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 = RBFKernel(ard_num_dims=2)
kernel.initialize(lengthscale=lengthscales)
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()
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
actual = scaled_a.transpose(-1, -2).unsqueeze(-1) - scaled_b.transpose(
-1, -2).unsqueeze(-2)
actual = actual.pow(2).mul_(-0.5).exp()
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_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)
kernel = RBFKernel(batch_shape=torch.Size([2]), ard_num_dims=3)
kernel.initialize(lengthscale=lengthscales)
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()
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)
# batch_dims
double_batch_a = scaled_a.transpose(-1, -2).unsqueeze(-1)
double_batch_b = scaled_b.transpose(-1, -2).unsqueeze(-2)
actual = double_batch_a - double_batch_b
actual = actual.pow(2).mul_(-0.5).exp()
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)
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)
kernel = RBFKernel(batch_size=2, ard_num_dims=3)
kernel.initialize(lengthscale=lengthscales)
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()
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.unsqueeze(0).transpose(0, -1)
double_batch_b = scaled_b.unsqueeze(0).transpose(0, -1)
actual = double_batch_a.transpose(-1, -2).unsqueeze(-1) - double_batch_b.transpose(-1, -2).unsqueeze(-2)
actual = actual.pow(2).mul_(-0.5).exp().view(3, 2, 2, 2)
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 = actual.diagonal(dim1=-2, dim2=-1)
self.assertLess(torch.norm(res - actual), 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, 1, 2)
kernel = RBFKernel(ard_num_dims=2)
kernel.initialize(log_lengthscale=lengthscales.log())
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()
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(2, 2, 2)
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_computes_radial_basis_function(self):
a = torch.Tensor([4, 2, 8]).view(3, 1)
b = torch.Tensor([0, 2]).view(2, 1)
lengthscale = 2
kernel = RBFKernel().initialize(log_lengthscale=math.log(lengthscale))
kernel.eval()
actual = torch.Tensor([[16, 4], [4, 0], [64, 36]]).mul_(-0.5).div_(lengthscale ** 2).exp()
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
def test_ard(self):
a = torch.Tensor([[1, 2], [2, 4]])
b = torch.Tensor([1, 3]).view(1, 1, 2)
lengthscales = torch.Tensor([1, 2]).view(1, 1, 2)
kernel = RBFKernel(ard_num_dims=2)
kernel.initialize(log_lengthscale=lengthscales.log())
kernel.eval()
actual = (a - b).div_(lengthscales).pow(2).sum(dim=-1).mul_(-0.5).exp()
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual.unsqueeze(-1)), 1e-5)
def test_forward_diag(self):
a = torch.Tensor([4, 2, 8]).view(1, 3, 1)
b = torch.Tensor([2, 0, 6]).view(1, 3, 1)
lengthscale = 2
kernel = RBFKernel().initialize(log_lengthscale=math.log(lengthscale))
kernel.eval()
res = kernel.forward_diag(a, b).squeeze()
actual = torch.Tensor([0.60653066, 0.60653066, 0.60653066])
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)
lengthscales = torch.tensor([[[1, 2, 1]]], dtype=torch.float)
kernel = RBFKernel(batch_size=2, ard_num_dims=3)
kernel.initialize(log_lengthscale=lengthscales.log())
kernel.eval()
actual = (a - b).div_(lengthscales).pow(2).sum(dim=-1).mul_(-0.5).exp()
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual.unsqueeze(-1)), 1e-5)
def test_subset_active_compute_radial_basis_function(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], dtype=torch.float).view(2, 1)
lengthscale = 2
kernel = RBFKernel(active_dims=[0])
kernel.initialize(log_lengthscale=math.log(lengthscale))
kernel.eval()
actual = torch.tensor([[16, 4], [4, 0], [64, 36]], dtype=torch.float)
actual.mul_(-0.5).div_(lengthscale**2).exp_()
res = kernel(a, b).evaluate()
self.assertLess(torch.norm(res - actual), 1e-5)
def test_computes_radial_basis_function():
a = torch.Tensor([4, 2, 8]).view(3, 1)
b = torch.Tensor([0, 2, 2]).view(3, 1)
lengthscale = 2
kernel = RBFKernel().initialize(log_lengthscale=math.log(lengthscale))
kernel.eval()
actual = torch.Tensor([
[16, 4, 4],
[4, 0, 0],
[64, 36, 36],
]).mul_(-1).div_(lengthscale).exp()
res = kernel(Variable(a), Variable(b)).data
assert(torch.norm(res - actual) < 1e-5)
def test_computes_radial_basis_function_gradient():
a = torch.Tensor([4, 2, 8]).view(3, 1)
b = torch.Tensor([0, 2, 2]).view(3, 1)
lengthscale = 2
kernel = RBFKernel().initialize(log_lengthscale=math.log(lengthscale))
