rc.gpr.models§

Contains the MOGP class implementing Gaussian Process Regression.

Classes§

`Likelihood`	`NamedTables(NamedTuple)` in a folder alongside `Meta`. Abstract base class for any model.
`GPR`	Interface to a Gaussian Process.
`MOGP`	Implementation of a Gaussian Process.

Module Contents§

class Likelihood(parent, read_data=False, **kwargs)§

Bases: rc.base.models.DataBase

Inheritance diagram of rc.gpr.models.Likelihood

NamedTables(NamedTuple) in a folder alongside Meta. Abstract base class for any model.

DataBase subclasses must be implemented according to the template (copy and paste it):

class MyDataBase(DataBase):

    class NT(NamedTuple):

        names[i]: Table | Matrix | MetaData = pd.DataFrame(defaults[names[i]].pd)   #: Comment
        ...

        def __call__(self, name: str) -> Table | Matrix | MetaData:
            """ Returns the Table named ``name``."""
            return getattr(self, name)


    options: NamedTables[MetaData] = NamedTables(**{name: table.options for name, table in {}.items()})
    """ Class attribute of the form ``NamedTables(**{names[i]: options[i], ...})``.
    Override as necessary for bespoke ``Table.options``.
    Elements of ``options[i]`` found in ``Table.writeOptions`` populate ``self[i].options.write``,
    the remainder populate ``self[i].options.read``."""

    defaultMetaData: MetaData = {'Tables': Tables.options._asdict()}

Parameters:

parent (GPR)
read_data (bool)
kwargs (NP.Matrix)

class Data§

Bases: rc.base.models.Tables

Inheritance diagram of rc.gpr.models.Likelihood.Data

The Data set of a MOGP.

property NamedTuple: rc.base.definitions.Type[rc.base.definitions.NamedTuple]§

Classmethod:
Return type:: rc.base.definitions.Type[rc.base.definitions.NamedTuple]

The NamedTuple underpinning this Data set.

calibrate(**kwargs)§

Merely sets the trainable data.

Return type:: rc.base.definitions.Dict[str, rc.base.definitions.Any]

class GPR(name, fold, is_read, is_covariant, is_isotropic, kernel_parameters=None, likelihood_variance=None)§

Bases: rc.base.models.DataBase

Inheritance diagram of rc.gpr.models.GPR

Interface to a Gaussian Process.

Parameters:

name (str)
fold (rc.data.models.Fold)
is_read (bool | None)
is_covariant (bool)
is_isotropic (bool)
kernel_parameters (Data | None)
likelihood_variance (NP.Matrix | None)

class Data§

Bases: rc.base.models.Tables

Inheritance diagram of rc.gpr.models.GPR.Data

The Data set of a MOGP.

property NamedTuple: rc.base.definitions.Type[rc.base.definitions.NamedTuple]§

Classmethod:
Return type:: rc.base.definitions.Type[rc.base.definitions.NamedTuple]

The NamedTuple underpinning this Data set.

property META: rc.base.definitions.Dict[str, rc.base.definitions.Any]§

Classmethod:
Abstractmethod:
Return type:: rc.base.definitions.Dict[str, rc.base.definitions.Any]

Hyper-parameter optimizer meta

property KERNEL_FOLDER_NAME: str§

Classmethod:
Return type:: str

The name of the folder where kernel data are stored.

property fold: rc.data.models.Fold§

The parent fold.

Return type:: rc.data.models.Fold

property implementation: rc.base.definitions.Tuple[rc.base.definitions.Any, Ellipsis]§

Abstractmethod:
Return type:: rc.base.definitions.Tuple[rc.base.definitions.Any, Ellipsis]

The implementation of this MOGP in GPFlow. If noise_variance.shape == (1,L) an L-tuple of kernels is returned. If noise_variance.shape == (L,L) a 1-tuple of multi-output kernels is returned.

property L: int§

The output (Y) dimensionality.

Return type:: int

property M: int§

The input (X) dimensionality.

Return type:: int

property N: int§

The the number of training samples.

Return type:: int

property X: rc.base.definitions.Any§

Abstractmethod:
Return type:: rc.base.definitions.Any

The implementation training inputs.

property Y: rc.base.definitions.Any§

Abstractmethod:
Return type:: rc.base.definitions.Any

The implementation training outputs.

property K_cho: rc.base.definitions.Union[NP.Matrix, TF.Tensor]§

Abstractmethod:
Return type:: rc.base.definitions.Union[NP.Matrix, TF.Tensor]

The Cholesky decomposition of the LNxLN noisy kernel(X, X) + likelihood.variance. Shape is (LN, LN) if self.kernel.is_covariant, else (L,N,N).

property K_inv_Y: rc.base.definitions.Union[NP.Matrix, TF.Tensor]§

Abstractmethod:
Return type:: rc.base.definitions.Union[NP.Matrix, TF.Tensor]

The LN-Vector, which pre-multiplied by the LoxLN kernel k(x, X) gives the Lo-Vector predictive mean f(x). Shape is (L,1,N). Returns: ChoSolve(self.K_cho, self.Y)

abstractmethod predict(x, y_instead_of_f=True)§

Predicts the response to input X.

Parameters:

x (NP.Matrix) – An (o, M) design Matrix of inputs.
y_instead_of_f (bool) – True to include noise in the variance of the result.

Return type:

rc.base.definitions.Tuple[NP.Matrix, NP.Matrix]

Returns: The distribution of y or f, as a pair (mean (o, L) Matrix, std (o, L) Matrix).

predict_df(x, y_instead_of_f=True, is_normalized=True)§

Predicts the response to input X.

