How do I use Lasso and elastic net as feature selectors? I have a data set with 900,000 rows and 8 features. I want to look at the significance of each feature so that I can evaluate whether the features I add are viable or not.
One method I am using after doing some research is the Lasso method, which from my understanding comes up with coefficients for each variable by trying to minimize this function.

After changing my alpha to .001 I was able to get these coeffecients for each feature but I am not sure what to do with them and what they mean. Is it the higher it is the more important or am I supposed to apply these coeffecients to my Data?
Feature 1 : 11.3697897122
Feature 2 : 0.210785096352
Feature 3 : 4.94093396164e-05
Feature 4 : 0.0
Feature 5 : 0.0
Feature 6 : 0.0
Feature 7 : -0.0370673794819
Feature 8 : -0.15121827904

 A: Lasso basically selects variables in a linear model, $Y=X\beta+e$ using a tuning parameter ($\alpha$ in your case). It utilizes a penalty term to penalize some coefficients toward zero. Notice that the main advantage of lasso is in high-dimensional data (when there are more variables than observations). The procedure is easy, if a coefficient is close to zero, then pushes that to zero.
In your case, you have more observations than variables. You need to normalize your data and then run Lasso algorithm. It is preferred to choose tuning parameter using a criteria like BIC AIC CV etc. If you use R, then MSGPS package does all of the steps for you.
Finally if some coefficients are zero, that means their effect can be neglected and then can be removed from the model. Moreover, (sorted) non-zero coefficients can be ranked as their importance.
Notice: If there are collinearities among variables, then lasso just selects one variable and push others toward zero. Then, some notice is needed if you think there is collinearity among variables. If you are suspected that there is a kind of collinearity in data then the easiest way of checking is to find covariance matrix (in R cov(x)) and then find eigenvalues of that covariance matrix (in R eigen(cov(X))$values ). If there is any zero (or close to zero) eigenvalue, that means there is collinearity in data.
A: The coefficients displayed are the estimates for $w$ in your equation. When $|w|$ is large, a 1-unit change in the corresponding feature is estimated to have a large effect on $y$, all else being equal. That is, the usual interpretation of a linear model applies.
Features with coefficients that are $0$ are deemed to have no influence on $y$ given the sample size and choice of $\alpha$, i.e. they have been removed from the model.
