# LASSO

## Definition of LASSO

Lasso: A type of regression where the researcher deliberately chooses a subset of the independent variables for inclusion in the model. It is also known as the “Least Absolute Shrinkage and Selection Operator”, or “LASSO” for short.

## How is LASSO used?

LASSO, or Least Absolute Shrinkage and Selection Operator, is an algorithm for regularized linear regression used to reduce the complexity of a model. It does this by introducing a penalty term that shrinks the coefficients related to less important features in order to prevent overfitting. The lasso penalty (also known as L1 norm) encourages some feature coefficients to become 0, effectively reducing their impact on the model. This helps eliminate redundant features from the model and can help simplify it.

The lasso algorithm works by minimizing an objective function with a constraint on the sum of the absolute values of the coefficients:

J(β)=∥ y−Xβ ∥^2 + λ∥ β ∥_1

Where X represents training data, β represents parameters being optimized, y is labels/target outputs, and λ is a hyperparameter representing the strength of regularization. As λ increases, more feature coefficients shrink towards 0 and eventually become eliminated from the model completely. This process can be controlled by optimally tuning λ in order to achieve optimal performance.

In practice, lasso is used when building machine learning models with large numbers of features that are not all necessarily relevant for predicting outcomes or generating insights about data. By using lasso, machine learning practitioners can quickly reduce complexity in their models without sacrificing performance due to overfitting or noise in noisy datasets.