def test_riemannian_gradient(self):
"""Test Riemannian gradient of a Gamma node."""
#
# Without observations
#
# Construct model
a = np.random.rand()
b = np.random.rand()
tau = Gamma(a, b)
# Random initialization
tau.initialize_from_parameters(np.random.rand(),
np.random.rand())
# Initial parameters
phi0 = tau.phi
# Gradient
g = tau.get_riemannian_gradient()
# Parameters after VB-EM update
tau.update()
phi1 = tau.phi
# Check
self.assertAllClose(g[0],
phi1[0] - phi0[0])
self.assertAllClose(g[1],
phi1[1] - phi0[1])
#
# With observations
#
# Construct model
a = np.random.rand()
b = np.random.rand()
tau = Gamma(a, b)
mu = np.random.randn()
Y = GaussianARD(mu, tau)
Y.observe(np.random.randn())
# Random initialization
tau.initialize_from_parameters(np.random.rand(),
np.random.rand())
# Initial parameters
phi0 = tau.phi
# Gradient
g = tau.get_riemannian_gradient()
# Parameters after VB-EM update
tau.update()
phi1 = tau.phi
# Check
self.assertAllClose(g[0],
phi1[0] - phi0[0])
self.assertAllClose(g[1],
phi1[1] - phi0[1])
pass
def test_gradient(self):
"""Test standard gradient of a Gamma node."""
D = 3
np.random.seed(42)
#
# Without observations
#
# Construct model
a = np.random.rand(D)
b = np.random.rand(D)
tau = Gamma(a, b)
Q = VB(tau)
# Random initialization
tau.initialize_from_parameters(np.random.rand(D),
np.random.rand(D))
# Initial parameters
phi0 = tau.phi
# Gradient
rg = tau.get_riemannian_gradient()
g = tau.get_gradient(rg)
# Numerical gradient
eps = 1e-8
p0 = tau.get_parameters()
l0 = Q.compute_lowerbound(ignore_masked=False)
g_num = [np.zeros(D), np.zeros(D)]
for i in range(D):
e = np.zeros(D)
e[i] = eps
p1 = p0[0] + e
tau.set_parameters([p1, p0[1]])
l1 = Q.compute_lowerbound(ignore_masked=False)
g_num[0][i] = (l1 - l0) / eps
for i in range(D):
e = np.zeros(D)
e[i] = eps
p1 = p0[1] + e
tau.set_parameters([p0[0], p1])
l1 = Q.compute_lowerbound(ignore_masked=False)
g_num[1][i] = (l1 - l0) / eps
# Check
self.assertAllClose(g[0],
g_num[0])
self.assertAllClose(g[1],
g_num[1])
#
# With observations
#
# Construct model
a = np.random.rand(D)
b = np.random.rand(D)
tau = Gamma(a, b)
mu = np.random.randn(D)
Y = GaussianARD(mu, tau)
Y.observe(np.random.randn(D))
Q = VB(Y, tau)
# Random initialization
tau.initialize_from_parameters(np.random.rand(D),
np.random.rand(D))
# Initial parameters
phi0 = tau.phi
# Gradient
rg = tau.get_riemannian_gradient()
g = tau.get_gradient(rg)
# Numerical gradient
eps = 1e-8
p0 = tau.get_parameters()
l0 = Q.compute_lowerbound(ignore_masked=False)
g_num = [np.zeros(D), np.zeros(D)]
for i in range(D):
e = np.zeros(D)
e[i] = eps
p1 = p0[0] + e
tau.set_parameters([p1, p0[1]])
l1 = Q.compute_lowerbound(ignore_masked=False)
g_num[0][i] = (l1 - l0) / eps
for i in range(D):
e = np.zeros(D)
e[i] = eps
p1 = p0[1] + e
tau.set_parameters([p0[0], p1])
l1 = Q.compute_lowerbound(ignore_masked=False)
g_num[1][i] = (l1 - l0) / eps
# Check
self.assertAllClose(g[0],
g_num[0])
self.assertAllClose(g[1],
g_num[1])
pass
