def testValuesAreCorrectVectorTransform(self, feature_ndims, dims):
amplitude = self.dtype(5.)
length_scale = self.dtype(0.2)
kernel = tfpk.ExponentiatedQuadratic(amplitude, length_scale,
feature_ndims)
input_shape = [dims] * feature_ndims
scale_diag = np.random.uniform(-1, 1, size=(dims, )).astype(self.dtype)
bij = bijectors.Affine(scale_diag=scale_diag)
# Scaling the last dimension.
def vector_transform(x, feature_ndims, param_expansion_ndims):
del feature_ndims, param_expansion_ndims
return bij.forward(x)
vector_transformed_kernel = tfpk.FeatureTransformed(
kernel, transformation_fn=vector_transform)
x = np.random.uniform(-1, 1, size=input_shape).astype(self.dtype)
y = np.random.uniform(-1, 1, size=input_shape).astype(self.dtype)
self.assertAllClose(
_numpy_exp_quad(amplitude,
length_scale,
scale_diag * x,
scale_diag * y,
feature_ndims=feature_ndims),
self.evaluate(vector_transformed_kernel.apply(x, y)))
def testValuesAreCorrectScalarTransform(self, feature_ndims, dims):
amplitude = self.dtype(5.)
length_scale = self.dtype(0.2)
kernel = tfpk.ExponentiatedQuadratic(amplitude, length_scale,
feature_ndims)
input_shape = [dims] * feature_ndims
bij = bijectors.AffineScalar(self.dtype(0.), self.dtype(2.))
# Flat multiplication by 2.
def scale_transform(x, feature_ndims, param_expansion_ndims):
del feature_ndims, param_expansion_ndims
return bij.forward(x)
scale_transformed_kernel = tfpk.FeatureTransformed(
kernel, transformation_fn=scale_transform)
x = np.random.uniform(-1, 1, size=input_shape).astype(self.dtype)
y = np.random.uniform(-1, 1, size=input_shape).astype(self.dtype)
self.assertAllClose(
_numpy_exp_quad(amplitude,
length_scale,
2. * x,
2. * y,
feature_ndims=feature_ndims),
self.evaluate(scale_transformed_kernel.apply(x, y)))
def testKernelParametersBroadcast(self, feature_ndims, dims):
# Batch shape [10, 2]
amplitude = np.random.uniform(low=1., high=10.,
size=[10, 2]).astype(self.dtype)
length_scale = np.random.uniform(low=1., high=10.,
size=[1, 2]).astype(self.dtype)
kernel = tfpk.ExponentiatedQuadratic(amplitude, length_scale,
feature_ndims)
input_shape = [dims] * feature_ndims
# Batch shape [3, 1, 2].
scale_diag = np.random.uniform(-1, 1, size=(
3,
1,
2,
dims,
)).astype(self.dtype)
# Scaling the last dimension.
def vector_transform(x, feature_ndims, param_expansion_ndims):
diag = util.pad_shape_with_ones(scale_diag,
param_expansion_ndims +
feature_ndims - 1,
start=-2)
return diag * x
vector_transformed_kernel = tfpk.FeatureTransformed(
kernel, transformation_fn=vector_transform)
x = np.random.uniform(-1, 1, size=input_shape).astype(self.dtype)
y = np.random.uniform(-1, 1, size=input_shape).astype(self.dtype)
# Pad for each feature dimension.
expanded_scale_diag = scale_diag
for _ in range(feature_ndims - 1):
expanded_scale_diag = expanded_scale_diag[..., None, :]
self.assertAllClose(
_numpy_exp_quad(amplitude,
length_scale,
expanded_scale_diag * x,
expanded_scale_diag * y,
feature_ndims=feature_ndims),
self.evaluate(vector_transformed_kernel.apply(x, y)))
z = np.random.uniform(-1, 1,
size=[10] + input_shape).astype(self.dtype)
self.assertAllClose(
_numpy_exp_quad_matrix(
# We need to take in to account the event dimension.
amplitude[..., None, None],
length_scale[..., None, None],
# Extra dimension for the event dimension.
expanded_scale_diag[..., None, :] * z,
feature_ndims=feature_ndims),
self.evaluate(vector_transformed_kernel.matrix(z, z)))
def testValuesAreCorrectIdentity(self, feature_ndims, dims):
amplitude = self.dtype(5.)
length_scale = self.dtype(0.2)
kernel = tfpk.ExponentiatedQuadratic(amplitude, length_scale,
feature_ndims)
input_shape = [dims] * feature_ndims
identity_transformed_kernel = tfpk.FeatureTransformed(
kernel,
transformation_fn=lambda x, feature_ndims, param_expansion_ndims: x
)
x = np.random.uniform(-1, 1, size=input_shape).astype(self.dtype)
y = np.random.uniform(-1, 1, size=input_shape).astype(self.dtype)
self.assertAllClose(
_numpy_exp_quad(amplitude,
length_scale,
x,
y,
feature_ndims=feature_ndims),
self.evaluate(identity_transformed_kernel.apply(x, y)))