Lasso

• Modelo de regresión lineal con penalización L1.

• Para la estimación de los parámetros se minimiza la función objetivo:

\min_w \frac{1}{2n} ||Xw -y||_2^2 + \alpha * ||w||_1

• Tiende a preferir soluciones con pocos coeficientes diferentes de cero, reduciendo el número de características sobre las cuales la solución es dependiente.

• Bajo ciertas condiciones, puede recuperar el conjunto exacto de coeficientes diferentes de cero.

• La implementación de sklearn usa el algoritmo de coordenadas descendentes para estimar los parámetros del modelo.

from sklearn.linear_model import Lasso

lasso = Lasso(
    # --------------------------------------------------------------------------
    # Constant that multiplies the L1 term, controlling regularization strength.
    # alpha must be a non-negative float i.e. in [0, inf). When alpha = 0, the
    # objective is equivalent to ordinary least squares, solved by the
    # LinearRegression object.
    alpha=1.0,
    # ---------------------------------------------------------------------
    # Whether to fit the intercept for this model.
    fit_intercept=True,
    # ---------------------------------------------------------------------
    # Maximum number of iterations.
    max_iter=1000,
    # --------------------------------------------------------------------------
    # The tolerance for the optimization
    tol=1e-4,
    # --------------------------------------------------------------------------
    # When set to True, reuse the solution of the previous call to fit as
    # initialization, otherwise, just erase the previous solution.
    warm_start=False,
    # --------------------------------------------------------------------------
    # When set to True, forces the coefficients to be positive.
    positive=False,
    # --------------------------------------------------------------------------
    # The seed of the pseudo random number generator that selects a random
    # feature to update. Used when selection == ‘random’. Pass an int for
    # reproducible output across multiple function calls.
    random_state=None,
    # --------------------------------------------------------------------------
    # If set to ‘random’, a random coefficient is updated every iteration rather
    # than looping over features sequentially by default. This (setting to
    # ‘random’) often leads to significantly faster convergence especially when
    # tol is higher than 1e-4.
    selection='cyclic',
)

from sklearn.datasets import load_diabetes

X, y = load_diabetes(return_X_y=True)

lasso.fit(X, y)

lasso.score(X, y)

0.357378738231628

lasso.coef_

array([  0.        ,  -0.        , 367.70385976,   6.29885756,
         0.        ,   0.        ,  -0.        ,   0.        ,
       307.6054181 ,   0.        ])

lasso.intercept_

152.133484162896