def test_last_dim_is_batch(self):
a = (
torch.tensor([[0.1, 0.2], [0.3, 0.4], [0.5, 0.5]])
.view(3, 2)
.transpose(-1, -2)
)
b = (
torch.tensor([[0.5, 0.6], [0.7, 0.8], [0.6, 0.6]])
.view(3, 2)
.transpose(-1, -2)
)
power = 1
offset = 1
kernel = DownsamplingKernel()
kernel.initialize(power=power, offset=offset)
kernel.eval()
res = kernel(a, b, last_dim_is_batch=True).evaluate()
actual = torch.zeros(3, 2, 2)
diff = torch.tensor([[0.45, 0.36], [0.4, 0.32]])
actual[0, :, :] = offset + diff.pow(1 + power)
diff = torch.tensor([[0.21, 0.14], [0.18, 0.12]])
actual[1, :, :] = offset + diff.pow(1 + power)
diff = torch.tensor([[0.2, 0.2], [0.2, 0.2]])
actual[2, :, :] = offset + diff.pow(1 + power)
self.assertLess(torch.norm(res - actual), 1e-5)
def test_subset_computes_active_downsampling_function_batch(self):
a = torch.tensor([[0.1, 0.2, 0.2], [0.3, 0.4, 0.2], [0.5, 0.5, 0.5]]).view(
3, 3, 1
)
a_p = torch.tensor([[0.1, 0.2, 0.2], [0.3, 0.4, 0.2], [0.5, 0.5, 0.5]]).view(
3, 3, 1
)
a = torch.cat((a, a_p), 2)
b = torch.tensor([[0.5, 0.6, 0.1], [0.7, 0.8, 0.2], [0.6, 0.6, 0.5]]).view(
3, 3, 1
)
power = 1
offset = 1
kernel = DownsamplingKernel(batch_shape=torch.Size([3]), active_dims=[0])
kernel.initialize(power=power, offset=offset)
kernel.eval()
res = kernel(a, b).evaluate()
actual = torch.zeros(3, 3, 3)
diff = torch.tensor([[0.45, 0.36, 0.81], [0.4, 0.32, 0.72], [0.4, 0.32, 0.72]])
actual[0, :, :] = offset + diff.pow(1 + power)
diff = torch.tensor(
[[0.21, 0.14, 0.56], [0.18, 0.12, 0.48], [0.24, 0.16, 0.64]]
)
actual[1, :, :] = offset + diff.pow(1 + power)
diff = torch.tensor([[0.2, 0.2, 0.25], [0.2, 0.2, 0.25], [0.2, 0.2, 0.25]])
actual[2, :, :] = offset + diff.pow(1 + power)
self.assertLess(torch.norm(res - actual), 1e-5)
def test_computes_downsampling_function(self):
a = torch.tensor([0.1, 0.2]).view(2, 1)
b = torch.tensor([0.2, 0.4]).view(2, 1)
power = 1
offset = 1
kernel = DownsamplingKernel()
kernel.initialize(power=power, offset=offset)
kernel.eval()
diff = torch.tensor([[0.72, 0.54], [0.64, 0.48]])
actual = offset + diff.pow(1 + power)
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
def test_diag_calculation(self):
a = torch.tensor([0.1, 0.2]).view(2, 1)
b = torch.tensor([0.2, 0.4]).view(2, 1)
power = 1
offset = 1
kernel = DownsamplingKernel()
kernel.initialize(power=power, offset=offset)
kernel.eval()
diff = torch.tensor([[0.72, 0.54], [0.64, 0.48]])
actual = offset + diff.pow(1 + power)
res = kernel(a, b, diag=True)
self.assertLess(torch.norm(res - torch.diag(actual)), 1e-5)
def test_computes_downsampling_function_batch(self):
a = torch.tensor([[0.1, 0.2], [0.3, 0.4], [0.5, 0.5]]).view(3, 2, 1)
b = torch.tensor([[0.5, 0.6], [0.7, 0.8], [0.6, 0.6]]).view(3, 2, 1)
power = 1
offset = 1
kernel = DownsamplingKernel(batch_shape=torch.Size([3]))
kernel.initialize(power=power, offset=offset)
kernel.eval()
res = kernel(a, b).evaluate()
actual = torch.zeros(3, 2, 2)
diff = torch.tensor([[0.45, 0.36], [0.4, 0.32]])
actual[0, :, :] = offset + diff.pow(1 + power)
diff = torch.tensor([[0.21, 0.14], [0.18, 0.12]])
actual[1, :, :] = offset + diff.pow(1 + power)
diff = torch.tensor([[0.2, 0.2], [0.2, 0.2]])
actual[2, :, :] = offset + diff.pow(1 + power)
self.assertLess(torch.norm(res - actual), 1e-5)
def _setup_multifidelity_covar_module(
dim: int,
aug_batch_shape: torch.Size,
iteration_fidelity: Optional[int],
data_fidelity: Optional[int],
linear_truncated: bool,
nu: float,
) -> Tuple[ScaleKernel, Dict]:
"""Helper function to get the covariance module and associated subset_batch_dict
for the multifidelity setting.
