def test_ard(self):
a = torch.tensor([[[1, 2], [2, 4]]], dtype=torch.float).repeat(2, 1, 1)
b = torch.tensor([[[1, 3], [0, 4]]], dtype=torch.float).repeat(2, 1, 1)
lengthscales = torch.tensor([1, 2], dtype=torch.float).view(1, 1, 2)
base_kernel = RBFKernel(ard_num_dims=2)
base_kernel.initialize(lengthscale=lengthscales)
kernel = ScaleKernel(base_kernel)
kernel.initialize(outputscale=torch.tensor([3], dtype=torch.float))
kernel.eval()
scaled_a = a.div(lengthscales)
scaled_b = b.div(lengthscales)
actual = (scaled_a.unsqueeze(-2) - scaled_b.unsqueeze(-3)).pow(2).sum(dim=-1).mul_(-0.5).exp()
actual.mul_(3)
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# Diag
res = kernel(a, b).diag()
actual = torch.cat([actual[i].diag().unsqueeze(0) for i in range(actual.size(0))])
self.assertLess(torch.norm(res - actual), 1e-5)
# batch_dims
actual = scaled_a.transpose(-1, -2).unsqueeze(-1) - scaled_b.transpose(-1, -2).unsqueeze(-2)
actual = actual.pow(2).mul_(-0.5).exp().view(4, 2, 2)
actual.mul_(3)
res = kernel(a, b, batch_dims=(0, 2)).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# batch_dims and diag
res = kernel(a, b, batch_dims=(0, 2)).diag()
actual = torch.cat([actual[i].diag().unsqueeze(0) for i in range(actual.size(0))])
self.assertLess(torch.norm(res - actual), 1e-5)
def test_inherit_active_dims(self):
lengthscales = torch.tensor([1, 1], dtype=torch.float)
base_kernel = RBFKernel(active_dims=(1, 2), ard_num_dims=2)
base_kernel.initialize(lengthscale=lengthscales)
kernel = ScaleKernel(base_kernel)
kernel.initialize(outputscale=torch.tensor([3], dtype=torch.float))
kernel.eval()
self.assertTrue(
torch.all(kernel.active_dims == base_kernel.active_dims))
def test_forward_batch_mode(self):
a = torch.Tensor([4, 2, 8]).view(1, 3, 1).repeat(4, 1, 1)
b = torch.Tensor([0, 2]).view(1, 2, 1).repeat(4, 1, 1)
lengthscale = 2
base_kernel = RBFKernel().initialize(log_lengthscale=math.log(lengthscale))
kernel = ScaleKernel(base_kernel, batch_size=4)
kernel.initialize(log_outputscale=torch.Tensor([1, 2, 3, 4]).log())
kernel.eval()
base_actual = torch.Tensor([[16, 4], [4, 0], [64, 36]]).mul_(-0.5).div_(lengthscale ** 2).exp()
actual = base_actual.unsqueeze(0).mul(torch.Tensor([1, 2, 3, 4]).view(4, 1, 1))
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
def test_forward(self):
a = torch.Tensor([4, 2, 8]).view(3, 1)
b = torch.Tensor([0, 2]).view(2, 1)
lengthscale = 2
base_kernel = RBFKernel().initialize(log_lengthscale=math.log(lengthscale))
kernel = ScaleKernel(base_kernel)
kernel.initialize(log_outputscale=torch.Tensor([3]).log())
kernel.eval()
actual = torch.Tensor([[16, 4], [4, 0], [64, 36]]).mul_(-0.5).div_(lengthscale ** 2).exp()
actual = actual * 3
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
def test_ard_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]]], dtype=torch.float)
base_kernel = RBFKernel(batch_shape=torch.Size([2]), ard_num_dims=3)
base_kernel.initialize(lengthscale=lengthscales)
kernel = ScaleKernel(base_kernel, batch_shape=torch.Size([2]))
kernel.initialize(outputscale=torch.tensor([1, 2], dtype=torch.float))
kernel.eval()
scaled_a = a.div(lengthscales)
scaled_b = b.div(lengthscales)
actual = (scaled_a.unsqueeze(-2) -
scaled_b.unsqueeze(-3)).pow(2).sum(dim=-1).mul_(-0.5).exp()
actual[1].mul_(2)
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
# diag
res = kernel(a, b).diag()
actual = torch.cat(
[actual[i].diag().unsqueeze(0) for i in range(actual.size(0))])
self.assertLess(torch.norm(res - actual), 1e-5)
# batch_dims
double_batch_a = scaled_a.transpose(-1, -2)
double_batch_b = scaled_b.transpose(-1, -2)
actual = double_batch_a.unsqueeze(-1) - double_batch_b.unsqueeze(-2)
actual = actual.pow(2).mul_(-0.5).exp()
actual[1, :, :, :].mul_(2)
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=-2, dim2=-1)
self.assertLess(torch.norm(res - actual), 1e-5)
