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HistoricalLinearRegression#

class skfda.ml.regression.HistoricalLinearRegression(*, n_intervals, fit_intercept=True, lag=inf)[source]#

Historical functional linear regression.

This is a linear regression method where the covariate and the response are both functions \(\mathbb{R}\) to \(\mathbb{R}\) with the same domain. In order to predict the value of the response function at point \(t\), only the information of the covariate at points \(s < t\) is used. Is thus an “historical” model in the sense that, if the domain represents time, only the data from the past, or historical data, is used to predict a given point[1].

The model assumed by this method is:

\[y_i = \alpha(t) + \int_{s_0(t)}^t x_i(s) \beta(s, t) ds\]

where \(s_0(t) = \max(0, t - \delta)\) and \(\delta\) is a predefined time lag that can be specified so that points far in the past do not affect the predicted value.

Parameters:

  • n_intervals (int) – Number of intervals used to create the basis of the coefficients. This will be a bidimensional FiniteElement basis, and this parameter indirectly specifies the number of elements of that basis, and thus the granularity.

  • fit_intercept (bool) – Whether to calculate the intercept for this model. If set to False, no intercept will be used in calculations (i.e. data is expected to be centered).

  • lag (float) – The maximum time lag at which points in the past can still influence the prediction.

Attributes:

  • basis_coef_ – The fitted coefficient function as a FDataBasis.

  • coef_ – The fitted coefficient function as a FDataGrid.

  • intercept_ – Independent term in the linear model. Set to the constant function 0 if fit_intercept = False.

Examples

The following example test a case that conforms to this model.

>>> from skfda import FDataGrid
>>> from skfda.ml.regression import HistoricalLinearRegression
>>> import numpy as np
>>> import scipy.integrate

>>> random_state = np.random.RandomState(0)
>>> data_matrix = random_state.choice(10, size=(8, 6))
>>> data_matrix
array([[5, 0, 3, 3, 7, 9],
       [3, 5, 2, 4, 7, 6],
       [8, 8, 1, 6, 7, 7],
       [8, 1, 5, 9, 8, 9],
       [4, 3, 0, 3, 5, 0],
       [2, 3, 8, 1, 3, 3],
       [3, 7, 0, 1, 9, 9],
       [0, 4, 7, 3, 2, 7]])
>>> intercept = random_state.choice(10, size=(1, 6))
>>> intercept
array([[2, 0, 0, 4, 5, 5]])
>>> y_data = scipy.integrate.cumtrapz(
...              data_matrix,
...              initial=0,
...              axis=1,
...          ) + intercept
>>> y_data
array([[  2. ,   2.5,   4. ,  11. ,  17. ,  25. ],
       [  2. ,   4. ,   7.5,  14.5,  21. ,  27.5],
       [  2. ,   8. ,  12.5,  20. ,  27.5,  34.5],
       [  2. ,   4.5,   7.5,  18.5,  28. ,  36.5],
       [  2. ,   3.5,   5. ,  10.5,  15.5,  18. ],
       [  2. ,   2.5,   8. ,  16.5,  19.5,  22.5],
       [  2. ,   5. ,   8.5,  13. ,  19. ,  28. ],
       [  2. ,   2. ,   7.5,  16.5,  20. ,  24.5]])
>>> X = FDataGrid(data_matrix)
>>> y = FDataGrid(y_data)
>>> hist = HistoricalLinearRegression(n_intervals=8)
>>> _ = hist.fit(X, y)
>>> hist.predict(X).data_matrix[..., 0].round(1)
array([[  2. ,   2.5,   4. ,  11. ,  17. ,  25. ],
       [  2. ,   4. ,   7.5,  14.5,  21. ,  27.5],
       [  2. ,   8. ,  12.5,  20. ,  27.5,  34.5],
       [  2. ,   4.5,   7.5,  18.5,  28. ,  36.5],
       [  2. ,   3.5,   5. ,  10.5,  15.5,  18. ],
       [  2. ,   2.5,   8. ,  16.5,  19.5,  22.5],
       [  2. ,   5. ,   8.5,  13. ,  19. ,  28. ],
       [  2. ,   2. ,   7.5,  16.5,  20. ,  24.5]])
>>> abs(hist.intercept_.data_matrix[..., 0].round())
array([[ 2.,  0.,  0.,  4.,  5.,  5.]])

References

Methods

fit(X, y)

fit_predict(X, y)

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_params(**params)

Set the parameters of this estimator.

set_score_request(*[, sample_weight])

Request metadata passed to the score method.
fit(X, y)[source]#
Parameters:
Return type:

HistoricalLinearRegression

fit_predict(X, y)[source]#
Parameters:
Return type:

FDataGrid

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 (FDataGrid) –

Return type:

FDataGrid

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 (HistoricalLinearRegression) –

Returns:

self – The updated object.

Return type:

object

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