def test_message_to_parent(self):
"""
Test the message from SumMultiply node to its parents.
"""
data = 2
tau = 3
def check_message(true_m0, true_m1, parent, *args, F=None):
if F is None:
A = SumMultiply(*args)
B = GaussianARD(A, tau)
B.observe(data*np.ones(A.plates + A.dims[0]))
else:
A = F
(A_m0, A_m1) = A._message_to_parent(parent)
self.assertAllClose(true_m0, A_m0)
self.assertAllClose(true_m1, A_m1)
pass
# Check: different message to each of multiple parents
X1 = GaussianARD(np.random.randn(2),
np.random.rand(2),
ndim=1)
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(2),
np.random.rand(2),
ndim=1)
x2 = X2.get_moments()
m0 = tau * data * x2[0]
m1 = -0.5 * tau * x2[1] * np.identity(2)
check_message(m0, m1, 0,
'i,i->i',
X1,
X2)
check_message(m0, m1, 0,
X1,
[9],
X2,
[9],
[9])
m0 = tau * data * x1[0]
m1 = -0.5 * tau * x1[1] * np.identity(2)
check_message(m0, m1, 1,
'i,i->i',
X1,
X2)
check_message(m0, m1, 1,
X1,
[9],
X2,
[9],
[9])
# Check: key not in output
X1 = GaussianARD(np.random.randn(2),
np.random.rand(2),
ndim=1)
x1 = X1.get_moments()
m0 = tau * data * np.ones(2)
m1 = -0.5 * tau * np.ones((2,2))
check_message(m0, m1, 0,
'i',
X1)
check_message(m0, m1, 0,
'i->',
X1)
check_message(m0, m1, 0,
X1,
[9])
check_message(m0, m1, 0,
X1,
[9],
[])
# Check: key not in some input
X1 = GaussianARD(np.random.randn(),
np.random.rand())
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(2),
np.random.rand(2),
ndim=1)
x2 = X2.get_moments()
m0 = tau * data * np.sum(x2[0], axis=-1)
m1 = -0.5 * tau * np.sum(x2[1] * np.identity(2),
axis=(-1,-2))
check_message(m0, m1, 0,
',i->i',
X1,
X2)
check_message(m0, m1, 0,
X1,
[],
X2,
[9],
[9])
m0 = tau * data * x1[0] * np.ones(2)
m1 = -0.5 * tau * x1[1] * np.identity(2)
check_message(m0, m1, 1,
',i->i',
X1,
X2)
check_message(m0, m1, 1,
X1,
[],
X2,
[9],
[9])
# Check: keys in different order
Y1 = GaussianARD(np.random.randn(3,2),
np.random.rand(3,2),
ndim=2)
y1 = Y1.get_moments()
Y2 = GaussianARD(np.random.randn(2,3),
np.random.rand(2,3),
ndim=2)
y2 = Y2.get_moments()
m0 = tau * data * y2[0].T
m1 = -0.5 * tau * np.einsum('ijlk->jikl', y2[1] * misc.identity(2,3))
check_message(m0, m1, 0,
'ij,ji->ij',
Y1,
Y2)
check_message(m0, m1, 0,
Y1,
['i','j'],
Y2,
['j','i'],
['i','j'])
m0 = tau * data * y1[0].T
m1 = -0.5 * tau * np.einsum('ijlk->jikl', y1[1] * misc.identity(3,2))
check_message(m0, m1, 1,
'ij,ji->ij',
Y1,
Y2)
check_message(m0, m1, 1,
Y1,
['i','j'],
Y2,
['j','i'],
['i','j'])
# Check: plates when different dimensionality
X1 = GaussianARD(np.random.randn(5),
np.random.rand(5),
shape=(),
plates=(5,))
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(5,3),
np.random.rand(5,3),
shape=(3,),
plates=(5,))
x2 = X2.get_moments()
m0 = tau * data * np.sum(np.ones((5,3)) * x2[0], axis=-1)
m1 = -0.5 * tau * np.sum(x2[1] * misc.identity(3), axis=(-1,-2))
