def _init_posterior(self):
"""
Get an initial guess at the variational posterior over the induced
outputs.
Just build a GP out of a few data and use its posterior.
This could be far worse than expected if the likelihood is non-Gaussian,
but we don't need this to be great--just good enough to get started.
"""
i = np.random.permutation(self.num_data)[0:min(self.num_data, 100)]
x, y = self.X[i].data.numpy(), self.Y[i].data.numpy()
# Likelihood needs to be Gaussian for exact inference in GPR
likelihood = (self.likelihood if isinstance(self.likelihood, Gaussian)
else Gaussian(variance=0.01 * y.var()))
model = GPR(x,
y,
self.kernel,
mean_function=self.mean_function,
likelihood=likelihood)
mean, cov = model.predict_f(self.Z, diag=False)
mean -= self.mean_function(self.Z)
chol_cov = cholesky(cov)
return Param(mean), Param(chol_cov, transform=LowerCholeskyTransform())
def get_transforms(cache_size):
transforms = [
AbsTransform(cache_size=cache_size),
ExpTransform(cache_size=cache_size),
PowerTransform(exponent=2,
cache_size=cache_size),
PowerTransform(exponent=torch.tensor(5.).normal_(),
cache_size=cache_size),
PowerTransform(exponent=torch.tensor(5.).normal_(),
cache_size=cache_size),
SigmoidTransform(cache_size=cache_size),
TanhTransform(cache_size=cache_size),
AffineTransform(0, 1, cache_size=cache_size),
AffineTransform(1, -2, cache_size=cache_size),
AffineTransform(torch.randn(5),
torch.randn(5),
cache_size=cache_size),
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
SoftmaxTransform(cache_size=cache_size),
SoftplusTransform(cache_size=cache_size),
StickBreakingTransform(cache_size=cache_size),
LowerCholeskyTransform(cache_size=cache_size),
CorrCholeskyTransform(cache_size=cache_size),
ComposeTransform([
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
]),
ComposeTransform([
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
ExpTransform(cache_size=cache_size),
]),
ComposeTransform([
AffineTransform(0, 1, cache_size=cache_size),
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
AffineTransform(1, -2, cache_size=cache_size),
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
]),
ReshapeTransform((4, 5), (2, 5, 2)),
IndependentTransform(
AffineTransform(torch.randn(5),
torch.randn(5),
cache_size=cache_size),
1),
CumulativeDistributionTransform(Normal(0, 1)),
]
transforms += [t.inv for t in transforms]
return transforms
def test_compose_transform_shapes():
transform0 = ExpTransform()
transform1 = SoftmaxTransform()
transform2 = LowerCholeskyTransform()
assert transform0.event_dim == 0
assert transform1.event_dim == 1
assert transform2.event_dim == 2
assert ComposeTransform([transform0, transform1]).event_dim == 1
assert ComposeTransform([transform0, transform2]).event_dim == 2
assert ComposeTransform([transform1, transform2]).event_dim == 2
def get_transforms(cache_size):
transforms = [
AbsTransform(cache_size=cache_size),
ExpTransform(cache_size=cache_size),
PowerTransform(exponent=2,
cache_size=cache_size),
PowerTransform(exponent=torch.tensor(5.).normal_(),
cache_size=cache_size),
SigmoidTransform(cache_size=cache_size),
TanhTransform(cache_size=cache_size),
AffineTransform(0, 1, cache_size=cache_size),
AffineTransform(1, -2, cache_size=cache_size),
AffineTransform(torch.randn(5),
torch.randn(5),
cache_size=cache_size),
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
SoftmaxTransform(cache_size=cache_size),
StickBreakingTransform(cache_size=cache_size),
LowerCholeskyTransform(cache_size=cache_size),
CorrCholeskyTransform(cache_size=cache_size),
ComposeTransform([
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
]),
ComposeTransform([
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
ExpTransform(cache_size=cache_size),
]),
ComposeTransform([
AffineTransform(0, 1, cache_size=cache_size),
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
AffineTransform(1, -2, cache_size=cache_size),
AffineTransform(torch.randn(4, 5),
torch.randn(4, 5),
cache_size=cache_size),
]),
]
transforms += [t.inv for t in transforms]
return transforms
def test_compose_transform_shapes():
transform0 = ExpTransform()
transform1 = SoftmaxTransform()
transform2 = LowerCholeskyTransform()
assert transform0.event_dim == 0
assert transform1.event_dim == 1
assert transform2.event_dim == 2
assert ComposeTransform([transform0, transform1]).event_dim == 1
assert ComposeTransform([transform0, transform2]).event_dim == 2
assert ComposeTransform([transform1, transform2]).event_dim == 2
transform0 = ExpTransform()
transform1 = SoftmaxTransform()
transform2 = LowerCholeskyTransform()
base_dist0 = Normal(torch.zeros(4, 4), torch.ones(4, 4))
base_dist1 = Dirichlet(torch.ones(4, 4))
base_dist2 = Normal(torch.zeros(3, 4, 4), torch.ones(3, 4, 4))
@pytest.mark.parametrize('batch_shape, event_shape, dist', [
((4, 4), (), base_dist0),
((4,), (4,), base_dist1),
((4, 4), (), TransformedDistribution(base_dist0, [transform0])),
((4,), (4,), TransformedDistribution(base_dist0, [transform1])),
((4,), (4,), TransformedDistribution(base_dist0, [transform0, transform1])),
((), (4, 4), TransformedDistribution(base_dist0, [transform0, transform2])),
((4,), (4,), TransformedDistribution(base_dist0, [transform1, transform0])),
((), (4, 4), TransformedDistribution(base_dist0, [transform1, transform2])),
((), (4, 4), TransformedDistribution(base_dist0, [transform2, transform0])),
def _transform_to_positive_definite(constraint):
return ComposeTransform([LowerCholeskyTransform(), CholeskyTransform().inv])