def create_lazy_tensor(self):
chol = torch.tensor(
[[3, 0, 0, 0, 0], [-1, 2, 0, 0, 0], [1, 4, 1, 0, 0],
[0, 2, 3, 2, 0], [-4, -2, 1, 3, 4]],
dtype=torch.float,
requires_grad=True,
)
return CholLazyTensor(TriangularLazyTensor(chol))
def test_natgrad(self, D=5):
mu = torch.randn(D)
cov = torch.randn(D, D).tril_()
dist = MultivariateNormal(mu, CholLazyTensor(TriangularLazyTensor(cov)))
sample = dist.sample()
v_dist = NaturalVariationalDistribution(D)
v_dist.initialize_variational_distribution(dist)
mu = v_dist().mean.detach()
v_dist().log_prob(sample).squeeze().backward()
eta1 = mu.clone().requires_grad_(True)
eta2 = (mu[:, None] * mu + cov @ cov.t()).requires_grad_(True)
L = torch.cholesky(eta2 - eta1[:, None] * eta1)
dist2 = MultivariateNormal(eta1, CholLazyTensor(TriangularLazyTensor(L)))
dist2.log_prob(sample).squeeze().backward()
assert torch.allclose(v_dist.natural_vec.grad, eta1.grad)
assert torch.allclose(v_dist.natural_mat.grad, eta2.grad)
def test_invertible_init(self, D=5):
mu = torch.randn(D)
cov = torch.randn(D, D).tril_()
dist = MultivariateNormal(mu, CholLazyTensor(TriangularLazyTensor(cov)))
v_dist = TrilNaturalVariationalDistribution(D, mean_init_std=0.0)
v_dist.initialize_variational_distribution(dist)
out_dist = v_dist()
assert torch.allclose(out_dist.mean, dist.mean)
assert torch.allclose(out_dist.covariance_matrix, dist.covariance_matrix)
def create_lazy_tensor(self):
chol = torch.tensor(
[
[[3, 0, 0, 0, 0], [-1, 2, 0, 0, 0], [1, 4, 1, 0, 0],
[0, 2, 3, 2, 0], [-4, -2, 1, 3, 4]],
[[2, 0, 0, 0, 0], [3, 1, 0, 0, 0], [-2, 3, 2, 0, 0],
[-2, 1, -1, 3, 0], [-4, -4, 5, 2, 3]],
],
dtype=torch.float,
)
chol.add_(torch.eye(5).unsqueeze(0))
chol.requires_grad_(True)
return CholLazyTensor(TriangularLazyTensor(chol))
def test_natgrad(self, D=5):
mu = torch.randn(D)
cov = torch.randn(D, D)
cov = cov @ cov.t()
dist = MultivariateNormal(
mu,
CholLazyTensor(TriangularLazyTensor(torch.linalg.cholesky(cov))))
sample = dist.sample()
v_dist = TrilNaturalVariationalDistribution(D, mean_init_std=0.0)
v_dist.initialize_variational_distribution(dist)
v_dist().log_prob(sample).squeeze().backward()
dout_dnat1 = v_dist.natural_vec.grad
dout_dnat2 = v_dist.natural_tril_mat.grad
# mean_init_std=0. because we need to ensure both have the same distribution
v_dist_ref = NaturalVariationalDistribution(D, mean_init_std=0.0)
v_dist_ref.initialize_variational_distribution(dist)
v_dist_ref().log_prob(sample).squeeze().backward()
dout_dnat1_noforward_ref = v_dist_ref.natural_vec.grad
dout_dnat2_noforward_ref = v_dist_ref.natural_mat.grad
def f(natural_vec, natural_tril_mat):
"Transform natural_tril_mat to L"
Sigma = torch.inverse(-2 * natural_tril_mat)
mu = natural_vec
return mu, torch.linalg.cholesky(Sigma).inverse().tril()
(mu_ref, natural_tril_mat_ref), (dout_dmu_ref, dout_dnat2_ref) = jvp(
f,
(v_dist_ref.natural_vec.detach(), v_dist_ref.natural_mat.detach()),
(dout_dnat1_noforward_ref, dout_dnat2_noforward_ref),
)
assert torch.allclose(natural_tril_mat_ref,
v_dist.natural_tril_mat), "Sigma transformation"
assert torch.allclose(dout_dnat2_ref, dout_dnat2), "Sigma gradient"
assert torch.allclose(mu_ref, v_dist.natural_vec), "mu transformation"
assert torch.allclose(dout_dmu_ref, dout_dnat1), "mu gradient"
