def create_rq(sigma2, lengthscale, alpha):
rq = RQKernel()
rq.lengthscale = lengthscale
rq.alpha = alpha
kernel = ScaleKernel(rq)
kernel.outputscale = sigma2
return kernel
def test_ard_separate_batch(self):
a = torch.tensor([[[1, 2, 3], [2, 4, 0]], [[-1, 1, 2], [2, 1, 4]]],
dtype=torch.float)
b = torch.tensor([[[1, 3, 1]], [[2, -1, 0]]],
dtype=torch.float).repeat(1, 2, 1)
lengthscales = torch.tensor([[[1, 2, 1]], [[2, 1, 0.5]]],
dtype=torch.float)
kernel = RQKernel(batch_shape=torch.Size([2]), ard_num_dims=3)
kernel.initialize(lengthscale=lengthscales)
kernel.initialize(alpha=3.0)
kernel.eval()
scaled_a = a.div(lengthscales)
scaled_b = b.div(lengthscales)
dist = (scaled_a.unsqueeze(-2) -
scaled_b.unsqueeze(-3)).pow(2).sum(dim=-1)
actual = dist.div_(2 * kernel.alpha).add_(1.0).pow(-kernel.alpha)
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# diag
res = kernel(a, b).diag()
actual = actual.diagonal(dim1=-1, dim2=-2)
self.assertLess(torch.norm(res - actual), 1e-5)
def test_subset_active_computes_rational_quadratic_gradient(self):
softplus = torch.nn.functional.softplus
a_1 = torch.tensor([4, 2, 8], dtype=torch.float).view(3, 1)
a_p = torch.tensor([1, 2, 3], dtype=torch.float).view(3, 1)
a = torch.cat((a_1, a_p), 1)
b = torch.tensor([0, 2, 2], dtype=torch.float).view(3, 1)
kernel = RQKernel(active_dims=[0])
kernel.initialize(lengthscale=2.0)
kernel.initialize(alpha=3.0)
kernel.eval()
raw_lengthscale = torch.tensor(math.log(math.exp(2.0) - 1))
raw_lengthscale.requires_grad_()
raw_alpha = torch.tensor(math.log(math.exp(3.0) - 1))
raw_alpha.requires_grad_()
lengthscale, alpha = softplus(raw_lengthscale), softplus(raw_alpha)
dist = (a_1.expand(3, 3) -
b.expand(3, 3).transpose(0, 1)).div(lengthscale).pow(2)
actual_output = dist.div(2 * alpha).add(1).pow(-alpha)
actual_output.backward(gradient=torch.eye(3))
output = kernel(a, b).evaluate()
output.backward(gradient=torch.eye(3))
res = kernel.raw_lengthscale.grad
self.assertLess(torch.norm(res - raw_lengthscale.grad), 1e-5)
res = kernel.raw_alpha.grad
self.assertLess(torch.norm(res - raw_alpha.grad), 1e-5)
def test_ard(self):
a = torch.tensor([[1, 2], [2, 4]], dtype=torch.float)
b = torch.tensor([[1, 3], [0, 4]], dtype=torch.float)
lengthscales = torch.tensor([1, 2], dtype=torch.float).view(1, 2)
kernel = RQKernel(ard_num_dims=2)
kernel.initialize(lengthscale=lengthscales)
kernel.initialize(alpha=3.0)
kernel.eval()
scaled_a = a.div(lengthscales)
scaled_b = b.div(lengthscales)
dist = (scaled_a.unsqueeze(-2) -
scaled_b.unsqueeze(-3)).pow(2).sum(dim=-1)
actual = dist.div_(2 * kernel.alpha).add_(1.0).pow(-kernel.alpha)
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# Diag
res = kernel(a, b).diag()
actual = actual.diag()
self.assertLess(torch.norm(res - actual), 1e-5)
# batch_dims
diff = scaled_a.transpose(-1, -2).unsqueeze(-1) - scaled_b.transpose(
-1, -2).unsqueeze(-2)
actual = diff.pow(2).div_(2 *
kernel.alpha).add_(1.0).pow(-kernel.alpha)
res = kernel(a, b, last_dim_is_batch=True).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# batch_dims and diag
res = kernel(a, b, last_dim_is_batch=True).diag()
actual = actual.diagonal(dim1=-1, dim2=-2)
self.assertLess(torch.norm(res - actual), 1e-5)
def test_computes_rational_quadratic(self):
a = torch.tensor([4, 2, 8], dtype=torch.float).view(3, 1)
b = torch.tensor([0, 2, 4], dtype=torch.float).view(3, 1)
lengthscale = 2
kernel = RQKernel().initialize(lengthscale=lengthscale)
kernel.eval()
dist = torch.tensor([[16, 4, 0], [4, 0, 4], [64, 36, 16]], dtype=torch.float).div(lengthscale ** 2)
