def test_initialization(self):
"""
Test initialization methods of GaussianARD
"""
X = GaussianARD(1, 2, shape=(2, ), plates=(3, ))
# Prior initialization
mu = 1 * np.ones((3, 2))
alpha = 2 * np.ones((3, 2))
X.initialize_from_prior()
u = X._message_to_child()
self.assertAllClose(u[0] * np.ones((3, 2)), mu)
self.assertAllClose(
u[1] * np.ones((3, 2, 2)),
linalg.outer(mu, mu, ndim=1) + misc.diag(1 / alpha, ndim=1))
# Parameter initialization
mu = np.random.randn(3, 2)
alpha = np.random.rand(3, 2)
X.initialize_from_parameters(mu, alpha)
u = X._message_to_child()
self.assertAllClose(u[0], mu)
self.assertAllClose(
u[1],
linalg.outer(mu, mu, ndim=1) + misc.diag(1 / alpha, ndim=1))
# Value initialization
x = np.random.randn(3, 2)
X.initialize_from_value(x)
u = X._message_to_child()
self.assertAllClose(u[0], x)
self.assertAllClose(u[1], linalg.outer(x, x, ndim=1))
# Random initialization
X.initialize_from_random()
pass
def test_initialization(self):
"""
Test initialization methods of GaussianARD
"""
X = GaussianARD(1, 2, shape=(2,), plates=(3,))
# Prior initialization
mu = 1 * np.ones((3, 2))
alpha = 2 * np.ones((3, 2))
X.initialize_from_prior()
u = X._message_to_child()
self.assertAllClose(u[0]*np.ones((3,2)),
mu)
self.assertAllClose(u[1]*np.ones((3,2,2)),
linalg.outer(mu, mu, ndim=1) +
misc.diag(1/alpha, ndim=1))
# Parameter initialization
mu = np.random.randn(3, 2)
alpha = np.random.rand(3, 2)
X.initialize_from_parameters(mu, alpha)
u = X._message_to_child()
self.assertAllClose(u[0], mu)
self.assertAllClose(u[1], linalg.outer(mu, mu, ndim=1) +
misc.diag(1/alpha, ndim=1))
# Value initialization
x = np.random.randn(3, 2)
X.initialize_from_value(x)
u = X._message_to_child()
self.assertAllClose(u[0], x)
self.assertAllClose(u[1], linalg.outer(x, x, ndim=1))
# Random initialization
X.initialize_from_random()
pass
x = np.random.randn(2, 100)
data = np.dot(c, x) + 0.1 * np.random.randn(10, 100)
# data:10×100
Y.observe(data)
#（ Missing values）
Y.observe(data,
mask=[[True], [False], [False], [True], [True], [False], [True],
[True], [True], [False]])
# ２： Choosing the inference method
from bayespy.inference import VB
Q = VB(Y, C, X, alpha, tau)
# ３： Initializing the posterior approximation
X.initialize_from_parameters(np.random.randn(1, 100, D), 10)
# ４： Running the inference algorithm
# Q.update()
# Q.update(C, X)
# Q.update(C, X, C, tau)
# Q.update(repeat=10)
# Q.update(repeat=1000)
Q.update(repeat=10000, tol=1e-5)
# C.update()
#( 5 : Parameter expansion 収束が遅い時)
# from bayespy.inference.vmp import transformations
# rotX = transformations.RotateGaussianARD(X)
# rotC = transformations.RotateGaussianARD(C, alpha)
# R = transformations.RotationOptimizer(rotC, rotX, D)
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
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
