Lasso model fit with Least Angle Regression a.k.a. Lars
It is a Linear Model trained with an L1 prior as regularizer.
The optimization objective for Lasso is:
(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1
Read more in the User Guide.
Parameters: |
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alpha : float -
Constant that multiplies the penalty term. Defaults to 1.0. alpha = 0 is equivalent to an ordinary least square, solved by LinearRegression . For numerical reasons, using alpha = 0 with the LassoLars object is not advised and you should prefer the LinearRegression object. -
fit_intercept : boolean -
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered). -
verbose : boolean or integer, optional -
Sets the verbosity amount -
normalize : boolean, optional, default True -
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False . -
precompute : True | False | ‘auto’ | array-like -
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument. -
max_iter : integer, optional -
Maximum number of iterations to perform. -
eps : float, optional -
The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Unlike the tol parameter in some iterative optimization-based algorithms, this parameter does not control the tolerance of the optimization. -
copy_X : boolean, optional, default True -
If True, X will be copied; else, it may be overwritten. -
fit_path : boolean -
If True the full path is stored in the coef_path_ attribute. If you compute the solution for a large problem or many targets, setting fit_path to False will lead to a speedup, especially with a small alpha. -
positive : boolean (default=False) -
Restrict coefficients to be >= 0. Be aware that you might want to remove fit_intercept which is set True by default. Under the positive restriction the model coefficients will not converge to the ordinary-least-squares solution for small values of alpha. Only coefficients up to the smallest alpha value (alphas_[alphas_ >
0.].min() when fit_path=True) reached by the stepwise Lars-Lasso algorithm are typically in congruence with the solution of the coordinate descent Lasso estimator. |
Attributes: |
-
alphas_ : array, shape (n_alphas + 1,) | list of n_targets such arrays -
Maximum of covariances (in absolute value) at each iteration. n_alphas is either max_iter , n_features , or the number of nodes in the path with correlation greater than alpha , whichever is smaller. -
active_ : list, length = n_alphas | list of n_targets such lists -
Indices of active variables at the end of the path. -
coef_path_ : array, shape (n_features, n_alphas + 1) or list -
If a list is passed it’s expected to be one of n_targets such arrays. The varying values of the coefficients along the path. It is not present if the fit_path parameter is False . -
coef_ : array, shape (n_features,) or (n_targets, n_features) -
Parameter vector (w in the formulation formula). -
intercept_ : float | array, shape (n_targets,) -
Independent term in decision function. -
n_iter_ : array-like or int. -
The number of iterations taken by lars_path to find the grid of alphas for each target. |
Examples
>>> from sklearn import linear_model
>>> reg = linear_model.LassoLars(alpha=0.01)
>>> reg.fit([[-1, 1], [0, 0], [1, 1]], [-1, 0, -1])
...
LassoLars(alpha=0.01, copy_X=True, eps=..., fit_intercept=True,
fit_path=True, max_iter=500, normalize=True, positive=False,
precompute='auto', verbose=False)
>>> print(reg.coef_)
[ 0. -0.963257...]
Methods
fit (X, y[, Xy]) | Fit the model using X, y as training data. |
get_params ([deep]) | Get parameters for this estimator. |
predict (X) | Predict using the linear model |
score (X, y[, sample_weight]) | Returns the coefficient of determination R^2 of the prediction. |
set_params (**params) | Set the parameters of this estimator. |
-
__init__(alpha=1.0, fit_intercept=True, verbose=False, normalize=True, precompute=’auto’, max_iter=500, eps=2.220446049250313e-16, copy_X=True, fit_path=True, positive=False)
[source]
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fit(X, y, Xy=None)
[source]
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Fit the model using X, y as training data.
Parameters: |
-
X : array-like, shape (n_samples, n_features) -
Training data. -
y : array-like, shape (n_samples,) or (n_samples, n_targets) -
Target values. -
Xy : array-like, shape (n_samples,) or (n_samples, n_targets), optional -
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed. |
Returns: |
-
self : object -
returns an instance of self. |
-
get_params(deep=True)
[source]
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Get parameters for this estimator.
Parameters: |
-
deep : boolean, optional -
If True, will return the parameters for this estimator and contained subobjects that are estimators. |
Returns: |
-
params : mapping of string to any -
Parameter names mapped to their values. |
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predict(X)
[source]
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Predict using the linear model
Parameters: |
-
X : array_like or sparse matrix, shape (n_samples, n_features) -
Samples. |
Returns: |
-
C : array, shape (n_samples,) -
Returns predicted values. |
-
score(X, y, sample_weight=None)
[source]
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Returns the coefficient of determination R^2 of the prediction.
The coefficient R^2 is defined as (1 - 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, shape = (n_samples, n_features) -
Test samples. For some estimators this may be a precomputed kernel matrix instead, 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, shape = (n_samples) or (n_samples, n_outputs) -
True values for X. -
sample_weight : array-like, shape = [n_samples], optional -
Sample weights. |
Returns: |
-
score : float -
R^2 of self.predict(X) wrt. y. |
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set_params(**params)
[source]
-
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter>
so that it’s possible to update each component of a nested object.