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I am experimenting different loss functions for my regression model. I noticed that in the sklearn, there are:

sklearn.linear_model.HuberRegressor and sklearn.linear_model.ElasticNet

To me, both use the combination of L1 and L2 loss. What exactly is the difference of this? Thanks!

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Yes, many loss functions in regression models are using a combination of L1 and L2 for different purposes. To realize the difference, I start with Ridge regression.

Ridge regression addresses some of the problems of Ordinary Least Squares by imposing a penalty on the size of the coefficients. The ridge coefficients minimize a penalized residual sum of squares.

The HuberRegressor is different to Ridge because it applies a linear loss to samples that are classified as outliers. A sample is classified as an inlier if the absolute error of that sample is lesser than a certain threshold.

ElasticNet is a linear regression model trained with both $\iota_1$ and $\iota_2$-norm regularization of the coefficients. This combination allows for learning a sparse model where few of the weights are non-zero like Lasso, while still maintaining the regularization properties of Ridge. Elastic-net is useful when there are multiple features which are correlated with one another. Lasso is likely to pick one of these at random, while elastic-net is likely to pick both.

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