kernel.eval()
param = Variable(torch.Tensor(3, 3).fill_(math.log(lengthscale)), requires_grad=True)
diffs = Variable(a.expand(3, 3) - b.expand(3, 3).transpose(0, 1))
actual_output = (-(diffs ** 2) / param.exp()).exp()
actual_output.backward(torch.eye(3))
actual_param_grad = param.grad.data.sum()
output = kernel(Variable(a), Variable(b))
output.backward(gradient=torch.eye(3))
res = kernel.log_lengthscale.grad.data
assert(torch.norm(res - actual_param_grad) < 1e-5)
def test_subset_active_compute_radial_basis_function(self):
a = torch.Tensor([4, 2, 8]).view(3, 1)
a_p = torch.Tensor([1, 2, 3]).view(3, 1)
a = torch.cat((a, a_p), 1)
b = torch.Tensor([0, 2]).view(2, 1)
lengthscale = 2
kernel = RBFKernel(active_dims=[0]).initialize(log_lengthscale=math.log(lengthscale))
kernel.eval()
actual = torch.Tensor([
[16, 4],
[4, 0],
[64, 36],
]).mul_(-1).div_(lengthscale).exp()
res = kernel(Variable(a), Variable(b)).data
self.assertLess(torch.norm(res - actual), 1e-5)
def test_computes_radial_basis_function(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 = RBFKernel().initialize(lengthscale=lengthscale)
kernel.eval()
actual = torch.tensor([[16, 4, 0], [4, 0, 4], [64, 36, 16]], dtype=torch.float)
actual.mul_(-0.5).div_(lengthscale ** 2).exp_()
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_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 = RBFKernel(batch_size=2, ard_num_dims=3)
kernel.initialize(log_lengthscale=lengthscales.log())
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()
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)
def test_computes_radial_basis_function_gradient(self):
a = torch.Tensor([4, 2, 8]).view(3, 1)
b = torch.Tensor([0, 2, 2]).view(3, 1)
lengthscale = 2
kernel = RBFKernel().initialize(log_lengthscale=math.log(lengthscale))
kernel.eval()
param = math.log(lengthscale) * torch.ones(3, 3)
param.requires_grad_()
diffs = a.expand(3, 3) - b.expand(3, 3).transpose(0, 1)
actual_output = (-0.5 * (diffs / param.exp()) ** 2).exp()
actual_output.backward(gradient=torch.eye(3))
actual_param_grad = param.grad.sum()
output = kernel(a, b).evaluate()
output.backward(gradient=torch.eye(3))
res = kernel.log_lengthscale.grad
self.assertLess(torch.norm(res - actual_param_grad), 1e-5)
def test_computes_radial_basis_function_gradient(self):
softplus = torch.nn.functional.softplus
a = torch.tensor([4, 2, 8], dtype=torch.float).view(3, 1)
b = torch.tensor([0, 2, 2], dtype=torch.float).view(3, 1)
lengthscale = 2
kernel = RBFKernel().initialize(lengthscale=lengthscale)
kernel.eval()
param = math.log(math.exp(lengthscale) - 1) * torch.ones(3, 3)
param.requires_grad_()
diffs = a.expand(3, 3) - b.expand(3, 3).transpose(0, 1)
actual_output = (-0.5 * (diffs / softplus(param)) ** 2).exp()
actual_output.backward(gradient=torch.eye(3))
actual_param_grad = param.grad.sum()
output = kernel(a, b).evaluate()
output.backward(gradient=torch.eye(3))
res = kernel.raw_lengthscale.grad
self.assertLess(torch.norm(res - actual_param_grad), 1e-5)
def test_subset_active_computes_radial_basis_function_gradient(self):
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)
lengthscale = 2
param = math.log(lengthscale) * torch.ones(3, 3)
param.requires_grad_()
diffs = a_1.expand(3, 3) - b.expand(3, 3).transpose(0, 1)
actual_output = (-0.5 * (diffs / param.exp()) ** 2).exp()
actual_output.backward(torch.eye(3))
actual_param_grad = param.grad.sum()
kernel = RBFKernel(active_dims=[0])
kernel.initialize(log_lengthscale=math.log(lengthscale))
kernel.eval()
output = kernel(a, b).evaluate()
output.backward(gradient=torch.eye(3))
res = kernel.log_lengthscale.grad
self.assertLess(torch.norm(res - actual_param_grad), 1e-5)
def test_subset_active_computes_radial_basis_function_gradient(self):
a_1 = torch.Tensor([4, 2, 8]).view(3, 1)
a_p = torch.Tensor([1, 2, 3]).view(3, 1)
a = torch.cat((a_1, a_p), 1)
b = torch.Tensor([0, 2, 2]).view(3, 1)
lengthscale = 2
kernel = RBFKernel(active_dims=[0]).initialize(log_lengthscale=math.log(lengthscale))
kernel.eval()
param = Variable(
torch.Tensor(3, 3).fill_(math.log(lengthscale)),
requires_grad=True,
)
output = kernel(Variable(a), Variable(b))
output.backward(gradient=torch.eye(3))
res = kernel.log_lengthscale.grad.data
diffs = Variable(a_1.expand(3, 3) - b.expand(3, 3).transpose(0, 1))
actual_output = (-(diffs ** 2) / (param.exp())).exp()
actual_output.backward(torch.eye(3))
actual_param_grad = param.grad.data.sum()
self.assertLess(torch.norm(res - actual_param_grad), 1e-5)
