def test_lower_bound(self):
"""
Test the Wishart VB lower bound
"""
#
# By having the Wishart node as the only latent node, VB will give exact
# results, thus the VB lower bound is the true marginal log likelihood.
# Thus, check that they are equal. The true marginal likelihood is the
# multivariate Student-t distribution.
#
np.random.seed(42)
D = 3
n = (D-1) + np.random.uniform(0.1, 0.5)
V = random.covariance(D)
Lambda = Wishart(n, V)
mu = np.random.randn(D)
Y = Gaussian(mu, Lambda)
y = np.random.randn(D)
Y.observe(y)
Lambda.update()
L = Y.lower_bound_contribution() + Lambda.lower_bound_contribution()
mu = mu
nu = n + 1 - D
Cov = V / nu
self.assertAllClose(L,
_student_logpdf(y,
mu,
Cov,
nu))
pass
def test_lower_bound(self):
"""
Test the Wishart VB lower bound
"""
#
# By having the Wishart node as the only latent node, VB will give exact
# results, thus the VB lower bound is the true marginal log likelihood.
# Thus, check that they are equal. The true marginal likelihood is the
# multivariate Student-t distribution.
#
np.random.seed(42)
D = 3
n = (D-1) + np.random.uniform(0.1, 0.5)
V = random.covariance(D)
Lambda = Wishart(n, V)
mu = np.random.randn(D)
Y = Gaussian(mu, Lambda)
y = np.random.randn(D)
Y.observe(y)
Lambda.update()
L = Y.lower_bound_contribution() + Lambda.lower_bound_contribution()
mu = mu
nu = n + 1 - D
Cov = V / nu
self.assertAllClose(L,
_student_logpdf(y,
mu,
Cov,
nu))
pass
