When would you use L1 regularization instead of L2 regularization?
From a practical standpoint, L1 tends to shrink coefficients to zero whereas L2 tends to shrink coefficients evenly. L1 is therefore useful for feature selection, as we can drop any variables associated with coefficients that go to zero. L2, on the other hand, is useful when you have collinear/codependent features.
Why would you use the square of the L2 norm?
The squared L2 norm is convenient because it removes the square root and we end up with the simple sum of every squared value of the vector. The squared Euclidean norm is widely used in machine learning partly because it can be calculated with the vector operation xTx. There can be performance gain due to optimization.
What’s the difference between L1 and L2 regularization?
2. L2 Regularization. A regression model that uses L1 regularization technique is called Lasso Regression and model which uses L2 is called Ridge Regression. The key difference between these two is the penalty term. Ridge regression adds “ squared magnitude ” of coefficient as penalty term to the loss function.
When does Lasso regression with L1 penalty work?
Computationally, Lasso regression (regression with an L1 penalty) is a quadratic program which requires some special tools to solve. When you have more features than observations N, lasso will keep at most N non-zero coefficients.
When to use L1 penalty and sparsity?
Comparison of the sparsity (percentage of zero coefficients) of solutions when L1, L2 and Elastic-Net penalty are used for different values of C. We can see that large values of C give more freedom to the model. Conversely, smaller values of C constrain the model more. In the L1 penalty case, this leads to sparser solutions.
When to use L1, L2, and elastic-net penalty?
Comparison of the sparsity (percentage of zero coefficients) of solutions when L1, L2 and Elastic-Net penalty are used for different values of C. We can see that large values of C give more freedom to the model.