check_message(m0, m1, 0,
',i->i',
X1,
X2)
check_message(m0, m1, 0,
X1,
[],
X2,
['i'],
['i'])
m0 = tau * data * x1[0][:,np.newaxis] * np.ones((5,3))
m1 = -0.5 * tau * x1[1][:,np.newaxis,np.newaxis] * misc.identity(3)
check_message(m0, m1, 1,
',i->i',
X1,
X2)
check_message(m0, m1, 1,
X1,
[],
X2,
['i'],
['i'])
# Check: other parent's moments broadcasts over plates when node has the
# same plates
X1 = GaussianARD(np.random.randn(5,4,3),
np.random.rand(5,4,3),
shape=(3,),
plates=(5,4))
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(3),
np.random.rand(3),
shape=(3,),
plates=(5,4))
x2 = X2.get_moments()
m0 = tau * data * np.ones((5,4,3)) * x2[0]
m1 = -0.5 * tau * x2[1] * misc.identity(3)
check_message(m0, m1, 0,
'i,i->i',
X1,
X2)
check_message(m0, m1, 0,
X1,
['i'],
X2,
['i'],
['i'])
# Check: other parent's moments broadcasts over plates when node does
# not have that plate
X1 = GaussianARD(np.random.randn(3),
np.random.rand(3),
shape=(3,),
plates=())
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(3),
np.random.rand(3),
shape=(3,),
plates=(5,4))
x2 = X2.get_moments()
m0 = tau * data * np.sum(np.ones((5,4,3)) * x2[0], axis=(0,1))
m1 = -0.5 * tau * np.sum(np.ones((5,4,1,1))
* misc.identity(3)
* x2[1],
axis=(0,1))
check_message(m0, m1, 0,
'i,i->i',
X1,
X2)
check_message(m0, m1, 0,
X1,
['i'],
X2,
['i'],
['i'])
# Check: other parent's moments broadcasts over plates when the node
# only broadcasts that plate
X1 = GaussianARD(np.random.randn(3),
np.random.rand(3),
shape=(3,),
plates=(1,1))
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(3),
np.random.rand(3),
shape=(3,),
plates=(5,4))
x2 = X2.get_moments()
m0 = tau * data * np.sum(np.ones((5,4,3)) * x2[0], axis=(0,1), keepdims=True)
m1 = -0.5 * tau * np.sum(np.ones((5,4,1,1))
* misc.identity(3)
* x2[1],
axis=(0,1),
keepdims=True)
check_message(m0, m1, 0,
'i,i->i',
X1,
X2)
check_message(m0, m1, 0,
X1,
['i'],
X2,
['i'],
['i'])
# Check: broadcasted dimensions
X1 = GaussianARD(np.random.randn(1,1),
np.random.rand(1,1),
ndim=2)
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(3,2),
np.random.rand(3,2),
ndim=2)
x2 = X2.get_moments()
m0 = tau * data * np.sum(np.ones((3,2)) * x2[0],
keepdims=True)
m1 = -0.5 * tau * np.sum(misc.identity(3,2) * x2[1],
keepdims=True)
check_message(m0, m1, 0,
'ij,ij->ij',
X1,
X2)
check_message(m0, m1, 0,
X1,
[0,1],
X2,
[0,1],
[0,1])
m0 = tau * data * np.ones((3,2)) * x1[0]
m1 = -0.5 * tau * misc.identity(3,2) * x1[1]
check_message(m0, m1, 1,
'ij,ij->ij',
X1,
X2)
check_message(m0, m1, 1,
X1,
[0,1],
X2,
[0,1],
[0,1])
# Check: non-ARD observations
X1 = GaussianARD(np.random.randn(2),
np.random.rand(2),
ndim=1)
x1 = X1.get_moments()
Lambda = np.array([[2, 1.5], [1.5, 2]])
F = SumMultiply('i->i', X1)
Y = Gaussian(F, Lambda)
y = np.random.randn(2)
Y.observe(y)
m0 = np.dot(Lambda, y)
m1 = -0.5 * Lambda
check_message(m0, m1, 0,
