# Difference between L1 and L2 regularization?

Regularization is a machine-learning strategy that avoids overfitting. Overfitting happens when a model fits the training data too well and is too complicated yet fails to function adequately on unobserved data. The model's loss function is regularized to include a penalty term, which helps prevent the parameters from growing out of control and simplifies the model. As a result, the model has a lower risk of overfitting and performs better when applied to new data. When working with high-dimensional data, regularization is especially crucial since it lowers the likelihood of overfitting and keeps the model from becoming overly complicated. In this post, we'll look at regularization and the differences between L1 and L2 regularization.

## What is regularization in machine learning?

Regularization is a machine-learning approach that prevents overfitting by including a penalty term into the model's loss function. Regularization has two objectives: to lessen a model's complexity and to improve its ability to generalize to new inputs. Different penalty terms are added to the loss function using numerous regularization methods, including L1 and L2 regularization. In contrast to L2 regularization, which adds a punishment term based on the squares of the parameters, L1 regularization adds a penalty term based on the absolute values of the model's parameters. Regularization decreases the chance of overfitting and helps keep the model's parameters from going out of control, both of which can enhance the model's performance on untested data.

## What is L1 regularization?

L1 regularization, also known as Lasso regularization, is a machine-learning strategy that inhibits overfitting by introducing a penalty term into the model's loss function based on the absolute values of the model's parameters. L1 regularization seeks to reduce some model parameters toward zero in order to lower the number of non-zero parameters in the model (sparse model).

L1 regularization is particularly useful when working with high-dimensional data since it enables one to choose a subset of the most important attributes. This lessens the risk of overfitting and also makes the model easier to understand. The size of a penalty term is controlled by the hyperparameter lambda, which regulates the L1 regularization's regularization strength. As lambda rises, more parameters will be lowered to zero, improving regularization.

## What is L2 regularization?

L2 regularization, also known as Ridge regularization, is a machine learning technique that avoids overfitting by introducing a penalty term into the model's loss function based on the squares of the model's parameters. The goal of L2 regularization is to keep the model's parameter sizes short and prevent oversizing.

In order to achieve L2 regularization, a term that is proportionate to the squares of the model's parameters is added to the loss function. This word works as a limiter on the parameters' size, preventing them from growing out of control. A hyperparameter called lambda that controls the regularization's intensity also controls the size of the penalty term. The parameters will be smaller and the regularization will be stronger the greater the lambda.

## Difference between L1 & L2 regularization

L1 Regularization

L2 Regularization

The penalty term is based on the absolute values of the model's parameters.

The penalty term is based on the squares of the model's parameters.

Produces sparse solutions (some parameters are shrunk towards zero).

Produces non-sparse solutions (all parameters are used by the model).

Sensitive to outliers.

Robust to outliers.

Selects a subset of the most important features.

All features are used by the model.

Optimization is non-convex.

Optimization is convex.

The penalty term is less sensitive to correlated features.

The penalty term is more sensitive to correlated features.

Useful when dealing with high-dimensional data with many correlated features.

Useful when dealing with high-dimensional data with many correlated features and when the goal is to have a less complex model.

Also known as Lasso regularization.

Also known as Ridge regularization.

## Conclusion

L1 and L2 regularization are two methods for preventing overfitting in machine learning models, to sum up. L1 regularization, which generates sparse solutions and is based on the absolute values of the model's parameters, is helpful for feature selection. In contrast, L2 regularization yields non-sparse solutions and is based on the squares of the model's parameters, making it beneficial for building simpler models. A hyperparameter called lambda that controls the degree of regularization controls both methods. Depending on the particular situation and the required model attributes, L1 or L2 regularization is chosen.