def test_elbo(self):
mu0 = 1.5
sigma = 1.0
y_obs = np.array([1.6, 1.4])
# Create a model for test
with Model() as model:
mu = Normal('mu', mu=mu0, sd=sigma)
Normal('y', mu=mu, sd=1, observed=y_obs)
model_vars = inputvars(model.vars)
# Create variational gradient tensor
elbo, _ = _calc_elbo(model_vars, model, n_mcsamples=10000, random_seed=self.random_seed)
# Variational posterior parameters
uw_ = np.array([1.88, np.log(1)])
# Calculate elbo computed with MonteCarlo
uw_shared = shared(uw_, 'uw_shared')
elbo = CallableTensor(elbo)(uw_shared)
f = function([], elbo)
elbo_mc = f()
# Exact value
elbo_true = (-0.5 * (
3 + 3 * uw_[0]**2 - 2 * (y_obs[0] + y_obs[1] + mu0) * uw_[0] +
y_obs[0]**2 + y_obs[1]**2 + mu0**2 + 3 * np.log(2 * np.pi)) +
0.5 * (np.log(2 * np.pi) + 1))
np.testing.assert_allclose(elbo_mc, elbo_true, rtol=0, atol=1e-1)
def test_elbo(self):
mu0 = 1.5
sigma = 1.0
y_obs = np.array([1.6, 1.4])
# Create a model for test
with Model() as model:
mu = Normal('mu', mu=mu0, sd=sigma)
Normal('y', mu=mu, sd=1, observed=y_obs)
model_vars = inputvars(model.vars)
# Create variational gradient tensor
elbo, _ = _calc_elbo(model_vars, model, n_mcsamples=10000, random_seed=self.random_seed)
# Variational posterior parameters
uw_ = np.array([1.88, np.log(1)])
# Calculate elbo computed with MonteCarlo
uw_shared = shared(uw_, 'uw_shared')
elbo = CallableTensor(elbo)(uw_shared)
f = function([], elbo)
elbo_mc = f()
# Exact value
elbo_true = (-0.5 * (
3 + 3 * uw_[0]**2 - 2 * (y_obs[0] + y_obs[1] + mu0) * uw_[0] +
y_obs[0]**2 + y_obs[1]**2 + mu0**2 + 3 * np.log(2 * np.pi)) +
0.5 * (np.log(2 * np.pi) + 1))
np.testing.assert_allclose(elbo_mc, elbo_true, rtol=0, atol=1e-1)