def backward(self, *inputs: Tensor) -> List[MultivariateNormal]:
"""Implement backwards pass."""
output_sequence, input_sequence = inputs
_, _, dim_inputs = input_sequence.shape
batch_size, sequence_length, dim_outputs = output_sequence.shape
dim_states = self.dim_states
num_particles = self.num_particles
dim_delta = dim_states - dim_outputs
shape = (batch_size, dim_delta, num_particles)
################################################################################
# Final Pseudo Measurement #
################################################################################
y = output_sequence[:, -1].expand(num_particles, -1, -1).permute(1, 2, 0)
x_tilde_obs = self.emissions(y)
loc = torch.cat((x_tilde_obs.loc, torch.zeros(*shape)), dim=1)
cov = torch.cat((x_tilde_obs.covariance_matrix,
torch.diag_embed(torch.ones(*shape))), dim=1)
x_tilde = MultivariateNormal(loc, cov)
outputs = [x_tilde]
for t in reversed(range(sequence_length - 1)):
############################################################################
# PREDICT Previous pseudo-measurement #
############################################################################
y = output_sequence[:, t].expand(num_particles, -1, -1).permute(1, 2, 0)
x_tilde_obs = self.emissions(y)
u = input_sequence[:, t].expand(num_particles, batch_size, dim_inputs)
u = u.permute(1, 2, 0)
# Here change the order of y_tilde for identity dynamics (those that
# return the first dim_output states). The reason for this is that we
# already append the y_ from emissions in the first components.
# We can check this by comparing before computing next_x_tilde
# loc[0, :, 0], x.loc[0, :, 0], x_tilde[0, :, 0]
delta_idx = torch.arange(dim_outputs, dim_states)
idx = torch.cat((delta_idx, torch.arange(dim_outputs)))
x_tilde_samples = x_tilde.rsample()[:, idx] # exchange indexes
x_tilde_u = torch.cat((x_tilde_samples, u), dim=1)
next_x_tilde = self.backward_model(x_tilde_u)
next_x_tilde.loc += x_tilde_samples[:, :dim_delta]
loc = torch.cat((x_tilde_obs.loc, next_x_tilde.loc), dim=1)
cov = torch.cat((x_tilde_obs.covariance_matrix,
next_x_tilde.covariance_matrix), dim=1)
############################################################################
# PREDICT Outputs #
############################################################################
x_tilde = MultivariateNormal(loc, cov)
outputs.append(x_tilde)
assert len(outputs) == sequence_length
return outputs[::-1]
def _draw_gp_function(self, X, lengthscale=10.0, kernel_str="RBF"):
if kernel_str == "RBF":
kernel = RBFKernel()
elif kernel_str == "Mat":
kernel = MaternKernel(nu=0.5)
else:
raise Exception("Invalid kernel string: {}".format(kernel_str))
kernel.lengthscale = lengthscale
with torch.no_grad():
lazy_cov = kernel(X)
mean = torch.zeros(lazy_cov.size(0))
mvn = MultivariateNormal(mean, lazy_cov)
Y = mvn.rsample()[:, None]
return Y
def test_base_sample_shape(self):
a = torch.randn(5, 10)
lazy_square_a = RootLazyTensor(lazify(a))
dist = MultivariateNormal(torch.zeros(5), lazy_square_a)
# check that providing the base samples is okay
samples = dist.rsample(torch.Size((16, )),
base_samples=torch.randn(16, 10))
self.assertEqual(samples.shape, torch.Size((16, 5)))
# check that an event shape of base samples fails
self.assertRaises(RuntimeError,
dist.rsample,
torch.Size((16, )),
base_samples=torch.randn(16, 5))
# check that the proper event shape of base samples is okay for
# a non root lt
nonlazy_square_a = lazify(lazy_square_a.evaluate())
dist = MultivariateNormal(torch.zeros(5), nonlazy_square_a)
samples = dist.rsample(torch.Size((16, )),
base_samples=torch.randn(16, 5))
self.assertEqual(samples.shape, torch.Size((16, 5)))
def test_gauss_hermite_quadrature_1D_mvn_batch(self, cuda=False):
func = lambda x: torch.sin(x)
means = torch.randn(3, 10)
variances = torch.randn(3, 10).abs()
quadrature = GaussHermiteQuadrature1D()
if cuda:
means = means.cuda()
variances = variances.cuda()
quadrature = quadrature.cuda()
dist = MultivariateNormal(means, DiagLazyTensor(variances.sqrt()))
# Use quadrature
results = quadrature(func, dist)
# Use Monte-Carlo
samples = dist.rsample(torch.Size([20000]))
actual = func(samples).mean(0)
self.assertLess(torch.mean(torch.abs(actual - results)), 0.1)