P-Splines#

class pyspline.psplines.PSplines(penalty: Tuple[float] = (1.0,), *, n_segments: Tuple[int] = (10,), degree: Tuple[int] = (3,), order_penalty: int = 2)#

Bases: BaseEstimator, RegressorMixin

P-Splines Smoothing.

Parameters:

penalty: Tuple[float], default=(1.0,): A tuple of penalty parameters for each dimension.
n_segments: Tuple[int], default=(10,): The number of evenly spaced segments.
degree: Tuple[int], default=(3,): The number of the degree of the basis.
order_penalty: int, default=2: The number of the order of the difference penalty.

Notes

This code is adapted from _[2]. See [1] for more details.

References

[1]

Eilers, P., Marx, B.D., (2021) Practical Smoothing: The Joys of P-splines. Cambridge University Press, Cambridge.

[2]

Eilers, P., Marx, B., Li, B., Gampe, J., Rodriguez-Alvarez, M.X., (2023) JOPS: Practical Smoothing with P-Splines.

Examples

>>> from skltemplate import TemplateEstimator
>>> import numpy as np
>>> X = np.arange(100).reshape(100, 1)
>>> y = np.zeros((100, ))
>>> estimator = TemplateEstimator()
>>> estimator.fit(X, y)
TemplateEstimator()

Methods

`derivative`(X[, order_derivative])	Estimate the derivative of the data.
`errors`(X)	Estimate the standard errors of the fitted values.
`fit`(X, y[, sample_weights, domains])	Fit a P-splines model to the given data.
`get_metadata_routing`()	Get metadata routing of this object.
`get_params`([deep])	Get parameters for this estimator.
`predict`(X)	Predict the response variable values.
`score`(X, y[, sample_weight])	Return the coefficient of determination of the prediction.
`set_fit_request`(*[, domains, sample_weights])	Request metadata passed to the `fit` method.
`set_params`(**params)	Set the parameters of this estimator.
`set_score_request`(*[, sample_weight])	Request metadata passed to the `score` method.

fit(X: ndarray[Any, dtype[float64]], y: ndarray[Any, dtype[float64]], sample_weights: ndarray[Any, dtype[float64]] | None = None, domains: list[tuple[float64]] | tuple[float64] | None = None) → PSplines#

Fit a P-splines model to the given data.

The method fits a P-splines model to the given data using a B-splines basis and an optional weights matrix.

Parameters:

X: npt.NDArray[np.float_], shape=(n_obs, n_dimension): An array containing the predictor variable values.
y: npt.NDArray[np.float_], shape=(n_obs,): An array containing the response variable values.
sample_weights: npt.NDArray[np.float64] | None, default=None: An array of shape (n_obs,) containing the weights for each observation. If not provided, all observations are assumed to have equal weight.
domains: list[tuple[np.float_]] | tuple[np.float_] | None, default=None: The domains of the B-splines basis.

Returns:

self: PSplines: Returns self.

predict(X: ndarray[Any, dtype[float64]]) → ndarray[Any, dtype[float64]]#

Predict the response variable values.

The method predicts the response variable values for the given predictor variable values using the fitted P-splines model. If X is not provided, the method returns the fitted values.

Parameters:

X: npt.NDArray[np.float_]: An array containing the predictor variable values.

Returns:

npt.NDArray[np.float_]: An array containing the estimated response variable values.

errors(X: ndarray[Any, dtype[float64]]) → ndarray[Any, dtype[float64]]#

Estimate the standard errors of the fitted values.

Parameters:

X: npt.NDArray[np.float_]: An array containing the predictor variable values.

Returns:

npt.NDArray[np.float_]: An array containing standard errors of the fitted values.

derivative(X: ndarray[Any, dtype[float64]], order_derivative: int = 1)#

Estimate the derivative of the data.

Parameters:

X: npt.NDArray[np.float_]: An array containing the predictor variable values.
order_derivative: int, default=1: Order of the derivative to compute.

set_fit_request(*, domains: bool | None | str = '$UNCHANGED$', sample_weights: bool | None | str = '$UNCHANGED$') → PSplines#

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

domainsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for domains parameter in fit.
sample_weightsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for sample_weights parameter in fit.

Returns:

selfobject: The updated object.

set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → PSplines#

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for sample_weight parameter in score.

Returns:

selfobject: The updated object.