What is an advantage of L1 regularization over 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.

What effect does L1 and L2 regularization have on model weights?

As previously stated, L2 regularization only shrinks the weights to values close to 0, rather than actually being 0. On the other hand, L1 regularization shrinks the values to 0. This in effect is a form of feature selection, because certain features are taken from the model entirely.

Why is L1 regularization used for feature selection?

L1 regularization adds a penalty \alpha \sum_{i=1}^n \left|w_i\right| to the loss function (L1-norm). Since each non-zero coefficient adds to the penalty, it forces weak features to have zero as coefficients. Thus L1 regularization produces sparse solutions, inherently performing feature selection.

Why Lasso tends to push some weights to be exactly zero?

Geometric Interpretation. The lasso performs shrinkage so that there are “corners” in the constraint, which in two dimensions corresponds to a diamond. If the sum of squares “hits” one of these corners, then the coefficient corresponding to the axis is shrunk to zero.

Which is better lasso or ridge?

Lasso tends to do well if there are a small number of significant parameters and the others are close to zero (ergo: when only a few predictors actually influence the response). Ridge works well if there are many large parameters of about the same value (ergo: when most predictors impact the response).

How does L2 regularization help?

L2 regularization forces weights toward zero but it does not make them exactly zero. L2 regularization acts like a force that removes a small percentage of weights at each iteration. Therefore, weights will never be equal to zero.

What is the effect of L2 regularization?

L2 Regularization shrinks all the weights to small values, preventing the model from learning any complex concept wrt. any particular node/feature, thereby preventing overfitting.

Why does Lasso do feature selection?

The LASSO method regularizes model parameters by shrinking the regression coefficients, reducing some of them to zero. The feature selection phase occurs after the shrinkage, where every non-zero value is selected to be used in the model. The larger λ becomes, then the more coefficients are forced to be zero.

How can lasso be interpreted?

Just as ridge regression can be interpreted as linear regression for which the coefficients have been assigned normal prior distributions, lasso can be interpreted as linear regression for which the coefficients have Laplace prior distributions.

What is the importance of Lasso in statistics?

The features selection phase of the LASSO helps in the proper selection of the variables. Statistical models rely on LASSO for accurate variable selection and regularization. For example, in linear regression, LASSO introduces an upper bound for the sum of squares, hence minimizing the errors present in the model.

What happens when the lasso value is zero?

When λ is equal to zero, then the model becomes the Ordinary Least Squares regression. Consequently, when λ increases, the variance decreases significantly, and the bias in the result increases, too. Lasso is also a useful tool in eliminating all irrelevant variables that are not related to the response variable.

What is the features selection phase in a LASSO model?

LASSO forms an integral part of the model building process, especially using the features selection. The features selection phase helps in the selection of explanatory variables, which are the independent variables and, hence, the input variables in the model.

What shape does Lasso form in the plot?

LASSO forms a diamond shape in the plot for its constraint region, as shown in the image above. The diamond shape includes corners, unlike the circular shape formed by ridge regression. The proximity of the first point to the corner shows that the model comes with one coefficient, which is equal to zero.