本文整理汇总了Python中bayespy.nodes.GaussianARD.update方法的典型用法代码示例。如果您正苦于以下问题：Python GaussianARD.update方法的具体用法？Python GaussianARD.update怎么用？Python GaussianARD.update使用的例子？那么恭喜您, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类bayespy.nodes.GaussianARD的用法示例。
在下文中一共展示了GaussianARD.update方法的8个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: check_lower_bound
# 需要导入模块: from bayespy.nodes import GaussianARD [as 别名]
# 或者: from bayespy.nodes.GaussianARD import update [as 别名]
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())示例2: test_rotate_plates
# 需要导入模块: from bayespy.nodes import GaussianARD [as 别名]
# 或者: from bayespy.nodes.GaussianARD import update [as 别名]
def test_rotate_plates(self):
# Basic test for Gaussian vectors
X = GaussianARD(np.random.randn(3,2),
np.random.rand(3,2),
shape=(2,),
plates=(3,))
(u0, u1) = X.get_moments()
Cov = u1 - linalg.outer(u0, u0, ndim=1)
Q = np.random.randn(3,3)
Qu0 = np.einsum('ik,kj->ij', Q, u0)
QCov = np.einsum('k,kij->kij', np.sum(Q, axis=0)**2, Cov)
Qu1 = QCov + linalg.outer(Qu0, Qu0, ndim=1)
X.rotate_plates(Q, plate_axis=-1)
(u0, u1) = X.get_moments()
self.assertAllClose(u0, Qu0)
self.assertAllClose(u1, Qu1)
# Test full covariance, that is, with observations
X = GaussianARD(np.random.randn(3,2),
np.random.rand(3,2),
shape=(2,),
plates=(3,))
Y = Gaussian(X, [[2.0, 1.5], [1.5, 3.0]],
plates=(3,))
Y.observe(np.random.randn(3,2))
X.update()
(u0, u1) = X.get_moments()
Cov = u1 - linalg.outer(u0, u0, ndim=1)
Q = np.random.randn(3,3)
Qu0 = np.einsum('ik,kj->ij', Q, u0)
QCov = np.einsum('k,kij->kij', np.sum(Q, axis=0)**2, Cov)
Qu1 = QCov + linalg.outer(Qu0, Qu0, ndim=1)
X.rotate_plates(Q, plate_axis=-1)
(u0, u1) = X.get_moments()
self.assertAllClose(u0, Qu0)
self.assertAllClose(u1, Qu1)
pass示例3: check
# 需要导入模块: from bayespy.nodes import GaussianARD [as 别名]
# 或者: from bayespy.nodes.GaussianARD import update [as 别名]
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示例4: test_lowerbound
# 需要导入模块: from bayespy.nodes import GaussianARD [as 别名]
# 或者: from bayespy.nodes.GaussianARD import update [as 别名]
def test_lowerbound(self):
"""
Test the variational Bayesian lower bound term for GaussianARD.