Args:
dim: The dimensionality of the training data.
aug_batch_shape: The output-augmented batch shape as defined in
`BatchedMultiOutputGPyTorchModel`.
iteration_fidelity: The column index for the training iteration fidelity
parameter (optional).
data_fidelity: The column index for the downsampling fidelity parameter
(optional).
linear_truncated: If True, use a `LinearTruncatedFidelityKernel` instead
of the default kernel.
nu: The smoothness parameter for the Matern kernel: either 1/2, 3/2, or
5/2. Only used when `linear_truncated=True`.
Returns:
The covariance module and subset_batch_dict.
"""
if iteration_fidelity is not None and iteration_fidelity < 0:
iteration_fidelity = dim + iteration_fidelity
if data_fidelity is not None and data_fidelity < 0:
data_fidelity = dim + data_fidelity
if linear_truncated:
fidelity_dims = [
i for i in (iteration_fidelity, data_fidelity) if i is not None
]
kernel = LinearTruncatedFidelityKernel(
fidelity_dims=fidelity_dims,
dimension=dim,
nu=nu,
batch_shape=aug_batch_shape,
power_prior=GammaPrior(3.0, 3.0),
)
else:
active_dimsX = [
i for i in range(dim)
if i not in {iteration_fidelity, data_fidelity}
]
kernel = RBFKernel(
ard_num_dims=len(active_dimsX),
batch_shape=aug_batch_shape,
lengthscale_prior=GammaPrior(3.0, 6.0),
active_dims=active_dimsX,
)
additional_kernels = []
if iteration_fidelity is not None:
exp_kernel = ExponentialDecayKernel(
batch_shape=aug_batch_shape,
lengthscale_prior=GammaPrior(3.0, 6.0),
offset_prior=GammaPrior(3.0, 6.0),
power_prior=GammaPrior(3.0, 6.0),
active_dims=[iteration_fidelity],
)
additional_kernels.append(exp_kernel)
if data_fidelity is not None:
ds_kernel = DownsamplingKernel(
batch_shape=aug_batch_shape,
offset_prior=GammaPrior(3.0, 6.0),
power_prior=GammaPrior(3.0, 6.0),
active_dims=[data_fidelity],
)
additional_kernels.append(ds_kernel)
kernel = ProductKernel(kernel, *additional_kernels)
covar_module = ScaleKernel(kernel,
batch_shape=aug_batch_shape,
outputscale_prior=GammaPrior(2.0, 0.15))
if linear_truncated:
subset_batch_dict = {
"covar_module.base_kernel.raw_power": -2,
"covar_module.base_kernel.covar_module_unbiased.raw_lengthscale":
-3,
"covar_module.base_kernel.covar_module_biased.raw_lengthscale": -3,
}
else:
subset_batch_dict = {
"covar_module.base_kernel.kernels.0.raw_lengthscale": -3,
"covar_module.base_kernel.kernels.1.raw_power": -2,
"covar_module.base_kernel.kernels.1.raw_offset": -2,
}
if iteration_fidelity is not None:
subset_batch_dict = {
"covar_module.base_kernel.kernels.1.raw_lengthscale": -3,
**subset_batch_dict,
}
if data_fidelity is not None:
subset_batch_dict = {
"covar_module.base_kernel.kernels.2.raw_power": -2,
"covar_module.base_kernel.kernels.2.raw_offset": -2,
**subset_batch_dict,
}
return covar_module, subset_batch_dict
def test_initialize_offset_prior(self):
kernel = DownsamplingKernel()
kernel.offset_prior = NormalPrior(1, 1)
self.assertTrue(isinstance(kernel.offset_prior, NormalPrior))
kernel2 = DownsamplingKernel(offset_prior=GammaPrior(1, 1))
self.assertTrue(isinstance(kernel2.offset_prior, GammaPrior))
def test_initialize_power_batch(self):
kernel = DownsamplingKernel(batch_shape=torch.Size([2]))
power_init = torch.tensor([1.0, 2.0])
kernel.initialize(power=power_init)
actual_value = power_init.view_as(kernel.power)
self.assertLess(torch.norm(kernel.power - actual_value), 1e-5)
def create_kernel_no_ard(self, **kwargs):
return DownsamplingKernel(**kwargs)
def test_initialize_power(self):
kernel = DownsamplingKernel()
kernel.initialize(power=1)
actual_value = torch.tensor(1.0).view_as(kernel.power)
self.assertLess(torch.norm(kernel.power - actual_value), 1e-5)
def test_initialize_offset_batch(self):
kernel = DownsamplingKernel(batch_shape=torch.Size([2]))
off_init = torch.tensor([1.0, 2.0])
kernel.initialize(offset=off_init)
actual_value = off_init.view_as(kernel.offset)
self.assertLess(torch.norm(kernel.offset - actual_value), 1e-5)
def test_initialize_offset(self):
kernel = DownsamplingKernel()
kernel.initialize(offset=1)
actual_value = torch.tensor(1.0).view_as(kernel.offset)
self.assertLess(torch.norm(kernel.offset - actual_value), 1e-5)
