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 the coefficient of determination of the prediction.
`set_params`(**params)	Set the parameters of this estimator.
`set_score_request`(*[, sample_weight])	Request metadata passed to the `score` method.

fit(X, y)[source]#

Fit the model according to the given training data.

Parameters:

X (FData) – Functional data.
y (ndarray[Any, dtype[float64]]) – Target values.

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[Any, dtype[float64]]

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

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_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 (FPCARegression) –

Returns:

self – The updated object.

Return type:

object

Examples using `skfda.ml.regression.FPCARegression`#

Functional Principal Component Analysis Regression.

FPCARegression#

Examples using skfda.ml.regression.FPCARegression#

Examples using `skfda.ml.regression.FPCARegression`#