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ElasticNet

API Reference

Signature

model = sp.ElasticNet(
    alpha=1.0,
    l1_ratio=0.5,
    max_iter=1000,
    tol=1e-4,
    fit_intercept=True,
)

model.fit(X, y)
model.predict(X)   -> list[float]
model.score(X, y)  -> float
model.get_params() -> dict
model.set_params(alpha=..., l1_ratio=..., max_iter=..., tol=..., fit_intercept=...)

Constructor parameters

ParameterTypeDefaultDescription
alphafloat1.0Overall penalty strength
l1_ratiofloat0.5Mix between L1 and L2: 0 = pure Ridge, 1 = pure Lasso
max_iterint1000Maximum coordinate descent iterations
tolfloat1e-4Convergence tolerance
fit_interceptboolTrueFit a bias term

Attributes

AttributeTypeDescription
coef_list[float]Fitted coefficients
intercept_floatBias term
n_iter_intActual iterations performed
Example 
import seraplot as sp
import numpy as np

X = np.random.randn(400, 15)
true_coef = np.zeros(15)
true_coef[:5] = [2.0, -1.5, 1.0, -0.5, 0.8]
y = X @ true_coef + np.random.randn(400) * 0.3

model = sp.ElasticNet(alpha=0.1, l1_ratio=0.7)
model.fit(X, y)
non_zero = sum(1 for c in model.coef_ if abs(c) > 1e-6)
print(f"R2: {model.score(X, y):.4f}")
print(f"Non-zero: {non_zero} / 15")

Algorithmic Functioning

ElasticNet combines both L1 and L2 penalties:

$$\hat{\beta} = \underset{\beta}{\arg\min}\ \frac{1}{2n}\|y - X\beta\|_2^2 + \alpha\!\left[\rho\|\beta\|_1 + \frac{1-\rho}{2}\|\beta\|_2^2\right]$$

where $\rho$ = l1_ratio. Setting $\rho = 1$ recovers Lasso; $\rho = 0$ recovers Ridge.

Coordinate descent update for coefficient $j$:

$$\hat{\beta}_j \leftarrow \frac{S\!\left(X_j^T r_j / n,\ \alpha\rho\right)}{\|X_j\|_2^2 / n + \alpha(1-\rho)}$$

where $S(\cdot, \lambda)$ is the soft-threshold operator. The L2 term appears in the denominator, providing grouping behaviour: correlated features tend to receive similar non-zero coefficients.

l1_ratioBehaviour
1Lasso — sparse solutions
0Ridge — dense, shrunk solutions
(0, 1)ElasticNet — sparse + stable

The checkpoint_id argument enables training resumed across multiple Python calls.

Référence API

Signature

model = sp.ElasticNet(
    alpha=1.0,
    l1_ratio=0.5,
    max_iter=1000,
    tol=1e-4,
    fit_intercept=True,
)

model.fit(X, y)
model.predict(X)   -> list[float]
model.score(X, y)  -> float
model.get_params() -> dict
model.set_params(alpha=..., l1_ratio=..., max_iter=..., tol=..., fit_intercept=...)

Paramètres du constructeur

ParamètreTypeDéfautDescription
alphafloat1.0Force globale de pénalité
l1_ratiofloat0.5Mélange L1/L2 : 0 = Ridge pur, 1 = Lasso pur
max_iterint1000Nombre maximum d'itérations
tolfloat1e-4Tolérance de convergence
fit_interceptboolTrueAjuster un terme de biais

Attributs

AttributTypeDescription
coef_list[float]Coefficients ajustés
intercept_floatTerme de biais
n_iter_intNombre d'itérations réalisées
Exemple 
import seraplot as sp
import numpy as np

X = np.random.randn(400, 15)
true_coef = np.zeros(15)
true_coef[:5] = [2.0, -1.5, 1.0, -0.5, 0.8]
y = X @ true_coef + np.random.randn(400) * 0.3

model = sp.ElasticNet(alpha=0.1, l1_ratio=0.7)
model.fit(X, y)
non_zero = sum(1 for c in model.coef_ if abs(c) > 1e-6)
print(f"R2 : {model.score(X, y):.4f}")
print(f"Non nuls : {non_zero} / 15")

Fonctionnement algorithmique

ElasticNet combine les pénalités L1 et L2 :

$$\hat{\beta} = \underset{\beta}{\arg\min}\ \frac{1}{2n}\|y - X\beta\|_2^2 + \alpha\!\left[\rho\|\beta\|_1 + \frac{1-\rho}{2}\|\beta\|_2^2\right]$$

où $\rho$ = l1_ratio. Avec $\rho = 1$ on retrouve Lasso ; avec $\rho = 0$ on retrouve Ridge.

Descente de coordonnées pour le coefficient $j$ :

$$\hat{\beta}_j \leftarrow \frac{S\!\left(X_j^T r_j / n,\ \alpha\rho\right)}{\|X_j\|_2^2 / n + \alpha(1-\rho)}$$

où $S(\cdot, \lambda)$ est l'opérateur de seuillage doux. Le terme L2 apparaît au dénominateur, favorisant le regroupement : les variables corrélées tendent à recevoir des coefficients non nuls similaires.

l1_ratioComportement
1Lasso — solutions creuses
0Ridge — solutions denses et rétrécies
(0, 1)ElasticNet — creux + stable

L'argument checkpoint_id permet de reprendre l'entraînement entre plusieurs appels Python.