KernelRegression

class skfda.ml.regression.KernelRegression(*, kernel_estimator=None, metric=LpDistance(p=2, vector_norm=None))

Kernel regression with scalar response.

Let \(fd_1 = (X_1, X_2, ..., X_n)\) be the functional data set and \(y = (y_1, y_2, ..., y_n)\) be the scalar response corresponding to each function in \(fd_1\). Then, the estimation for the functions in \(fd_2 = (X'_1, X'_2, ..., X'_n)\) can be calculated as

\[\hat{y} = \hat{H}y\]

Where \(\hat{H}\) is a matrix described in HatMatrix.

Parameters:

• kernel_estimator (HatMatrix | None) – Method used to calculate the hat matrix (default = NadarayaWatsonHatMatrix).

• metric (Metric[Input]) – Metric used to calculate the distances (default = L2 distance).

Examples

>>> import numpy as np
>>> from skfda import FDataGrid
>>> from skfda.misc.hat_matrix import NadarayaWatsonHatMatrix
>>> from skfda.misc.hat_matrix import KNeighborsHatMatrix

>>> grid_points = np.linspace(0, 1, num=11)
>>> data1 = np.array([i + grid_points for i in range(1, 9, 2)])
>>> data2 = np.array([i + grid_points for i in range(2, 7, 2)])

>>> fd_1 = FDataGrid(grid_points=grid_points, data_matrix=data1)
>>> y = np.array([1, 3, 5, 7])
>>> fd_2 = FDataGrid(grid_points=grid_points, data_matrix=data2)

>>> kernel_estimator = NadarayaWatsonHatMatrix(bandwidth=1)
>>> estimator = KernelRegression(kernel_estimator=kernel_estimator)
>>> _ = estimator.fit(fd_1, y)
>>> estimator.predict(fd_2)
array([ 2.02723928,  4.        ,  5.97276072])

>>> kernel_estimator = KNeighborsHatMatrix(n_neighbors=2)
>>> estimator = KernelRegression(kernel_estimator=kernel_estimator)
>>> _ = estimator.fit(fd_1, y)
>>> estimator.predict(fd_2)
array([ 2.,  4.,  6.])

Methods

fit(X, y[, weight])
get_metadata_routing()	Get metadata routing of this object.
get_params([deep])	Get parameters for this estimator.
predict(X)
score(X, y[, sample_weight])	Return the coefficient of determination of the prediction.
set_fit_request(*[, weight])	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, y, weight=None)

Parameters:

• X (Input) –

• y (Prediction) –

• weight (NDArrayFloat | None) –

Return type:

KernelRegression[Input, Prediction]

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routing – A MetadataRequest encapsulating routing information.

Return type:

MetadataRequest

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

params – Parameter names mapped to their values.

Return type:

dict

predict(X)

Parameters:

X (Input) –

Return type:

Prediction

score(X, y, sample_weight=None)

Return the coefficient of determination of the prediction.

The coefficient of determination \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)** 2).sum() and \(v\) is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.

Parameters:

• X (array-like of shape (n_samples, n_features)) – Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.

• y (array-like of shape (n_samples,) or (n_samples, n_outputs)) – True values for X.

• sample_weight (array-like of shape (n_samples,), default=None) – Sample weights.

Returns:

score – \(R^2\) of self.predict(X) w.r.t. y.

Return type:

float

Notes

The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score(). This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_fit_request(*, weight='$UNCHANGED$')

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.

New 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:

• weight (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for weight parameter in fit.

• self (KernelRegression) –

Returns:

self – The updated object.

Return type:

object

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**params (dict) – Estimator parameters.

Returns:

self – Estimator instance.

Return type:

estimator instance

set_score_request(*, sample_weight='$UNCHANGED$')

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.

New 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_weight (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for sample_weight parameter in score.

• self (KernelRegression) –

Returns:

self – The updated object.

Return type:

object

Examples using skfda.ml.regression.KernelRegression

Kernel Regression

Kernel Regression