superstats.transition.stochastic.kernel.rbf#

Radial basis function covariance kernels.

Functions

`build_sq_dist_mat`(num_steps)	Squared pairwise distances for num_steps evenly spaced points on [0, 1].
`get_rbf_kernel`(num_steps, length_scale, ...)	Batched RBF kernel construction.

Classes

RBF kernel.

class superstats.transition.stochastic.kernel.rbf.RBFKernel(name=None)[source]#

RBF kernel. Requires hyperparameters length_scale, amplitude.

Parameters:

namestr, optional: Prefix for this kernel’s hyperparameter names. Leave unset for a single RBF kernel, or when combining with a kernel of a different type. Required when combining two RBF kernels, e.g. RBFKernel(name=”short”) + RBFKernel(name=”long”).

Parameters:

name (str | None)

build(num_steps, **hyperparams)[source]#

Construct the (batch_size, num_steps, num_steps) kernel matrix.

Parameters:

num_stepsint
**hyperparamsnp.ndarray: Must contain every name in self.hyperparam_names, each of shape (batch_size,). Extra keys (from sibling kernels in a composite) are ignored.

Returns:

kernel_matnp.ndarray of shape (batch_size, num_steps, num_steps)

Parameters:

Return type:

ndarray

superstats.transition.stochastic.kernel.rbf.build_sq_dist_mat(num_steps)[source]#

Squared pairwise distances for num_steps evenly spaced points on [0, 1].

Parameters:

Returns:

sq_distnp.ndarray of shape (num_steps, num_steps): Squared distance between point i and point j at [i, j].

Parameters:

num_steps (int)

Return type:

ndarray

superstats.transition.stochastic.kernel.rbf.get_rbf_kernel(num_steps, length_scale, amplitude)[source]#

Batched RBF kernel construction.

Parameters:

num_stepsint: Number of points in the 1D grid.
length_scalenp.ndarray of shape (batch_size,): Kernel width per trajectory; larger values mean smoother, slower-varying draws.
amplitudenp.ndarray of shape (batch_size,): Kernel variance / overall scale per trajectory.

Returns:

kernel_matnp.ndarray of shape (batch_size, num_steps, num_steps)

Parameters:

Return type:

ndarray