ModelKernel

class ModelKernel

Bases: QUBOConvertibleBase

Class to define a surrogate/acquisition function model based on second order polynomial kernels.

Methods

__init__	Initialize the kernel based model class.
generate_kernel_functions	Generate polynomial kernel functions for k_mu (for mean) and k_sigma (for sigma).
set_coefficient	Update the model coefficient matrices and vectors.
to_qubo	Convert a kernel-based model to the Amplify SDK-compatible QUBO based on the optimized FM parameters.

Attributes

beta	The beta value(s) for the sigma terms in LCB.
coef_matrix_combined	The coefficient matrix combined for the mean and for sigma with beta used for the current model.
coef_matrix_mu	The coefficient matrix for the mean used for the current model.
coef_matrix_sigma	The coefficient matrix for the sigma used for the current model.
coef_vector_combined	The coefficient vector combined for the mean and for sigma with beta used for the current model.
coef_vector_mu	The coefficient vector for the mean used for the current model.
coef_vector_sigma	The coefficient vector for sigma used for the current model.
current_beta	The value of beta used for the current model.
gamma	The gamma value for the kernel functions that corresponds to the linear terms in the model.
is_sigma_required	Whether the sigma is considered in the model.

__call__(x: list[list[Any]] | list[Any]) → list[float] | float

Perform prediction based on the current model.

Parameters:

x (list[list[Any]] | list[Any]) – An input vector or a list of input vectors.

Raises:

RuntimeError – If the coefficient matrix combined for the mean and for sigma is not set.

Returns:

A predicted value or a list of the predicted values (in case of multiple input vectors are given).

Return type:

list[float] | float

__init__(beta: float | list[float] = 0.0, gamma: float = 0.0) → None

Initialize the kernel based model class.

Parameters:

• beta (float | list[float], optional) – A weight for ‘sigma’ in the lower confidence bound (LCB). If multiple values of beta are given as a list, a value in the list is chosen and used in a cyclic manner each time the model is constructed (=in each optimization cycle). When beta = 0 or min(beta) = 0, ModelKernel.is_sigma_required = False, meaning the model uncertainty is not considered. Defaults to 0.0.

• gamma (float, optional) – A constant in the kernel function to define a linear term in the model. gamma = 0 means no linear term is considered in the model. Note that when the a priori encoding methods (()[conversion.ipynb]) are chosen for all decision variables, linear terms are expected to be modeled naturally in the quadratic terms. Defaults to 0.0.

__str__() → str

Return str(self).

generate_kernel_functions() → tuple[Callable, Callable]

Generate polynomial kernel functions for k_mu (for mean) and k_sigma (for sigma).

Returns:

The kernel functions, k_mu and k_sigma in a tuple in this order.

Return type:

tuple[Callable, Callable]

set_coefficient(

matrix_mu: ndarray,

vector_mu: ndarray | None = None,

matrix_lxx: ndarray | None = None,

vector_sigma: ndarray | None = None,

i_cycle: int = 0,

) → None

Update the model coefficient matrices and vectors.

Parameters:

• matrix_mu (np.ndarray) – The coefficient matrix for the mean

• vector_mu (np.ndarray | None, optional) – The coefficient vector for the mean. This is required when gamma > 0 is passed in ModelKernel.__init__. Defaults to None.

• matrix_lxx (np.ndarray | None, optional) – The matrix (L_ij X X) to be used to construct the coefficient matrix for sigma. This is required when current_beta > 0. Defaults to None.

• vector_sigma (np.ndarray | None, optional) – The coefficient vector for the sigma. This is required when gamma > 0 and current_beta > 0. Defaults to None.

• i_cycle (int, optional) – The cycle number from starting from 0 to be used for the cyclic beta. Defaults to 0.

to_qubo(x: PolyArray) → Poly

Convert a kernel-based model to the Amplify SDK-compatible QUBO based on the optimized FM parameters.

Parameters:

x (amplify.PolyArray) – The Amplify SDK variables relevant to the Variables instance involved in the FM.

Raises:

RuntimeError – If the coefficient matrix combined for the mean and sigma is not set.

Returns:

The Amplify SDK’s QUBO polynomial.

Return type:

amplify.Poly

__abstractmethods__ = frozenset({})

__dict__ = mappingproxy({'__module__': 'amplify_bbopt.model', '__doc__': 'Class to define a surrogate/acquisition function model based on second order polynomial kernels.', '__init__': <function ModelKernel.__init__>, 'generate_kernel_functions': <function ModelKernel.generate_kernel_functions>, 'is_sigma_required': <property object>, 'gamma': <property object>, 'beta': <property object>, 'current_beta': <property object>, 'coef_matrix_mu': <property object>, 'coef_matrix_sigma': <property object>, 'coef_matrix_combined': <property object>, 'coef_vector_mu': <property object>, 'coef_vector_sigma': <property object>, 'coef_vector_combined': <property object>, 'set_coefficient': <function ModelKernel.set_coefficient>, 'to_qubo': <function ModelKernel.to_qubo>, '_predict': <function ModelKernel._predict>, '__call__': <function ModelKernel.__call__>, '__str__': <function ModelKernel.__str__>, '__abstractmethods__': frozenset(), '_abc_impl': <_abc._abc_data object>, '__annotations__': {'_coef_matrix_combined': 'np.ndarray | None', '_coef_vector_combined': 'np.ndarray | None', '_coef_matrix_mu': 'np.ndarray | None', '_coef_vector_mu': 'np.ndarray | None', '_coef_matrix_sigma': 'np.ndarray | None'}})

__slots__ = ()

__weakref__

list of weak references to the object (if defined)

property beta: float | list[float]

The beta value(s) for the sigma terms in LCB.

property coef_matrix_combined: ndarray | None

The coefficient matrix combined for the mean and for sigma with beta used for the current model. If the matrix is not set yet, return None.

property coef_matrix_mu: ndarray | None

The coefficient matrix for the mean used for the current model. If the matrix is not set yet, return None.

property coef_matrix_sigma: ndarray | None

The coefficient matrix for the sigma used for the current model. If the matrix is not set yet, return None.

property coef_vector_combined: ndarray | None

The coefficient vector combined for the mean and for sigma with beta used for the current model. If the vector is not set yet, return None.

property coef_vector_mu: ndarray | None

The coefficient vector for the mean used for the current model. If the vector is not set yet, return None.

property coef_vector_sigma: ndarray | None

The coefficient vector for sigma used for the current model. If the vector is not set yet, return None.

property current_beta: float

The value of beta used for the current model. When beta is given as a list in ModelKernel.__init__, a value in the list is chosen and used in a cyclic manner each time the model is constructed, and this value will be returned.

property gamma: float

The gamma value for the kernel functions that corresponds to the linear terms in the model.

property is_sigma_required: bool

Whether the sigma is considered in the model.