'i->i',
X1,
F=F)
check_message(m0, m1, 0,
X1,
['i'],
['i'],
F=F)
# Check: mask with same shape
X1 = GaussianARD(np.random.randn(3,2),
np.random.rand(3,2),
shape=(2,),
plates=(3,))
x1 = X1.get_moments()
mask = np.array([True, False, True])
F = SumMultiply('i->i', X1)
Y = GaussianARD(F, tau, ndim=1)
Y.observe(data*np.ones((3,2)), mask=mask)
m0 = tau * data * mask[:,np.newaxis] * np.ones(2)
m1 = -0.5 * tau * mask[:,np.newaxis,np.newaxis] * np.identity(2)
check_message(m0, m1, 0,
'i->i',
X1,
F=F)
check_message(m0, m1, 0,
X1,
['i'],
['i'],
F=F)
# Check: mask larger
X1 = GaussianARD(np.random.randn(2),
np.random.rand(2),
shape=(2,),
plates=())
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(3,2),
np.random.rand(3,2),
shape=(2,),
plates=(3,))
x2 = X2.get_moments()
mask = np.array([True, False, True])
F = SumMultiply('i,i->i', X1, X2)
Y = GaussianARD(F, tau,
plates=(3,),
ndim=1)
Y.observe(data*np.ones((3,2)), mask=mask)
m0 = tau * data * np.sum(mask[:,np.newaxis] * x2[0], axis=0)
m1 = -0.5 * tau * np.sum(mask[:,np.newaxis,np.newaxis]
* x2[1]
* np.identity(2),
axis=0)
check_message(m0, m1, 0,
'i,i->i',
X1,
X2,
F=F)
check_message(m0, m1, 0,
X1,
['i'],
X2,
['i'],
['i'],
F=F)
# Check: mask for broadcasted plate
X1 = GaussianARD(np.random.randn(2),
np.random.rand(2),
ndim=1,
plates=(1,))
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(2),
np.random.rand(2),
ndim=1,
plates=(3,))
x2 = X2.get_moments()
mask = np.array([True, False, True])
F = SumMultiply('i,i->i', X1, X2)
Y = GaussianARD(F, tau,
plates=(3,),
ndim=1)
Y.observe(data*np.ones((3,2)), mask=mask)
m0 = tau * data * np.sum(mask[:,np.newaxis] * x2[0],
axis=0,
keepdims=True)
m1 = -0.5 * tau * np.sum(mask[:,np.newaxis,np.newaxis]
* x2[1]
* np.identity(2),
axis=0,
keepdims=True)
check_message(m0, m1, 0,
'i->i',
X1,
F=F)
check_message(m0, m1, 0,
X1,
['i'],
['i'],
F=F)
# Check: Gaussian-gamma parents
X1 = GaussianGamma(
np.random.randn(2),
random.covariance(2),
np.random.rand(),
np.random.rand()
)
x1 = X1.get_moments()
X2 = GaussianGamma(
np.random.randn(2),
random.covariance(2),
np.random.rand(),
np.random.rand()
)
x2 = X2.get_moments()
F = SumMultiply('i,i->i', X1, X2)
V = random.covariance(2)
y = np.random.randn(2)
Y = Gaussian(F, V)
Y.observe(y)
m0 = np.dot(V, y) * x2[0]
m1 = -0.5 * V * x2[1]
m2 = -0.5 * np.einsum('i,ij,j', y, V, y) * x2[2]#linalg.inner(V, x2[2], ndim=2)
m3 = 0.5 * 2 #linalg.chol_logdet(linalg.chol(V)) + 2*x2[3]
m = F._message_to_parent(0)
self.assertAllClose(m[0], m0)
self.assertAllClose(m[1], m1)
self.assertAllClose(m[2], m2)
self.assertAllClose(m[3], m3)
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_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_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_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 from SumMultiply node to its parents.
