def test_gradient(self):
"""Test standard gradient of a Gaussian node."""
D = 3
np.random.seed(42)
#
# Without observations
#
# Construct model
mu = np.random.randn(D)
Lambda = random.covariance(D)
X = Gaussian(mu, Lambda)
# Random initialization
mu0 = np.random.randn(D)
Lambda0 = random.covariance(D)
X.initialize_from_parameters(mu0, Lambda0)
Q = VB(X)
# Initial parameters
phi0 = X.phi
# Gradient
rg = X.get_riemannian_gradient()
g = X.get_gradient(rg)
# Numerical gradient
eps = 1e-6
p0 = X.get_parameters()
l0 = Q.compute_lowerbound(ignore_masked=False)
g_num = [np.zeros(D), np.zeros((D, D))]
for i in range(D):
e = np.zeros(D)
e[i] = eps
p1 = p0[0] + e
X.set_parameters([p1, p0[1]])
l1 = Q.compute_lowerbound(ignore_masked=False)
g_num[0][i] = (l1 - l0) / eps
for i in range(D):
for j in range(i + 1):
e = np.zeros((D, D))
e[i, j] += eps
e[j, i] += eps
p1 = p0[1] + e
X.set_parameters([p0[0], p1])
l1 = Q.compute_lowerbound(ignore_masked=False)
g_num[1][i, j] = (l1 - l0) / (2 * eps)
g_num[1][j, i] = (l1 - l0) / (2 * eps)
# Check
self.assertAllClose(g[0], g_num[0])
self.assertAllClose(g[1], g_num[1])
#
# With observations
#
# Construct model
mu = np.random.randn(D)
Lambda = random.covariance(D)
X = Gaussian(mu, Lambda)
# Random initialization
mu0 = np.random.randn(D)
Lambda0 = random.covariance(D)
X.initialize_from_parameters(mu0, Lambda0)
V = random.covariance(D)
Y = Gaussian(X, V)
Y.observe(np.random.randn(D))
Q = VB(Y, X)
# Initial parameters
phi0 = X.phi
# Gradient
rg = X.get_riemannian_gradient()
g = X.get_gradient(rg)
# Numerical gradient
eps = 1e-6
p0 = X.get_parameters()
l0 = Q.compute_lowerbound()
g_num = [np.zeros(D), np.zeros((D, D))]
for i in range(D):
e = np.zeros(D)
e[i] = eps
p1 = p0[0] + e
X.set_parameters([p1, p0[1]])
l1 = Q.compute_lowerbound()
g_num[0][i] = (l1 - l0) / eps
for i in range(D):
for j in range(i + 1):
e = np.zeros((D, D))
e[i, j] += eps
e[j, i] += eps
p1 = p0[1] + e
X.set_parameters([p0[0], p1])
l1 = Q.compute_lowerbound()
g_num[1][i, j] = (l1 - l0) / (2 * eps)
g_num[1][j, i] = (l1 - l0) / (2 * eps)
# Check
self.assertAllClose(g[0], g_num[0])
self.assertAllClose(g[1], g_num[1])
#
# With plates
#
# Construct model
K = D + 1
mu = np.random.randn(D)
Lambda = random.covariance(D)
X = Gaussian(mu, Lambda, plates=(K, ))
V = random.covariance(D, size=(K, ))
Y = Gaussian(X, V)
Y.observe(np.random.randn(K, D))
Q = VB(Y, X)
# Random initialization
mu0 = np.random.randn(*(X.get_shape(0)))
Lambda0 = random.covariance(D, size=X.plates)
X.initialize_from_parameters(mu0, Lambda0)
# Initial parameters
phi0 = X.phi
# Gradient
rg = X.get_riemannian_gradient()
g = X.get_gradient(rg)
# Numerical gradient
eps = 1e-6
p0 = X.get_parameters()
l0 = Q.compute_lowerbound()
g_num = [np.zeros(X.get_shape(0)), np.zeros(X.get_shape(1))]
for k in range(K):
for i in range(D):
e = np.zeros(X.get_shape(0))
e[k, i] = eps
p1 = p0[0] + e
X.set_parameters([p1, p0[1]])
l1 = Q.compute_lowerbound()
g_num[0][k, i] = (l1 - l0) / eps
for i in range(D):
for j in range(i + 1):
e = np.zeros(X.get_shape(1))
e[k, i, j] += eps
e[k, j, i] += eps
p1 = p0[1] + e
X.set_parameters([p0[0], p1])
l1 = Q.compute_lowerbound()
g_num[1][k, i, j] = (l1 - l0) / (2 * eps)
g_num[1][k, j, i] = (l1 - l0) / (2 * eps)
# Check
self.assertAllClose(g[0], g_num[0])
self.assertAllClose(g[1], g_num[1])
pass
def test_gradient(self):
"""Test standard gradient of a Gaussian node."""
