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L1 Regularization versus L1 Loss (absolute loss or mean absolute error (MAE))
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L1 Regularization and L1 Loss are two distinct concepts in machine learning, although they both involve the use of the L1 norm. Lasso stands for "Least Absolute Shrinkage and Selection Operator." It is a specific type of penalized regression that uses L1 regularization. Lasso adds a penalty term to the linear regression objective function that is proportional to the absolute values of the model coefficients. This encourages sparsity in the model, meaning it can set some coefficients to exactly zero, effectively performing feature selection. Table 3879a lists the key differences between the two regularization.

Table 3879a. Key differences between the two regularization.

  L1 Regularization L1 Loss
Purpose L1 regularization, often referred to as Lasso regularization, is a technique used to penalize the magnitude of the model's coefficients (weights) in a linear model, such as linear regression or logistic regression. L1 loss, also known as the absolute loss or mean absolute error (MAE), is a loss function used to measure the absolute difference between predicted and actual values in regression problems.
Objective The primary objective of L1 regularization is to encourage sparsity in the model, meaning it pushes some of the coefficients to exactly zero, effectively performing feature selection. The primary objective of using L1 loss as a loss function is to minimize the absolute errors between predictions and actual values during model training.
Usage L1 regularization is typically applied during the training phase of a machine learning model to prevent overfitting and simplify the model by removing less important features. L1 loss is used directly as the loss function during the training phase of regression models (e.g., linear regression) to optimize the model parameters (coefficients) to minimize the absolute error between predictions and true target values.
Penalty Term L1 regularization adds a penalty term to the loss function, which is proportional to the L1 norm (sum of absolute values) of the model's coefficients. The strength of this penalty is controlled by a hyperparameter called the regularization strength (often denoted as lambda or alpha). L1 loss computes the absolute differences between predictions and actual values for each data point and then computes the mean (or sum) of these absolute differences. It does not involve regularization or adding penalty terms to the model's coefficients.

Note that penalized regression, Lasso, and Ridge regression are related concepts in the field of linear regression, but they are not exactly the same as L1 and L2 regularization.

Table 3879b. Applications and related concepts of L1 regularization.

Applications Page
L1 soft margin

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