FPCARegression#

class skfda.ml.regression.FPCARegression(n_components=5, fit_intercept=True, pca_regularization=None, regression_regularization=None, components_basis=None)[source]#

Regression using Functional Principal Components Analysis.

It performs Functional Principal Components Analysis to reduce the dimension of the functional data, and then uses a linear regression model to relate the transformed data to a scalar value.

Parameters:

  • n_components (int) – Number of principal components to keep. Defaults to 5.

  • fit_intercept (bool) – If True, the linear model is calculated with an intercept. Defaults to True.

  • pca_regularization (L2Regularization | None) – Regularization parameter for the principal component extraction. If None then no regularization is applied. Defaults to None.

  • regression_regularization (L2Regularization | None) – Regularization parameter for the linear regression. If None then no regularization is applied. Defaults to None.

  • components_basis (Basis | None) – Basis used for the principal components. If None then the basis of the input data is used. Defaults to None. It is only used if the input data is a FDataBasis object.

Attributes:

  • n_components_ – Number of principal components used.

  • components_ – Principal components.

  • coef_ – Coefficients of the linear regression model.

  • explained_variance_ – Amount of variance explained by each of the selected components.

  • explained_variance_ratio_ – Percentage of variance explained by each of the selected components.

Examples

Using the Berkeley Growth Study dataset, we can fit the model.

>>> import skfda
>>> dataset = skfda.datasets.fetch_growth()
>>> fd = dataset["data"]
>>> y = dataset["target"]
>>> reg = skfda.ml.regression.FPCARegression(n_components=2)
>>> reg.fit(fd, y)
FPCARegression(n_components=2)

Then, we can predict the target values and calculate the score.

>>> score = reg.score(fd, y)
>>> reg.predict(fd)
array([...])

Methods

fit(X, y)

Fit the model according to the given training data.

get_metadata_routing()

Get metadata routing of this object.

get_params([deep])

Get parameters for this estimator.

predict(X)

Predict using the linear model.

score(X, y[, sample_weight])

Return coefficient of determination on test data.

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)[source]#

Fit the model according to the given training data.

Parameters:
Returns:

self

Return type:

FPCARegressionSelf

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]#

Predict using the linear model.

Parameters:

X (FData) – Functional data.

Returns:

Target values.

Return type:

ndarray[tuple[Any, …], dtype[floating[Any]]]

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_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 (FPCARegression)

Returns:

self – The updated object.

Return type:

object

Examples using skfda.ml.regression.FPCARegression#

Functional Principal Component Analysis Regression.

Functional Principal Component Analysis Regression.