generalized_additive_models.ExpectileGAM#

class generalized_additive_models.ExpectileGAM(terms=None, *, expectile=0.5, fit_intercept=True, solver='pirls', max_iter=100, tol=0.0001, verbose=-1)#

Initialize an ExpectileGAM.

A GAM with a Normal distribution and an Identity link minimizes a weighted least squares objective

\[\ell(\beta) = \sum_i w_i (f(x_i; \beta) - y_i)^2 + \operatorname{penalty}(\beta)\]

The ExpectileGAM minimizes a least asymmetrically weighted squares objective. The weights \(w_i\) are chosen based on the residuals \(\epsilon_i = f(x_i; \beta) - y_i\) and a desired expectile \(\tau\). The weights are given by

\[\begin{split}\epsilon_i = \begin{cases} \tau &\text{ if } \epsilon_i \leq 0 \\ 1 - \tau &\text{ if } \epsilon_i > 0 \end{cases}\end{split}\]

For more information, see:

Parameters:

  • terms (Term, TermList or list, optional) – The term(s) of the model. The argument can be a single term or a collection of terms. The features that the terms refer to must be present in the data set at fit and predict time. The default is None.

  • expectile (float, optional) – The expectile to fit to. The default is 0.5.

  • fit_intercept (TYPE, optional) – Whether or not to automatically add an intercept term to the terms. If an intercept is already present, then this setting has no effect. The default is True.

  • solver (str, optional) – The solver to use, currently only “pirls” is available, which stands for Penalized Iterated Reweighted Least Squares. The default is “pirls”.

  • max_iter (int, optional) – Maximum number of iterations in the solver. The default is 100.

  • tol (TYPE, optional) – Tolerance in the solver. The default is 0.0001.

  • verbose (int, optional) – Verbosity level. The higher the number, the more info is printed. The default is 0.

Return type:

None.

__init__(terms=None, *, expectile=0.5, fit_intercept=True, solver='pirls', max_iter=100, tol=0.0001, verbose=-1)#

Methods

__init__([terms, expectile, fit_intercept, ...])

fit(X, y[, sample_weight])

Fit model to data.

fit_quantile(X, y, quantile[, max_iter, ...])

Find the expectile such that the empirical quantile matches quantile.

get_metadata_routing()

Get metadata routing of this object.

get_params([deep])

Get parameters for this estimator.

predict(X)

Predict the expected value \(\mu\) with the model.

residuals(X, y, *[, residuals, standardized])

Compute a vector of residuals.

sample(mu[, size, random_state])

Sample from the posterior predictive distribution.

score(X, y[, sample_weight])

Proportion deviance explained (pseudo \(r^2\)).

set_fit_request(*[, sample_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.

summary([file])

Print a model summary.

Attributes

DISTRIBUTIONS

LINKS

fit_quantile(X, y, quantile, max_iter=20, tol=0.01, sample_weight=None)#

Find the expectile such that the empirical quantile matches quantile.

Finding the desired expectile is done by performing binary search.

Parameters:

  • X (array-like, shape (n_samples, m_features)) – Training vectors, where n_samples is the number of samples and m_features is the number of features.

  • y (array-like, shape (n_samples,)) – Target values (integers in classification, real numbers in regression) For classification, labels must correspond to classes.

  • quantile (float on (0, 1)) – desired quantile to fit.

  • max_iter (int, default: 20) – maximum number of binary search iterations to perform

  • tol (float > 0, default: 0.01) – maximum distance between desired quantile and fitted quantile

  • weights (array-like shape (n_samples,) or None, default: None) – containing sample weights if None, defaults to array of ones

Returns:

self

Return type:

Fitted GAM object with updated expectile parameter.

Examples

>>> import numpy as np
>>> from generalized_additive_models import ExpectileGAM, Intercept
>>> rng = np.random.default_rng(42)
>>> X = np.ones((1000, 1))
>>> y = rng.triangular(left=0, mode=0.5, right=1, size=(1000, 1))
>>> gam = ExpectileGAM(Intercept()).fit_quantile(X, y, quantile=0.9)
>>> float((gam.predict(X) > y).mean())
0.90...
>>> gam.expectile
0.976...
set_fit_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → ExpectileGAM#

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:

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

Returns:

self – The updated object.

Return type:

object

set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → ExpectileGAM#

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.

Returns:

self – The updated object.

Return type:

object