```
tags:
- AI/Regularization
aliases:
- Mean Absolute Error Loss (MAE)
- Least Absolute Deviation (LAD)
- L1 Loss
```

It calculates the absolute difference between the current output and the expected output divided by the number of output. It’s aim is to minimize this absolute differences.

- Where
determines the amount of regularization. - Mathematically it adds the sum of absolute values of the coefficients to the cost function.
- L1 regularization adds a penalty term to the cost function which is equal to the sum of modules of models coefficients multiplied by a
hyperparameter.

Notes:

- Robust to outliers: MAE is not very sensitive towards outliers as it is based on absolute value.
- A linear regression that uses the L1 regularization technique is called Lasso Regression.
- L1 Regularization performs Feature Selection by reducing the coefficients of some predictors.
- Complexity: MAE can’t be optimized by gradient descent, instead it’s optimized by Sub-Gradients, which adds complexity.
- We use MAE instead of simple difference calculation because it’s prone to
**Mean Bias Error**.E.g. the difference between actual value of (10,5) and estimated value of (8,7) can be calculated as which is misleading. - L1 Regularization can be used to induce sparsity in the learned Weights.

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