deformation

MuyGPyS.gp.deformation module reference.

class MuyGPyS.gp.deformation.Isotropy(metric, length_scale)

An isotropic deformation model.

Isotropy defines a scaled elementwise distance function \(d_ell(\cdot, \cdot)\), and is paramterized by a scalar \(\ell>0\) length scale hyperparameter.

\[d_\ell(\mathbf{x}, \mathbf{y}) = \sum_{i=0}^d \frac{d(\mathbf{x}_i, \mathbf{y}_i)}{\ell}\]

Parameters:

• metric (Callable) – A callable metric function that takes a tensor of shape (…, feature_count) whose last dimension lists the elementwise differences between a pair of feature vectors and returns a tensor of shape (…), having collapsed the last dimension into a scalar difference.

• length_scale (Parameter) – Some scalar nonnegative hyperparameter object.

__call__(diffs, length_scale=None, **kwargs)

Apply isotropic deformation to an elementwise difference tensor.

This function is not intended to be invoked directly by a user. It is instead functionally incorporated into some MuyGPyS.gp.kernels.KernelFn in its constructor.

Parameters:

• diffs (ndarray) – A tensor of pairwise differences of shape (…, feature_count).

• length_scale (Optional[float]) – A floating point length scale.

Return type:

ndarray

Returns:

A crosswise distance matrix of shape (data_count, nn_count) or a pairwise distance tensor of shape (data_count, nn_count, nn_count) whose last two dimensions are pairwise distance matrices.

embed_fn(fn)

Augments a function to automatically apply the deformation to a difference tensor.

Parameters:

fn (Callable) – A Callable with signature (diffs, *args, **kwargs) -> mm.ndarray taking a difference tensor diffs with shape (…, feature_count).

Return type:

Callable

Returns:

A new Callable that applies the deformation to diffs, removing the last tensor dimension by collapsing the feature-wise differences into scalar distances. Also adds a length_scale kwarg, making the function drivable by keyword optimization.

get_opt_params()

Report lists of unfixed hyperparameter names, values, and bounds.

Return type:

Tuple[List[str], List[float], List[Tuple[float, float]]]

Returns:

names:

A list of unfixed hyperparameter names.

params:

A list of unfixed hyperparameter values.

bounds:

A list of unfixed hyperparameter bound tuples.

populate_length_scale(hyperparameters)

Populates the hyperparameter dictionary of a KernelFn object with self.length_scale of the Isotropy object.

Parameters:

hyperparameters (Dict) – A dict containing the hyperparameters of a KernelFn object.

Return type:

None

class MuyGPyS.gp.deformation.Anisotropy(metric, **length_scales)

An anisotropic deformation model.

Anisotropy parameterizes a scaled elementwise distance function \(d_\ell(\cdot, \cdot)\), and is paramterized by a vector-valued \(\mathbf{\ell}>0\) length scale hyperparameter.

\[d_\ell(\mathbf{x}, \mathbf{y}) = \sum_{i=0}^d \frac{d(\mathbf{x}_i, \mathbf{y}_i)}{\ell_i}\]

Parameters:

• metric (Callable) – A callable metric function that takes a tensor of shape (…, feature_count) whose last dimension lists the elementwise differences between a pair of feature vectors and returns a tensor of shape (…), having collapsed the last dimension into a scalar difference.

• length_scales – Keyword arguments length_scale#, mapping to scalar hyperparameters.

__call__(diffs, **length_scales)

Apply anisotropic deformation to an elementwise difference tensor.

This function is not intended to be invoked directly by a user. It is instead functionally incorporated into some MuyGPyS.gp.kernels.KernelFn in its constructor.

Parameters:

• diffs (ndarray) – A tensor of pairwise differences of shape (…, feature_count).

• batch_features – A (batch_count, feature_count) matrix of features to be used with a hierarchical hyperparameter. None otherwise.

• length_scale – A floating point length scale, or a vector of (knot_count,) knot length scales.

Return type:

ndarray

Returns:

A crosswise distance matrix of shape (data_count, nn_count) or a pairwise distance tensor of shape (data_count, nn_count, nn_count) whose last two dimensions are pairwise distance matrices.

embed_fn(fn)

Augments a function to automatically apply the deformation to a difference tensor.

Parameters:

fn (Callable) – A Callable with signature (diffs, *args, **kwargs) -> mm.ndarray taking a difference tensor diffs with shape (…, feature_count).

Return type:

Callable

Returns:

A new Callable that applies the deformation to diffs, removing the last tensor dimension by collapsing the feature-wise differences into scalar distances. Propagates any length_scaleN kwargs to the deformation fn, making the function drivable by keyword optimization.

get_opt_params()

Report lists of unfixed hyperparameter names, values, and bounds.

Return type:

Tuple[List[str], List[float], List[Tuple[float, float]]]

Returns:

names:

A list of unfixed hyperparameter names.

params:

A list of unfixed hyperparameter values.

bounds:

A list of unfixed hyperparameter bound tuples.

populate_length_scale(hyperparameters)

Populates the hyperparameter dictionary of a KernelFn object with self.length_scales of the Anisotropy object.

Parameters:

hyperparameters (Dict) – A dict containing the hyperparameters of a KernelFn object.

Return type:

None