def check_lower_bound(shape_mu, shape_alpha, plates_mu=(), **kwargs):
M = GaussianARD(np.ones(plates_mu + shape_mu),
np.ones(plates_mu + shape_mu),
shape=shape_mu,
plates=plates_mu)
if not ('ndim' in kwargs or 'shape' in kwargs):
kwargs['ndim'] = len(shape_mu)
X = GaussianARD(M,
2*np.ones(shape_alpha),
**kwargs)
Y = GaussianARD(X,
3*np.ones(X.get_shape(0)),
**kwargs)
Y.observe(4*np.ones(Y.get_shape(0)))
X.update()
Cov = 1/(2+3)
mu = Cov * (2*1 + 3*4)
x2 = mu**2 + Cov
logH_X = (+ 0.5*(1+np.log(2*np.pi))
+ 0.5*np.log(Cov))
logp_X = (- 0.5*np.log(2*np.pi)
+ 0.5*np.log(2)
- 0.5*2*(x2 - 2*mu*1 + 1**2+1))
r = np.prod(X.get_shape(0))
self.assertAllClose(r * (logp_X + logH_X),
X.lower_bound_contribution())
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 check(indices, plates, shape, axis=-1, use_mask=False):
mu = np.random.rand(*(plates+shape))
alpha = np.random.rand(*(plates+shape))
X = GaussianARD(mu, alpha, shape=shape, plates=plates)
Y = Take(X, indices, plate_axis=axis)
Z = GaussianARD(Y, 1, shape=shape)
z = np.random.randn(*(Z.get_shape(0)))
if use_mask:
mask = np.mod(np.reshape(np.arange(np.prod(Z.plates)), Z.plates), 2) != 0
else:
mask = True
Z.observe(z, mask=mask)
X.update()
(x0, x1) = X.get_moments()
# For comparison, build the same model brute force
X = GaussianARD(mu, alpha, shape=shape, plates=plates)
# Number of trailing plate axes before the take axis
N = len(X.plates) + axis
# Reshape the take axes into a single axis
z_shape = X.plates[:axis] + (-1,)
if axis < -1:
z_shape = z_shape + X.plates[(axis+1):]
z_shape = z_shape + shape
z = np.reshape(z, z_shape)
# Reshape the take axes into a single axis
if use_mask:
mask_shape = X.plates[:axis] + (-1,)
if axis < -1:
mask_shape = mask_shape + X.plates[(axis+1):]
mask = np.reshape(mask, mask_shape)
for (j, i) in enumerate(range(np.size(indices))):
ind = np.array(indices).flatten()[i]
index_x = N*(slice(None),) + (ind,)
index_z = N*(slice(None),) + (j,)
# print(index)
Xi = X[index_x]
zi = z[index_z]
Zi = GaussianARD(Xi, 1, ndim=len(shape))
if use_mask:
maski = mask[index_z]
else:
maski = True
Zi.observe(zi, mask=maski)
X.update()
self.assertAllClose(
x0,
X.get_moments()[0],
)
self.assertAllClose(
x1,
X.get_moments()[1],
)
return
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
