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
