def test_degree3(self):
# just make sure it doesn't break here.
AddK = NewtonGirardAdditiveKernel(RBFKernel(ard_num_dims=3), 3, 3)
self.assertEqual(AddK.base_kernel.lengthscale.numel(), 3)
self.assertEqual(AddK.outputscale.numel(), 3)
testvals = torch.tensor([[1, 2, 3], [7, 5, 2]], dtype=torch.float)
add_k_val = AddK(testvals, testvals).evaluate()
manual_k1 = ScaleKernel(
AdditiveKernel(RBFKernel(active_dims=0), RBFKernel(active_dims=1),
RBFKernel(active_dims=2)))
manual_k1.initialize(outputscale=1 / 3)
manual_k2 = ScaleKernel(
AdditiveKernel(RBFKernel(active_dims=[0, 1]),
RBFKernel(active_dims=[1, 2]),
RBFKernel(active_dims=[0, 2])))
manual_k2.initialize(outputscale=1 / 3)
manual_k3 = ScaleKernel(AdditiveKernel(RBFKernel()))
manual_k3.initialize(outputscale=1 / 3)
manual_k = AdditiveKernel(manual_k1, manual_k2, manual_k3)
manual_add_k_val = manual_k(testvals, testvals).evaluate()
# np.testing.assert_allclose(add_k_val.detach().numpy(), manual_add_k_val.detach().numpy(), atol=1e-5)
self.assertTrue(torch.allclose(add_k_val, manual_add_k_val, atol=1e-5))
def test_optimizing(self):
# This tests should pass so long as nothing breaks.
torch.random.manual_seed(1)
data = torch.randn(40, 4)
target = torch.sin(data).sum(dim=-1)
d = 4
AddK = NewtonGirardAdditiveKernel(RBFKernel(ard_num_dims=d), d, max_degree=3)
class TestGPModel(ExactGP):
def __init__(self, train_x, train_y, likelihood, kernel):
super().__init__(train_x, train_y, likelihood)
self.mean_module = ConstantMean()
self.covar_module = kernel
def forward(self, x):
mean_x = self.mean_module(x)
covar_x = self.covar_module(x)
return MultivariateNormal(mean_x, covar_x)
model = TestGPModel(data, target, GaussianLikelihood(), ScaleKernel(AddK))
optim = torch.optim.Adam(model.parameters(), lr=0.1)
mll = ExactMarginalLogLikelihood(model.likelihood, model)
model.train()
for i in range(2):
optim.zero_grad()
out = model(data)
loss = -mll(out, target)
loss.backward()
optim.step()
def test_degree1(self):
AddK = NewtonGirardAdditiveKernel(RBFKernel(ard_num_dims=3), 3, 1)
self.assertEqual(AddK.base_kernel.lengthscale.numel(), 3)
self.assertEqual(AddK.outputscale.numel(), 1)
testvals = torch.tensor([[1, 2, 3], [7, 5, 2]], dtype=torch.float)
add_k_val = AddK(testvals, testvals).evaluate()
manual_k = ScaleKernel(AdditiveKernel(RBFKernel(active_dims=0),
RBFKernel(active_dims=1),
RBFKernel(active_dims=2)))
manual_k.initialize(outputscale=1.)
manual_add_k_val = manual_k(testvals, testvals).evaluate()
# np.testing.assert_allclose(add_k_val.detach().numpy(), manual_add_k_val.detach().numpy(), atol=1e-5)
self.assertTrue(torch.allclose(add_k_val, manual_add_k_val, atol=1e-5))
def test_ard(self):
base_k = RBFKernel(ard_num_dims=3)
base_k.initialize(lengthscale=[1., 2., 3.])
AddK = NewtonGirardAdditiveKernel(base_k, 3, max_degree=1)
testvals = torch.tensor([[1, 2, 3], [7, 5, 2]], dtype=torch.float)
add_k_val = AddK(testvals, testvals).evaluate()
ks = []
for i in range(3):
k = RBFKernel(active_dims=i)
k.initialize(lengthscale=i + 1)
ks.append(k)
manual_k = ScaleKernel(AdditiveKernel(*ks))
manual_k.initialize(outputscale=1.)
manual_add_k_val = manual_k(testvals, testvals).evaluate()
# np.testing.assert_allclose(add_k_val.detach().numpy(), manual_add_k_val.detach().numpy(), atol=1e-5)
self.assertTrue(torch.allclose(add_k_val, manual_add_k_val, atol=1e-5))
def create_kernel_ard(self, num_dims, **kwargs):
return NewtonGirardAdditiveKernel(RBFKernel(ard_num_dims=num_dims), num_dims, 2, **kwargs)
def create_kernel_no_ard(self, **kwargs):
return NewtonGirardAdditiveKernel(RBFKernel(), 4, 2, **kwargs)
def create_newton_girard_additive_kernel(d, max_degree):
"""Use the Newton-Girard formulae to model higher-order interactions."""
return NewtonGirardAdditiveKernel(RBFKernel(ard_num_dims=d), d, max_degree)