# lightning.regression.FistaRegressor¶

class lightning.regression.FistaRegressor(C=1.0, alpha=1.0, penalty='l1', max_iter=100, max_steps=30, eta=2.0, sigma=1e-05, callback=None, verbose=0)[source]

Estimator for learning linear classifiers by FISTA.

The objective functions considered take the form

minimize F(W) = C * L(W) + alpha * R(W),

where L(W) is a loss term and R(W) is a penalty term.

Parameters

penalty (str or Penalty object, {'l2', 'l1', 'l1/l2', 'tv1d', 'simplex'}) –

The penalty or constraint to be used.

• l2: ridge

• l1: lasso

• l1/l2: group lasso

• tv1d: 1-dimensional total variation (also known as fussed lasso)

• simplex: simplex constraint

The method can also take an arbitrary Penalty object, i.e., an instance that implements methods projection regularization method (see file penalty.py)

Cfloat

Weight of the loss term.

alphafloat

Weight of the penalty term.

max_iterint

Maximum number of iterations to perform.

max_stepsint

Maximum number of steps to use during the line search.

sigmafloat

Constant used in the line search sufficient decrease condition.

etafloat

Decrease factor for line-search procedure. For example, eta=2. will decrease the step size by a factor of 2 at each iteration of the line-search routine.

callbackcallable

Callback function.

verboseint

Verbosity level.

fit(X, y)[source]
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

n_nonzero(percentage=False)
predict(X)
score(X, y, sample_weight=None)

Return the coefficient of determination $$R^2$$ of the prediction.

The coefficient $$R^2$$ 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) wrt. 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