"""
data = 2
tau = 3
def check_message(true_m0, true_m1, parent, *args, F=None):
if F is None:
A = SumMultiply(*args)
B = GaussianARD(A, tau)
B.observe(data * np.ones(A.plates + A.dims[0]))
else:
A = F
(A_m0, A_m1) = A._message_to_parent(parent)
self.assertAllClose(true_m0, A_m0)
self.assertAllClose(true_m1, A_m1)
pass
# Check: different message to each of multiple parents
X1 = GaussianARD(np.random.randn(2), np.random.rand(2), ndim=1)
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(2), np.random.rand(2), ndim=1)
x2 = X2.get_moments()
m0 = tau * data * x2[0]
m1 = -0.5 * tau * x2[1] * np.identity(2)
check_message(m0, m1, 0, 'i,i->i', X1, X2)
check_message(m0, m1, 0, X1, [9], X2, [9], [9])
m0 = tau * data * x1[0]
m1 = -0.5 * tau * x1[1] * np.identity(2)
check_message(m0, m1, 1, 'i,i->i', X1, X2)
check_message(m0, m1, 1, X1, [9], X2, [9], [9])
# Check: key not in output
X1 = GaussianARD(np.random.randn(2), np.random.rand(2), ndim=1)
x1 = X1.get_moments()
m0 = tau * data * np.ones(2)
m1 = -0.5 * tau * np.ones((2, 2))
check_message(m0, m1, 0, 'i', X1)
check_message(m0, m1, 0, 'i->', X1)
check_message(m0, m1, 0, X1, [9])
check_message(m0, m1, 0, X1, [9], [])
# Check: key not in some input
X1 = GaussianARD(np.random.randn(), np.random.rand())
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(2), np.random.rand(2), ndim=1)
x2 = X2.get_moments()
m0 = tau * data * np.sum(x2[0], axis=-1)
m1 = -0.5 * tau * np.sum(x2[1] * np.identity(2), axis=(-1, -2))
check_message(m0, m1, 0, ',i->i', X1, X2)
check_message(m0, m1, 0, X1, [], X2, [9], [9])
m0 = tau * data * x1[0] * np.ones(2)
m1 = -0.5 * tau * x1[1] * np.identity(2)
check_message(m0, m1, 1, ',i->i', X1, X2)
check_message(m0, m1, 1, X1, [], X2, [9], [9])
# Check: keys in different order
Y1 = GaussianARD(np.random.randn(3, 2), np.random.rand(3, 2), ndim=2)
y1 = Y1.get_moments()
Y2 = GaussianARD(np.random.randn(2, 3), np.random.rand(2, 3), ndim=2)
y2 = Y2.get_moments()
m0 = tau * data * y2[0].T
m1 = -0.5 * tau * np.einsum('ijlk->jikl', y2[1] * misc.identity(2, 3))
check_message(m0, m1, 0, 'ij,ji->ij', Y1, Y2)
check_message(m0, m1, 0, Y1, ['i', 'j'], Y2, ['j', 'i'], ['i', 'j'])
m0 = tau * data * y1[0].T
m1 = -0.5 * tau * np.einsum('ijlk->jikl', y1[1] * misc.identity(3, 2))
check_message(m0, m1, 1, 'ij,ji->ij', Y1, Y2)
check_message(m0, m1, 1, Y1, ['i', 'j'], Y2, ['j', 'i'], ['i', 'j'])
# Check: plates when different dimensionality
X1 = GaussianARD(np.random.randn(5),
np.random.rand(5),
shape=(),
plates=(5, ))
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(5, 3),
np.random.rand(5, 3),
shape=(3, ),
plates=(5, ))
x2 = X2.get_moments()
m0 = tau * data * np.sum(np.ones((5, 3)) * x2[0], axis=-1)
m1 = -0.5 * tau * np.sum(x2[1] * misc.identity(3), axis=(-1, -2))
check_message(m0, m1, 0, ',i->i', X1, X2)
check_message(m0, m1, 0, X1, [], X2, ['i'], ['i'])
m0 = tau * data * x1[0][:, np.newaxis] * np.ones((5, 3))
m1 = -0.5 * tau * x1[1][:, np.newaxis, np.newaxis] * misc.identity(3)
check_message(m0, m1, 1, ',i->i', X1, X2)
check_message(m0, m1, 1, X1, [], X2, ['i'], ['i'])
# Check: other parent's moments broadcasts over plates when node has the
# same plates
X1 = GaussianARD(np.random.randn(5, 4, 3),
