KernelRegression#

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

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 coefficient of determination on test data.

set_fit_request(*[, weight])

Configure whether metadata should be requested to be passed to the fit method.

set_params(**params)

Set the parameters of this estimator.

set_score_request(*[, sample_weight])

Configure whether metadata should be requested to be passed to the score method.
fit(X, y, weight=None)[source]#
Parameters:
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)[source]#
Parameters:

X (Input)

Return type:

Prediction

score(X, y, sample_weight=None)[source]#

Return coefficient of determination on test data.

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='$UNCHANGED$')#

Configure whether metadata should be requested to be passed to the fit method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config()). Please check the 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.

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='$UNCHANGED$')#

Configure whether metadata should be requested to be passed to the score method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config()). Please check the 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.

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