mu, mu)
(Lambda, _) = Lambda._message_to_child()
(b, _) = b._message_to_child()
(tau, logtau) = Gamma(
a, b +
0.5 * np.sum(Lambda * Cov_mu, axis=(-1, -2)))._message_to_child()
self.assertAllClose(u[0] * np.ones((4, 1)),
np.ones((4, 1)) * tau[..., None] * mu)
self.assertAllClose(
u[1] * np.ones((4, 1, 1)),
np.ones((4, 1, 1)) *
(linalg.inv(Lambda) + tau[..., None, None] * linalg.outer(mu, mu)))
self.assertAllClose(u[2] * np.ones(4), np.ones(4) * tau)
self.assertAllClose(u[3] * np.ones(4), np.ones(4) * logtau)
pass
def test_message_to_child(self):
"""
Test the message to child of GaussianGamma node.
"""
# Simple test
mu = np.array([1,2,3])
Lambda = np.identity(3)
a = 2
b = 10
X_alpha = GaussianGamma(mu, Lambda, a, b)
u = X_alpha._message_to_child()
self.assertEqual(len(u), 4)
tau = np.array(a/b)
self.assertAllClose(u[0],
tau[...,None] * mu)
self.assertAllClose(u[1],
(linalg.inv(Lambda)
+ tau[...,None,None] * linalg.outer(mu, mu)))
self.assertAllClose(u[2],
tau)
self.assertAllClose(u[3],
-np.log(b) + special.psi(a))
# Test with unknown parents
mu = Gaussian(np.arange(3), 10*np.identity(3))
Lambda = Wishart(10, np.identity(3))
a = 2
b = Gamma(3, 15)
X_alpha = GaussianGamma(mu, Lambda, a, b)
u = X_alpha._message_to_child()
(mu, mumu) = mu._message_to_child()
Cov_mu = mumu - linalg.outer(mu, mu)
(Lambda, _) = Lambda._message_to_child()
(b, _) = b._message_to_child()
(tau, logtau) = Gamma(a, b + 0.5*np.sum(Lambda*Cov_mu))._message_to_child()
self.assertAllClose(u[0],
tau[...,None] * mu)
self.assertAllClose(u[1],
(linalg.inv(Lambda)
+ tau[...,None,None] * linalg.outer(mu, mu)))
self.assertAllClose(u[2],
tau)
self.assertAllClose(u[3],
logtau)
# Test with plates
mu = Gaussian(np.reshape(np.arange(3*4), (4,3)),
10*np.identity(3),
plates=(4,))
Lambda = Wishart(10, np.identity(3))
a = 2
b = Gamma(3, 15)
X_alpha = GaussianGamma(mu, Lambda, a, b, plates=(4,))
u = X_alpha._message_to_child()
(mu, mumu) = mu._message_to_child()
Cov_mu = mumu - linalg.outer(mu, mu)
(Lambda, _) = Lambda._message_to_child()
(b, _) = b._message_to_child()
(tau, logtau) = Gamma(a,
b + 0.5*np.sum(Lambda*Cov_mu,
axis=(-1,-2)))._message_to_child()
self.assertAllClose(u[0] * np.ones((4,1)),
np.ones((4,1)) * tau[...,None] * mu)
self.assertAllClose(u[1] * np.ones((4,1,1)),
np.ones((4,1,1)) * (linalg.inv(Lambda)
+ tau[...,None,None] * linalg.outer(mu, mu)))
self.assertAllClose(u[2] * np.ones(4),
np.ones(4) * tau)
self.assertAllClose(u[3] * np.ones(4),
np.ones(4) * logtau)
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
