Lasso Linear Regression (L1 Lasso)

Lasso regression, which stands for Least Absolute Shrinkage and Selection Operator, is a type of linear regression that uses shrinkage. Shrinkage is where data values are shrunk towards a central point, like the mean. The lasso procedure encourages simple, sparse models (i.e., models with fewer parameters). This particular type of regression is well-suited for models showing high levels of multicollinearity or when you want to automate certain parts of model selection, like variable selection/parameter elimination.

In lasso regression, you typically deal with a single response variable and multiple predictors (Multiple Linear Regression), but you can use it if your case is multivariate, simple and multivariate - multi linear regression.

Key Features and Uses

• Sparsity: By penalizing the absolute size of the coefficients, lasso regression tends to produce models where some of the coefficient estimates may be exactly zero when λ is sufficiently large. This zeroing out of coefficients leads to sparsity, which means that the model will ignore some of the less important features, effectively performing feature selection.
• Regularization: Lasso regression is a regularization technique, which helps to prevent overfitting by adding a penalty to the size of coefficients.
• Selection: Unlike ridge regression, which also adds a penalty to the size of coefficients but tends to shrink all coefficients evenly without zeroing any out, lasso can actually reduce the number of variables in the model because it can set some coefficient estimates to zero.
• Tuning: The λ parameter needs to be chosen carefully, as it determines the level of penalty. This is often done through cross-validation.

Application Areas

Lasso regression is particularly useful in the context of high-dimensional data where the number of predictors (p) is much larger than the number of observations (n), or when building a model that benefits from variable selection for reasons of prediction accuracy, interpretability, or both. It's widely used in fields such as bioinformatics, genomics, and other areas where predictive models benefit from identifying a relevant subset of the predictors for use in the model.