Question

When would you want to use L1 regularization as opposed to L2 regularization

Answer 1

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The main difference between L1 and L2 regularization is that L1 can yield sparse models while L2 doesn't. Sparse model is a great property to have when dealing with high dimensional data, for at least 2 reasons.

• Model compression: increasingly important due to the mobile growth
• Feature selection: it helps to know which features are important and which features are not or redundant.

The difference between L1 and L2 regularization are as follows:

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L1/Laplace tends to tolerate both large values as well as very small values of coefficients more than L2/Gaussian

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L1 can yield sparse models while L2 doesn't

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L1 and L2 regularization prevents overfitting by shrinking on the coefficients

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L2 (Ridge) shrinks all the coefficient by the same proportions but eliminates none, while L1 (Lasso) can shrink some coefficients to zero, performing variable selection

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L1 is the first moment norm |x1-x2| that is simply the absolute dıstance between two points where L2 is second moment norm corresponding to Euclidean Distance that is |x1-x2|^2.

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L2 regularization tends to spread error among all the terms, while L1 is more binary/sparse