Powered Exponential
gpjax.kernels.stationary.powered_exponential
PoweredExponential
dataclass
Bases: AbstractKernel
The powered exponential family of kernels. This also equivalent to the symmetric generalized normal distribution.
See Diggle and Ribeiro (2007) - "Model-based Geostatistics". and https://en.wikipedia.org/wiki/Generalized_normal_distribution#Symmetric_version
compute_engine: AbstractKernelComputation = static_field(DenseKernelComputation())
class-attribute
instance-attribute
active_dims: Optional[List[int]] = static_field(None)
class-attribute
instance-attribute
ndims
property
spectral_density: Optional[tfd.Distribution]
property
lengthscale: Union[ScalarFloat, Float[Array, ' D']] = param_field(jnp.array(1.0), bijector=tfb.Softplus())
class-attribute
instance-attribute
variance: ScalarFloat = param_field(jnp.array(1.0), bijector=tfb.Softplus())
class-attribute
instance-attribute
power: ScalarFloat = param_field(jnp.array(1.0), bijector=tfb.Sigmoid())
class-attribute
instance-attribute
name: str = 'Powered Exponential'
class-attribute
instance-attribute
__init_subclass__(mutable: bool = False)
replace(**kwargs: Any) -> Self
replace_meta(**kwargs: Any) -> Self
update_meta(**kwargs: Any) -> Self
replace_trainable(**kwargs: Dict[str, bool]) -> Self
Replace the trainability status of local nodes of the Module.
replace_bijector(**kwargs: Dict[str, tfb.Bijector]) -> Self
Replace the bijectors of local nodes of the Module.
constrain() -> Self
unconstrain() -> Self
stop_gradient() -> Self
trainables() -> Self
cross_covariance(x: Num[Array, 'N D'], y: Num[Array, 'M D'])
gram(x: Num[Array, 'N D'])
slice_input(x: Float[Array, '... D']) -> Float[Array, '... Q']
Slice out the relevant columns of the input matrix.
Select the relevant columns of the supplied matrix to be used within the kernel's evaluation.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
x |
Float[Array, '... D']
|
The matrix or vector that is to be sliced. |
required |
Returns
Float[Array, "... Q"]: A sliced form of the input matrix.
__add__(other: Union[AbstractKernel, ScalarFloat]) -> AbstractKernel
__radd__(other: Union[AbstractKernel, ScalarFloat]) -> AbstractKernel
__mul__(other: Union[AbstractKernel, ScalarFloat]) -> AbstractKernel
Multiply two kernels together.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
other |
AbstractKernel
|
The kernel to be multiplied with the current kernel. |
required |
Returns
AbstractKernel: A new kernel that is the product of the two kernels.
__call__(x: Float[Array, ' D'], y: Float[Array, ' D']) -> ScalarFloat
Compute the Powered Exponential kernel between a pair of arrays.
Evaluate the kernel on a pair of inputs with length-scale parameter , and power .
Parameters:
Name | Type | Description | Default |
---|---|---|---|
x |
Float[Array, ' D']
|
The left hand argument of the kernel function's call. |
required |
y |
Float[Array, ' D']
|
The right hand argument of the kernel function's call |
required |
Returns
ScalarFloat: The value of .