np.random.rand(5, 4, 3),
shape=(3, ),
plates=(5, 4))
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(3),
np.random.rand(3),
shape=(3, ),
plates=(5, 4))
x2 = X2.get_moments()
m0 = tau * data * np.ones((5, 4, 3)) * x2[0]
m1 = -0.5 * tau * x2[1] * misc.identity(3)
check_message(m0, m1, 0, 'i,i->i', X1, X2)
check_message(m0, m1, 0, X1, ['i'], X2, ['i'], ['i'])
# Check: other parent's moments broadcasts over plates when node does
# not have that plate
X1 = GaussianARD(np.random.randn(3),
np.random.rand(3),
shape=(3, ),
plates=())
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(3),
np.random.rand(3),
shape=(3, ),
plates=(5, 4))
x2 = X2.get_moments()
m0 = tau * data * np.sum(np.ones((5, 4, 3)) * x2[0], axis=(0, 1))
m1 = -0.5 * tau * np.sum(np.ones(
(5, 4, 1, 1)) * misc.identity(3) * x2[1],
axis=(0, 1))
check_message(m0, m1, 0, 'i,i->i', X1, X2)
check_message(m0, m1, 0, X1, ['i'], X2, ['i'], ['i'])
# Check: other parent's moments broadcasts over plates when the node
# only broadcasts that plate
X1 = GaussianARD(np.random.randn(3),
np.random.rand(3),
shape=(3, ),
plates=(1, 1))
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(3),
np.random.rand(3),
shape=(3, ),
plates=(5, 4))
x2 = X2.get_moments()
m0 = tau * data * np.sum(
np.ones((5, 4, 3)) * x2[0], axis=(0, 1), keepdims=True)
m1 = -0.5 * tau * np.sum(np.ones(
(5, 4, 1, 1)) * misc.identity(3) * x2[1],
axis=(0, 1),
keepdims=True)
check_message(m0, m1, 0, 'i,i->i', X1, X2)
check_message(m0, m1, 0, X1, ['i'], X2, ['i'], ['i'])
# Check: broadcasted dimensions
X1 = GaussianARD(np.random.randn(1, 1), np.random.rand(1, 1), ndim=2)
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(3, 2), np.random.rand(3, 2), ndim=2)
x2 = X2.get_moments()
m0 = tau * data * np.sum(np.ones((3, 2)) * x2[0], keepdims=True)
m1 = -0.5 * tau * np.sum(misc.identity(3, 2) * x2[1], keepdims=True)
check_message(m0, m1, 0, 'ij,ij->ij', X1, X2)
check_message(m0, m1, 0, X1, [0, 1], X2, [0, 1], [0, 1])
m0 = tau * data * np.ones((3, 2)) * x1[0]
m1 = -0.5 * tau * misc.identity(3, 2) * x1[1]
check_message(m0, m1, 1, 'ij,ij->ij', X1, X2)
check_message(m0, m1, 1, X1, [0, 1], X2, [0, 1], [0, 1])
# Check: non-ARD observations
X1 = GaussianARD(np.random.randn(2), np.random.rand(2), ndim=1)
x1 = X1.get_moments()
Lambda = np.array([[2, 1.5], [1.5, 2]])
F = SumMultiply('i->i', X1)
Y = Gaussian(F, Lambda)
y = np.random.randn(2)
Y.observe(y)
m0 = np.dot(Lambda, y)
m1 = -0.5 * Lambda
check_message(m0, m1, 0, 'i->i', X1, F=F)
check_message(m0, m1, 0, X1, ['i'], ['i'], F=F)
# Check: mask with same shape
X1 = GaussianARD(np.random.randn(3, 2),
np.random.rand(3, 2),
shape=(2, ),
plates=(3, ))
x1 = X1.get_moments()
mask = np.array([True, False, True])
F = SumMultiply('i->i', X1)
Y = GaussianARD(F, tau, ndim=1)
Y.observe(data * np.ones((3, 2)), mask=mask)
m0 = tau * data * mask[:, np.newaxis] * np.ones(2)
m1 = -0.5 * tau * mask[:, np.newaxis, np.newaxis] * np.identity(2)
check_message(m0, m1, 0, 'i->i', X1, F=F)
check_message(m0, m1, 0, X1, ['i'], ['i'], F=F)
# Check: mask larger
X1 = GaussianARD(np.random.randn(2),
np.random.rand(2),
shape=(2, ),
plates=())
