🪢Lasso Regression

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Also known as: L1 Regression

Linear regression with L1 regularization that encourages sparsity by shrinking some coefficients exactly to zero.

DESCRIPTION

Lasso Regression adds an L1 penalty to the loss, promoting sparse models that perform variable selection. It can reduce overfitting and improve interpretability by eliminating irrelevant features. The penalty strength, often denoted alpha or λ, controls sparsity and bias. Lasso is sensitive to feature scaling and correlated predictors, for which Elastic Net can help. It is widely used in high-dimensional settings and model selection pipelines.

ALTERNATIVE DEFINITIONS

Wikipedia

In statistics and machine learning, lasso is a regression analysis method that performs both variable selection and regularization.

Highlights dual role in selection and regularization.

Source

Robert Tibshirani (1996)

The lasso minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant.

Formal definition via constrained optimization in the seminal paper.

Source

scikit-learn

The Lasso is a linear model trained with ℓ1 prior as regularizer. Lasso estimates sparse coefficients.

Emphasizes sparsity outcome of ℓ1 regularization.

Source

The Elements of Statistical Learning

The ℓ1 penalty of the lasso tends to produce sparse solutions, with many coefficients estimated as exactly zero.

Focuses on sparsity property in high-dimensional models.

Source

RELATED TERMS

Regularization Feature Reduction Linear Model Least Squares Cross-Validation Sparsity Bias-Variance Tradeoff

COMPETING TERMS

Ridge Regression Elastic Net

RELATIONS

• Broader: Regression

KNOWLEDGE AREAS

Mathematics Data Science AI

TARGET AUDIENCE

Data Scientist AI Engineer Data Analyst Data Modeler

EXTERNAL SOURCES

• Wikipedia - Lasso (statistics)
• scikit-learn - API and theory for Lasso
• glmnet - Elastic net and lasso package
• Statistical Science - Original lasso paper

TOP QUESTIONS

Why use Lasso Regression for feature selection?

Lasso Regression drives some coefficients to zero, removing irrelevant features and improving interpretability and generalization in high-dimensional data.

Category: Relevancy

How do you tune Lasso Regression?

Use cross-validation to select the regularization strength (alpha/λ), ensuring a balance between sparsity and prediction error.

Category: HowTo

What are common mistakes with Lasso Regression?

Not scaling features, ignoring multicollinearity, or over-penalizing can lead to unstable or overly sparse models.

Category: Mistakes

When is Elastic Net preferable to Lasso Regression?

When features are highly correlated, Elastic Net’s mix of L1 and L2 stabilizes selection and improves performance.

Category: Opinion

What risk does Lasso Regression introduce?

Excessive sparsity can discard useful predictors and bias estimates, harming predictive performance.

Category: Risks

How does Lasso Regression relate to Least Squares?

It augments the least squares loss with an L1 penalty, altering the solution toward sparsity.

Category: Definition

Can Lasso Regression handle more features than samples?

Yes, lasso often performs well in p >> n regimes, but careful tuning and validation are needed.

Category: Example

What is the biggest misunderstanding about Lasso Regression?

Assuming lasso always finds the ‘best’ subset; it picks one among correlated features and may be unstable without Elastic Net.

Category: Misunderstanding

How to evaluate Lasso Regression performance?

Use held-out validation, cross-validation, and domain metrics; inspect selected features and residuals for bias and variance.

Category: Requirements