Parameters:

x (NP.Matrix) – An (o, M) design Matrix of inputs.
y_instead_of_f (bool) – True to include noise in the variance of the result.
is_normalized (bool) – Whether the results are normalized or not.

Return type:

rc.base.definitions.pd.DataFrame

Returns: The distribution of y or f, as a dataframe with M+L+L columns of the form (X, Mean, Predictive Std).

abstractmethod predict_gradient(x, y_instead_of_f=True)§

Predicts the gradient GP dy/dx (or df/dx) where self is the GP for y(x).

Parameters:

x (NP.Matrix) – An (o, M) design Matrix of inputs.
y_instead_of_f (bool) – True to include noise in the variance of the result.

Return type:

rc.base.definitions.Tuple[TF.Tensor, TF.Tensor]

Returns: The distribution of dy/dx or df/dx, as a pair (mean (o, L, M), cov (o, L, M, O, l, m)) if self.likelihood.is_covariant,: else (mean (o, L, M), cov (o, O, L, M)).

test()§

Tests the MOGP on the test data in self._fold.test_data. Test results comprise three values for each output at each sample: The mean prediction, the std error of prediction and the Z score of prediction (i.e. error of prediction scaled by std error of prediction).

Returns: The test_data results as a DataTable backed by MOGP.test_result_csv.

Return type:: rc.data.models.Table

broadcast_parameters(is_covariant, is_isotropic)§

Broadcast the data of the MOGP (including kernels) to higher dimensions. Shrinkage raises errors, unchanged dimensions silently do nothing.

Parameters:

is_covariant (bool) – Whether the outputs will be treated as dependent.
is_isotropic (bool) – Whether to restrict the kernel to be isotropic.

Return type:

GPR

Returns: self, for chaining calls.

class MOGP(name, fold, is_read, is_covariant, is_isotropic, kernel_parameters=None, likelihood_variance=None)§

Bases: GPR

Inheritance diagram of rc.gpr.models.MOGP

Implementation of a Gaussian Process.

Parameters:

name (str)
fold (rc.data.models.Fold)
is_read (bool | None)
is_covariant (bool)
is_isotropic (bool)
kernel_parameters (Data | None)
likelihood_variance (NP.Matrix | None)

property META: rc.base.definitions.Dict[str, rc.base.definitions.Any]§

Classmethod:
Return type:: rc.base.definitions.Dict[str, rc.base.definitions.Any]

Hyper-parameter optimizer meta

property implementation: rc.base.definitions.Tuple[rc.base.definitions.Any, Ellipsis]§

The implementation of this MOGP in GPFlow. If noise_variance.shape == (1,L) an L-tuple of kernels is returned. If noise_variance.shape == (L,L) a 1-tuple of multi-output kernels is returned.

Return type:: rc.base.definitions.Tuple[rc.base.definitions.Any, Ellipsis]

calibrate(method='L-BFGS-B', **kwargs)§

Optimize the MOGP hyper-data.

Parameters:

method (str) – The optimization algorithm (see https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html).
kwargs – A Dict of implementation-dependent optimizer meta, following the format of GPR.META. MetaData for the kernel should be passed as kernel={see kernel.META for format}. MetaData for the likelihood should be passed as likelihood={see likelihood.META for format}.

Return type:

rc.base.definitions.Dict[str, rc.base.definitions.Any]

predict(X, y_instead_of_f=True)§

Predicts the response to input X.

Parameters:

x – An (o, M) design Matrix of inputs.
y_instead_of_f (bool) – True to include noise in the variance of the result.
X (NP.Matrix)

Return type:

rc.base.definitions.Tuple[NP.Matrix, NP.Matrix]

Returns: The distribution of y or f, as a pair (mean (o, L) Matrix, std (o, L) Matrix).

predict_gradient(x, y_instead_of_f=True)§

Predicts the gradient GP dy/dx (or df/dx) where self is the GP for y(x).

Parameters:

x (NP.Matrix) – An (o, M) design Matrix of inputs.
y_instead_of_f (bool) – True to include noise in the variance of the result.

Return type:

rc.base.definitions.Tuple[TF.Tensor, TF.Tensor]

Returns: The distribution of dy/dx or df/dx, as a pair (mean (o, L, M), cov (o, L, M, O, l, m)) if self.likelihood.is_covariant,: else (mean (o, L, M), cov (o, O, L, M)).

property X: TF.Matrix§

The implementation training inputs as an (N,M) design matrix.

Return type:: TF.Matrix

property Y: TF.Matrix§

The implementation training outputs as an (N,L) design matrix.

Return type:: TF.Matrix

property K_cho: TF.Tensor§

The Cholesky decomposition of the LNxLN noisy kernel(X, X) + likelihood.variance. Shape is (LN, LN) if self.kernel.is_covariant, else (L,N,N).

Return type:: TF.Tensor

property K_inv_Y: TF.Tensor§

The LN-Vector, which pre-multiplied by the LoxLN kernel k(x, X) gives the Lo-Vector predictive mean f(x). Shape is (L,1,N). Returns: ChoSolve(self.K_cho, self.Y)

Return type:: TF.Tensor

check_K_inv_Y(x)§

FOR TESTING PURPOSES ONLY. Should return 0 Vector (to within numerical error tolerance).

Parameters:: x (NP.Matrix) – An (o, M) matrix of inputs.
Return type:: NP.Matrix

Returns: Should return zeros((Lo)) (to within numerical error tolerance).