"""
# Test vector formula with full noise covariance
m = np.random.randn(2)
alpha = np.random.rand(2)
y = np.random.randn(2)
X = GaussianARD(m, alpha, ndim=1)
V = np.array([[3,1],[1,3]])
Y = Gaussian(X, V)
Y.observe(y)
X.update()
Cov = np.linalg.inv(np.diag(alpha) + V)
mu = np.dot(Cov, np.dot(V, y) + alpha*m)
x2 = np.outer(mu, mu) + Cov
logH_X = (+ 2*0.5*(1+np.log(2*np.pi))
+ 0.5*np.log(np.linalg.det(Cov)))
logp_X = (- 2*0.5*np.log(2*np.pi)
+ 0.5*np.log(np.linalg.det(np.diag(alpha)))
- 0.5*np.sum(np.diag(alpha)
* (x2
- np.outer(mu,m)
- np.outer(m,mu)
+ np.outer(m,m))))
self.assertAllClose(logp_X + logH_X,
X.lower_bound_contribution())
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())
# Test scalar formula
check_lower_bound((), ())
# Test array formula
check_lower_bound((2,3), (2,3))
# Test dim-broadcasting of mu
check_lower_bound((3,1), (2,3,4))
# Test dim-broadcasting of alpha
check_lower_bound((2,3,4), (3,1))
# Test dim-broadcasting of mu and alpha
check_lower_bound((3,1), (3,1),
shape=(2,3,4))
# Test dim-broadcasting of mu with plates
check_lower_bound((), (),
plates_mu=(),
shape=(),
plates=(5,))
# BUG: Scalar parents for array variable caused einsum error
check_lower_bound((), (),
shape=(3,))
# BUG: Log-det was summed over plates
check_lower_bound((), (),
shape=(3,),
plates=(4,))
pass示例5: test_message_to_parent_alpha
# 需要导入模块: from bayespy.nodes import GaussianARD [as 别名]
# 或者: from bayespy.nodes.GaussianARD import update [as 别名]
def test_message_to_parent_alpha(self):
"""
Test the message from GaussianARD the 2nd parent (alpha).
"""
# Check formula with uncertain parent mu
mu = GaussianARD(1,1)
tau = Gamma(0.5*1e10, 1e10)
X = GaussianARD(mu,
tau)
X.observe(3)
(m0, m1) = tau._message_from_children()
self.assertAllClose(m0,
-0.5*(3**2 - 2*3*1 + 1**2+1))
self.assertAllClose(m1,
0.5)
# Check formula with uncertain node
tau = Gamma(1e10, 1e10)
X = GaussianARD(2, tau)
Y = GaussianARD(X, 1)
Y.observe(5)
X.update()
(m0, m1) = tau._message_from_children()
self.assertAllClose(m0,
-0.5*(1/(1+1)+3.5**2 - 2*3.5*2 + 2**2))
self.assertAllClose(m1,
0.5)
# Check alpha larger than mu
alpha = Gamma(np.ones((3,2,3))*1e10, 1e10)
X = GaussianARD(np.ones((2,3)),
alpha,
ndim=3)
X.observe(2*np.ones((3,2,3)))
(m0, m1) = alpha._message_from_children()
self.assertAllClose(m0 * np.ones((3,2,3)),
-0.5*(2**2 - 2*2*1 + 1**2) * np.ones((3,2,3)))
self.assertAllClose(m1*np.ones((3,2,3)),
0.5*np.ones((3,2,3)))
# Check mu larger than alpha
tau = Gamma(np.ones((2,3))*1e10, 1e10)
X = GaussianARD(np.ones((3,2,3)),
tau,
ndim=3)
X.observe(2*np.ones((3,2,3)))
(m0, m1) = tau._message_from_children()
self.assertAllClose(m0,
-0.5*(2**2 - 2*2*1 + 1**2) * 3 * np.ones((2,3)))
self.assertAllClose(m1 * np.ones((2,3)),
0.5 * 3 * np.ones((2,3)))
# Check node larger than mu and alpha
tau = Gamma(np.ones((3,))*1e10, 1e10)
X = GaussianARD(np.ones((2,3)),
tau,
shape=(3,2,3))
X.observe(2*np.ones((3,2,3)))
(m0, m1) = tau._message_from_children()
self.assertAllClose(m0 * np.ones(3),
-0.5*(2**2 - 2*2*1 + 1**2) * 6 * np.ones((3,)))
self.assertAllClose(m1 * np.ones(3),
0.5 * 6 * np.ones(3))
# Check plates for smaller mu than node
tau = Gamma(np.ones((4,1,2,3))*1e10, 1e10)
X = GaussianARD(GaussianARD(1, 1,
shape=(3,),
plates=(4,1,1)),
tau,
shape=(2,3),
plates=(4,5))
X.observe(2*np.ones((4,5,2,3)))
(m0, m1) = tau._message_from_children()
self.assertAllClose(m0 * np.ones((4,1,2,3)),
(-0.5 * (2**2 - 2*2*1 + 1**2+1)
* 5*np.ones((4,1,2,3))))
self.assertAllClose(m1 * np.ones((4,1,2,3)),
5*0.5 * np.ones((4,1,2,3)))
# Check mask
tau = Gamma(np.ones((4,3))*1e10, 1e10)
X = GaussianARD(np.ones(3),
tau,
shape=(3,),
plates=(2,4,))
X.observe(2*np.ones((2,4,3)), mask=[[True, False, True, False],
[False, True, True, False]])
(m0, m1) = tau._message_from_children()
self.assertAllClose(m0 * np.ones((4,3)),
(-0.5 * (2**2 - 2*2*1 + 1**2)
* np.ones((4,3))
* np.array([[1], [1], [2], [0]])))
self.assertAllClose(m1 * np.ones((4,3)),
0.5 * np.array([[1], [1], [2], [0]]) * np.ones((4,3)))
# Check non-ARD Gaussian child
mu = np.array([1,2])
alpha = np.array([3,4])
#.........这里部分代码省略.........