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(3, 2),
np.random.rand(3, 2),
shape=(2, ),
plates=(3, ))
x2 = X2.get_moments()
mask = np.array([True, False, True])
F = SumMultiply('i,i->i', X1, X2)
Y = GaussianARD(F, tau, plates=(3, ), ndim=1)
Y.observe(data * np.ones((3, 2)), mask=mask)
m0 = tau * data * np.sum(mask[:, np.newaxis] * x2[0], axis=0)
m1 = -0.5 * tau * np.sum(
mask[:, np.newaxis, np.newaxis] * x2[1] * np.identity(2), axis=0)
check_message(m0, m1, 0, 'i,i->i', X1, X2, F=F)
check_message(m0, m1, 0, X1, ['i'], X2, ['i'], ['i'], F=F)
# Check: mask for broadcasted plate
X1 = GaussianARD(np.random.randn(2),
np.random.rand(2),
ndim=1,
plates=(1, ))
x1 = X1.get_moments()
X2 = GaussianARD(np.random.randn(2),
np.random.rand(2),
ndim=1,
plates=(3, ))
x2 = X2.get_moments()
mask = np.array([True, False, True])
F = SumMultiply('i,i->i', X1, X2)
Y = GaussianARD(F, tau, plates=(3, ), ndim=1)
Y.observe(data * np.ones((3, 2)), mask=mask)
m0 = tau * data * np.sum(
mask[:, np.newaxis] * x2[0], axis=0, keepdims=True)
m1 = -0.5 * tau * np.sum(
mask[:, np.newaxis, np.newaxis] * x2[1] * np.identity(2),
axis=0,
keepdims=True)
check_message(m0, m1, 0, 'i->i', X1, F=F)
check_message(m0, m1, 0, X1, ['i'], ['i'], F=F)
# Test with constant nodes
N = 10
M = 8
D = 5
K = 3
a = np.random.randn(N, D)
B = Gaussian(
np.random.randn(D),
random.covariance(D),
)
C = GaussianARD(np.random.randn(M, 1, D, K),
np.random.rand(M, 1, D, K),
ndim=2)
F = SumMultiply('i,i,ij->', a, B, C)
tau = np.random.rand(M, N)
Y = GaussianARD(F, tau, plates=(M, N))
y = np.random.randn(M, N)
Y.observe(y)
(m0, m1) = F._message_to_parent(1)
np.testing.assert_allclose(
m0,
np.einsum('mn,ni,mnik->i', tau * y, a,
C.get_moments()[0]),
)
np.testing.assert_allclose(
m1,
np.einsum('mn,ni,nj,mnikjl->ij', -0.5 * tau, a, a,
C.get_moments()[1]),
)
# Check: Gaussian-gamma parents
X1 = GaussianGamma(np.random.randn(2), random.covariance(2),
np.random.rand(), np.random.rand())
x1 = X1.get_moments()
X2 = GaussianGamma(np.random.randn(2), random.covariance(2),
np.random.rand(), np.random.rand())
x2 = X2.get_moments()
F = SumMultiply('i,i->i', X1, X2)
V = random.covariance(2)
y = np.random.randn(2)
Y = Gaussian(F, V)
Y.observe(y)
m0 = np.dot(V, y) * x2[0]
m1 = -0.5 * V * x2[1]
m2 = -0.5 * np.einsum('i,ij,j', y, V,
y) * x2[2] #linalg.inner(V, x2[2], ndim=2)
m3 = 0.5 * 2 #linalg.chol_logdet(linalg.chol(V)) + 2*x2[3]
m = F._message_to_parent(0)
self.assertAllClose(m[0], m0)
self.assertAllClose(m[1], m1)
self.assertAllClose(m[2], m2)
self.assertAllClose(m[3], m3)
# Delta moments
N = 10
M = 8
D = 5
a = np.random.randn(N, D)
B = GaussianGamma(np.random.randn(D),
random.covariance(D),
np.random.rand(),
np.random.rand(),
ndim=1)
F = SumMultiply('i,i->', a, B)
tau = np.random.rand(M, N)
Y = GaussianARD(F, tau, plates=(M, N))
y = np.random.randn(M, N)
Y.observe(y)
(m0, m1, m2, m3) = F._message_to_parent(1)
np.testing.assert_allclose(
m0,
np.einsum('mn,ni->i', tau * y, a),
)
np.testing.assert_allclose(
m1,
np.einsum('mn,ni,nj->ij', -0.5 * tau, a, a),
)
np.testing.assert_allclose(
m2,
np.einsum('mn->', -0.5 * tau * y**2),
)
np.testing.assert_allclose(
m3,
np.einsum('mn->', 0.5 * np.ones(np.shape(tau))),
)
pass