D = 3
np.random.seed(42)
#
# Without observations
#
# Construct model
mu = np.random.randn(D)
Lambda = random.covariance(D)
X = Gaussian(mu, Lambda)
# Random initialization
mu0 = np.random.randn(D)
Lambda0 = random.covariance(D)
X.initialize_from_parameters(mu0, Lambda0)
Q = VB(X)
# Initial parameters
phi0 = X.phi
# Gradient
rg = X.get_riemannian_gradient()
g = X.get_gradient(rg)
# Numerical gradient
eps = 1e-6
p0 = X.get_parameters()
l0 = Q.compute_lowerbound(ignore_masked=False)
g_num = [np.zeros(D), np.zeros((D,D))]
for i in range(D):
e = np.zeros(D)
e[i] = eps
p1 = p0[0] + e
X.set_parameters([p1, p0[1]])
l1 = Q.compute_lowerbound(ignore_masked=False)
g_num[0][i] = (l1 - l0) / eps
for i in range(D):
for j in range(i+1):
e = np.zeros((D,D))
e[i,j] += eps
e[j,i] += eps
p1 = p0[1] + e
X.set_parameters([p0[0], p1])
l1 = Q.compute_lowerbound(ignore_masked=False)
g_num[1][i,j] = (l1 - l0) / (2*eps)
g_num[1][j,i] = (l1 - l0) / (2*eps)
# Check
self.assertAllClose(g[0],
g_num[0])
self.assertAllClose(g[1],
g_num[1])
#
# With observations
#
# Construct model
mu = np.random.randn(D)
Lambda = random.covariance(D)
X = Gaussian(mu, Lambda)
# Random initialization
mu0 = np.random.randn(D)
Lambda0 = random.covariance(D)
X.initialize_from_parameters(mu0, Lambda0)
V = random.covariance(D)
Y = Gaussian(X, V)
Y.observe(np.random.randn(D))
Q = VB(Y, X)
# Initial parameters
phi0 = X.phi
# Gradient
rg = X.get_riemannian_gradient()
g = X.get_gradient(rg)
# Numerical gradient
eps = 1e-6
p0 = X.get_parameters()
l0 = Q.compute_lowerbound()
g_num = [np.zeros(D), np.zeros((D,D))]
for i in range(D):
e = np.zeros(D)
e[i] = eps
p1 = p0[0] + e
X.set_parameters([p1, p0[1]])
l1 = Q.compute_lowerbound()
g_num[0][i] = (l1 - l0) / eps
for i in range(D):
for j in range(i+1):
e = np.zeros((D,D))
e[i,j] += eps
e[j,i] += eps
p1 = p0[1] + e
X.set_parameters([p0[0], p1])
l1 = Q.compute_lowerbound()
g_num[1][i,j] = (l1 - l0) / (2*eps)
g_num[1][j,i] = (l1 - l0) / (2*eps)
# Check
self.assertAllClose(g[0],
g_num[0])
self.assertAllClose(g[1],
g_num[1])
#
# With plates
#
# Construct model
K = D+1
mu = np.random.randn(D)
Lambda = random.covariance(D)
X = Gaussian(mu, Lambda, plates=(K,))
V = random.covariance(D, size=(K,))
Y = Gaussian(X, V)
Y.observe(np.random.randn(K,D))
Q = VB(Y, X)
# Random initialization
mu0 = np.random.randn(*(X.get_shape(0)))
Lambda0 = random.covariance(D, size=X.plates)
X.initialize_from_parameters(mu0, Lambda0)
# Initial parameters
phi0 = X.phi
# Gradient
rg = X.get_riemannian_gradient()
g = X.get_gradient(rg)
# Numerical gradient
eps = 1e-6
p0 = X.get_parameters()
l0 = Q.compute_lowerbound()
g_num = [np.zeros(X.get_shape(0)), np.zeros(X.get_shape(1))]
for k in range(K):
for i in range(D):
e = np.zeros(X.get_shape(0))
e[k,i] = eps
p1 = p0[0] + e
X.set_parameters([p1, p0[1]])
l1 = Q.compute_lowerbound()
g_num[0][k,i] = (l1 - l0) / eps
for i in range(D):
for j in range(i+1):
e = np.zeros(X.get_shape(1))
e[k,i,j] += eps
e[k,j,i] += eps
p1 = p0[1] + e
X.set_parameters([p0[0], p1])
l1 = Q.compute_lowerbound()
g_num[1][k,i,j] = (l1 - l0) / (2*eps)
g_num[1][k,j,i] = (l1 - l0) / (2*eps)
# Check
self.assertAllClose(g[0],
g_num[0])
self.assertAllClose(g[1],
g_num[1])
pass
