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_lower_bound_contribution(self):
a = 15
b = 21
y = 4
x = Gamma(a, b)
x.observe(y)
testing.assert_allclose(
x.lower_bound_contribution(),
(
a * np.log(b) +
(a - 1) * np.log(y) -
b * y -
special.gammaln(a)
)
)
# Just one latent node so we'll get exact marginal likelihood
#
# p(Y) = p(Y,X)/p(X|Y) = p(Y|X) * p(X) / p(X|Y)
a = 2.3
b = 4.1
x = 1.9
y = 4.8
tau = Gamma(a, b)
Y = GaussianARD(x, tau)
Y.observe(y)
mu = x
nu = 2 * a
s2 = b / a
a_post = a + 0.5
b_post = b + 0.5*(y - x)**2
tau.update()
testing.assert_allclose(
[-b_post, a_post],
tau.phi
)
testing.assert_allclose(
Y.lower_bound_contribution() + tau.lower_bound_contribution(), # + tau.g,
(
special.gammaln((nu+1)/2)
- special.gammaln(nu/2)
- 0.5 * np.log(nu)
- 0.5 * np.log(np.pi)
- 0.5 * np.log(s2)
- 0.5 * (nu + 1) * np.log(
1 + (y - mu)**2 / (nu * s2)
)
)
)
return