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Is lasso used for variable selection?
Lasso is a supervised algorithm wherein the process identifies the variables that are strongly associated with the response variable. This is called variable selection. Then, Lasso forces the coefficients of the variables towards zero. This is now the process of shrinkage.
Why would you want to use LASSO instead of ridge regression?
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 to estimate coefficients variance in Lasso test?
The original Lasso paper: suggests a bootstrap-based procedure to estimate the coefficients variance, which (again, I think) may be needed for the tests (section 2.5, last paragraph of page 272 and beginning of 273): One approach is via the bootstrap: either t can be fixed or we may optimize over t for each bootstrap sample.
How to check the statistical significance of a Lasso regression?
One possible remedy is to select the final feature space and feed it back into an lm command. This way, you would be able to compute the statistical significance of the final selected X variables. For instance, see the following code:
Can you use lasso to test Wald’s test?
I know Wald’s tests (for instance) are an option to test the significance of individual coefficients in full regression without regularization, but with Lasso I think further problems arise which do not allow to apply the usual Wald formulas. For instance, the variance estimates neded for the test do not follow the usual expressions.
What’s the problem with the usual significance test?
The problem with using the usual significance tests is that they assume the null that is that there are random variables, with no relationship with the outcome variables. However what you have with lasso, is a bunch of random variables, from which you select the best ones with the lasso, also the betas are shrunk.