Configure Lasso "positive" Parameter

The positive parameter in scikit-learn’s Lasso class constrains the coefficients to be non-negative when set to True. This can be useful when you have prior knowledge that the coefficients should be positive.

Lasso (Least Absolute Shrinkage and Selection Operator) is a linear regression technique that performs both feature selection and regularization. It adds a penalty term to the loss function, shrinking some coefficients and setting others to zero.

By default, positive is set to False, allowing coefficients to be either positive or negative. When set to True, it forces all coefficients to be non-negative.

In practice, positive=True is used when there is a strong prior belief that the features should have a non-negative impact on the target variable.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.linear_model import Lasso
from sklearn.metrics import r2_score
import numpy as np

# Generate synthetic dataset
X, y = make_regression(n_samples=100, n_features=5, n_informative=3, random_state=42)

# Make some coefficients negative
coef = [2, -1, 0, -0.5, 0]
y = np.dot(X, coef) + 0.1 * np.random.normal(size=X.shape[0])

# Split into train and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Fit Lasso with default (positive=False)
lasso = Lasso(alpha=0.1, random_state=42)
lasso.fit(X_train, y_train)
print(f"Default Lasso Coefficients: {lasso.coef_}")
print(f"Default Lasso R^2: {r2_score(y_test, lasso.predict(X_test)):.3f}")

# Fit Lasso with positive=True
lasso_pos = Lasso(alpha=0.1, positive=True, random_state=42)
lasso_pos.fit(X_train, y_train)
print(f"Positive Lasso Coefficients: {lasso_pos.coef_}")
print(f"Positive Lasso R^2: {r2_score(y_test, lasso_pos.predict(X_test)):.3f}")

Running the example gives an output like:

Default Lasso Coefficients: [ 1.90402002 -0.90527933 -0.         -0.44395165  0.        ]
Default Lasso R^2: 0.995
Positive Lasso Coefficients: [2.10419903 0.         0.         0.         0.        ]
Positive Lasso R^2: 0.864

The key steps in this example are:

Generate a synthetic regression dataset with some positive and negative coefficients
Split the data into train and test sets
Fit a default Lasso model (allowing negative coefficients)
Fit a Lasso model with positive=True (constraining coefficients to be non-negative)
Compare the coefficients and R^2 scores of the two models

Some tips and heuristics for using positive:

Set positive=True when you have strong domain knowledge that the features should have non-negative effects
Using positive=True can improve interpretability by eliminating counterintuitive negative coefficients

Issues to consider:

Constraining coefficients to be non-negative may lead to reduced performance if the true coefficients are negative
Only use positive=True when you have a strong prior belief about the sign of the coefficients

See Also