Lasso Regression

Lasso regression model vs ridge regression model

While both lasso and ridge regression are regularization techniques, they differ in their approaches.

Lasso regression model utilizes an ℓ1 penalty, which can shrink some coefficients to exactly zero, thereby performing variable selection.
Ridge regression: Employs an ℓ2 penalty, which shrinks coefficients uniformly but does not set any to zero, thus retaining all variables in the model.

This distinction makes lasso feature selection particularly useful when the goal is to simplify the model by selecting a subset of relevant features.

Lasso algorithm examples

Lasso regression is especially beneficial in scenarios involving high-dimensional data where the number of predictors exceeds the number of observations.

It is widely used in fields such as genomics, finance, and machine learning for a wide range of tasks.

Feature selection: Identifying and retaining only the most significant variables in the model.
Improving model interpretability: Simplifying models to make them more interpretable by reducing complexity.
Handling multicollinearity: Addressing issues arising from highly correlated predictors by selecting one variable from a group of correlated variables and setting others to zero.

Advantages and limitations of lasso regression

Advantages	Limitations
Simplicity: By setting insignificant coefficients to zero, lasso produces simpler and more interpretable models.	Bias in coefficients. The shrinkage of coefficients can introduce bias, especially when true coefficients are large.
Variable selection: Simultaneously performs variable selection and regularization, which is particularly useful in high-dimensional datasets.	Selection of tuning parameter. Choosing the appropriate value for the tuning parameter is crucial and often requires cross-validation.
Multicollinearity handling: Effectively manages multicollinearity by selecting among correlated predictors.	Performance with correlated variables. Lasso may arbitrarily select one variable from a group of highly correlated variables, potentially omitting others that are equally important.

Understanding these aspects of lasso regression helps understand when to use lasso regression.