actual = dist.div_(2 * kernel.alpha).add_(1.0).pow(-kernel.alpha)
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# diag
res = kernel(a, b).diag()
actual = actual.diag()
self.assertLess(torch.norm(res - actual), 1e-5)
def test_subset_active_compute_rational_quadratic(self):
a = torch.tensor([4, 2, 8], dtype=torch.float).view(3, 1)
a_p = torch.tensor([1, 2, 3], dtype=torch.float).view(3, 1)
a = torch.cat((a, a_p), 1)
b = torch.tensor([0, 2, 4], dtype=torch.float).view(3, 1)
lengthscale = 2
kernel = RQKernel(active_dims=[0])
kernel.initialize(lengthscale=lengthscale)
kernel.initialize(alpha=3.0)
kernel.eval()
actual = torch.tensor([[16, 4, 0], [4, 0, 4], [64, 36, 16]], dtype=torch.float)
actual.div_(lengthscale ** 2).div_(2 * kernel.alpha).add_(1).pow_(-kernel.alpha)
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# diag
res = kernel(a, b).diag()
actual = actual.diag()
self.assertLess(torch.norm(res - actual), 1e-5)
def test_initialize_alpha(self):
kernel = RQKernel()
kernel.initialize(alpha=3.0)
actual_value = torch.tensor(3.0).view_as(kernel.alpha)
self.assertLess(torch.norm(kernel.alpha - actual_value), 1e-5)
def test_initialize_lengthscale_batch(self):
kernel = RQKernel(batch_shape=torch.Size([2]))
ls_init = torch.tensor([3.14, 4.13])
kernel.initialize(lengthscale=ls_init)
actual_value = ls_init.view_as(kernel.lengthscale)
self.assertLess(torch.norm(kernel.lengthscale - actual_value), 1e-5)
def test_initialize_lengthscale(self):
kernel = RQKernel()
kernel.initialize(lengthscale=3.14)
actual_value = torch.tensor(3.14).view_as(kernel.lengthscale)
self.assertLess(torch.norm(kernel.lengthscale - actual_value), 1e-5)
def create_kernel_ard(self, num_dims, **kwargs):
return RQKernel(ard_num_dims=num_dims, **kwargs)
def create_kernel_no_ard(self, **kwargs):
return RQKernel(**kwargs)
def __init__(
self,
num_outputs,
initial_lengthscale,
initial_inducing_points,
separate_inducing_points=False,
kernel="RBF",
ard=None,
lengthscale_prior=False,
):
n_inducing_points = initial_inducing_points.shape[0]
if separate_inducing_points:
# Use independent inducing points per output GP
initial_inducing_points = initial_inducing_points.repeat(num_outputs, 1, 1)
if num_outputs > 1:
batch_shape = torch.Size([num_outputs])
else:
batch_shape = torch.Size([])
variational_distribution = CholeskyVariationalDistribution(
n_inducing_points, batch_shape=batch_shape
)
variational_strategy = VariationalStrategy(
self, initial_inducing_points, variational_distribution
)
if num_outputs > 1:
variational_strategy = IndependentMultitaskVariationalStrategy(
variational_strategy, num_tasks=num_outputs
)
super().__init__(variational_strategy)
if lengthscale_prior:
lengthscale_prior = SmoothedBoxPrior(math.exp(-1), math.exp(1), sigma=0.1)
else:
lengthscale_prior = None
kwargs = {
"ard_num_dims": ard,
"batch_shape": batch_shape,
"lengthscale_prior": lengthscale_prior,
}
if kernel == "RBF":
kernel = RBFKernel(**kwargs)
elif kernel == "Matern12":
kernel = MaternKernel(nu=1 / 2, **kwargs)
elif kernel == "Matern32":
kernel = MaternKernel(nu=3 / 2, **kwargs)
elif kernel == "Matern52":
kernel = MaternKernel(nu=5 / 2, **kwargs)
elif kernel == "RQ":
kernel = RQKernel(**kwargs)
else:
raise ValueError("Specified kernel not known.")
kernel.lengthscale = initial_lengthscale * torch.ones_like(kernel.lengthscale)
self.mean_module = ConstantMean(batch_shape=batch_shape)
self.covar_module = ScaleKernel(kernel, batch_shape=batch_shape)