示例6: test_message_to_parent_mu
# 需要导入模块: from bayespy.nodes import GaussianARD [as 别名]
# 或者: from bayespy.nodes.GaussianARD import update [as 别名]
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()
#.........这里部分代码省略.........
示例7: test_message_to_child
# 需要导入模块: from bayespy.nodes import GaussianARD [as 别名]
# 或者: from bayespy.nodes.GaussianARD import update [as 别名]
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示例8: test_annealing
# 需要导入模块: from bayespy.nodes import GaussianARD [as 别名]
# 或者: from bayespy.nodes.GaussianARD import update [as 别名]
def test_annealing(self):
X = GaussianARD(3, 4)
X.initialize_from_parameters(-1, 6)
Q = VB(X)
Q.set_annealing(0.1)
#
# Check that the gradient is correct
#
# Initial parameters
phi0 = X.phi
# Gradient
rg = X.get_riemannian_gradient()
g = X.get_gradient(rg)
# Numerical gradient of the first parameter
eps = 1e-6
p0 = X.get_parameters()
l0 = Q.compute_lowerbound(ignore_masked=False)
g_num = [(), ()]
e = eps
p1 = p0[0] + e
X.set_parameters([p1, p0[1]])
l1 = Q.compute_lowerbound(ignore_masked=False)
g_num[0] = (l1 - l0) / eps
# Numerical gradient of the second parameter
p1 = p0[1] + e
X.set_parameters([p0[0], p1])
l1 = Q.compute_lowerbound(ignore_masked=False)
g_num[1] = (l1 - l0) / (eps)
# Check
self.assertAllClose(g[0],
g_num[0])
self.assertAllClose(g[1],
g_num[1])
#
# Gradient should be zero after updating
#
X.update()
# Initial parameters
phi0 = X.phi
# Numerical gradient of the first parameter
eps = 1e-8
p0 = X.get_parameters()
l0 = Q.compute_lowerbound(ignore_masked=False)
g_num = [(), ()]
e = eps
p1 = p0[0] + e
X.set_parameters([p1, p0[1]])
l1 = Q.compute_lowerbound(ignore_masked=False)
g_num[0] = (l1 - l0) / eps
# Numerical gradient of the second parameter
p1 = p0[1] + e
X.set_parameters([p0[0], p1])
l1 = Q.compute_lowerbound(ignore_masked=False)
g_num[1] = (l1 - l0) / (eps)
# Check
self.assertAllClose(0,
g_num[0],
atol=1e-5)
self.assertAllClose(0,
g_num[1],
atol=1e-5)
# Not at the optimum
X.initialize_from_parameters(-1, 6)
# Initial parameters
phi0 = X.phi
# Gradient
g = X.get_riemannian_gradient()
# Parameters after VB-EM update
X.update()
phi1 = X.phi
# Check
self.assertAllClose(g[0],
phi1[0] - phi0[0])
self.assertAllClose(g[1],
phi1[1] - phi0[1])
pass