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### Sparsity in Lasso and advantage over ridge (Statistical Learning) [duplicate]

I'm learning about the Statistical learning and in the section comparing Lasso and Ridge Regression it shows that the main difference between these two problems is the way the constraint/penalty is ...
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### What is the mathematical rigorous proof that L1 regularization will give sparse solution? [duplicate]

It is given in the book Machine Learning A probabilistic Perspective, but i am not able to understand it. Can some one provide an explanation for that ? I am not clear with the way sub gradient is ...
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### why l1 norm can result in variable selection but not l2 [duplicate]

In applying a penalty term with either $l_1$ or $l_2$ norm, why would the former result in variable selection but not the latter?
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### Why L1 regularization can “zero out the weights” and therefore leads to sparse models? [duplicate]

I'm aware there is a very relevant explanation on L1 regularization's effect on feature selection at here: Why L1 norm for sparse models [Ref. 1]. To better understand it I'm reading Google's ...
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### Why does not ridge regression perform feature selection although it makes use of regularization? [duplicate]

Could somebody explain why ridge regression does not perform feature selection although it makes use of regularization? So, it penalizes the regression coefficients like LASSO does, but how come we ...
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### LASSO method. Intuitively how does it select variables? [duplicate]

Intuitively how does the LASSO method select its variables? Is it based on standard econometrics?
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### Comparing Ridge and Lasso Regression [duplicate]

I was thinking about main differences between ridge and lasso introducing a $\ell^2$ and $\ell^1$ penalty term respectively. The main thing is that with ridge I will keep all my features in the end ...
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### Why will ridge regression not shrink some coefficients to zero like lasso?

When explaining LASSO regression, the diagram of a diamond and circle is often used. It is said that because the shape of the constraint in LASSO is a diamond, the least squares solution obtained ...
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### Is there any special case where ridge regression can shrink coefficients to zero?

Are there some special cases, where the Ridge Regression can also lead to coefficients that are zero ? It is widely known, that lasso is shrinking coefficients towards or on zero, while the ridge ...
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### L1 and L2 penalty vs L1 and L2 norms

I understand the usages of L1 and L2 norms however I am unsure of usage of L1 and L2 penalty when building models. From what I understand: L1: Laplace Prior L2: Gaussian Prior are two of the ...
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### Is there a mathematical expression that shows how LASSO shrinks coefficients (including some to zero)?

By using singular value decomposition (SVD), I noticed from the derivation that ridge regression shrinks the coefficients by factor $\frac{D^2}{D^2+\lambda}$, where $D$ is the diagonal matrix of the ...
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### Which lambda is cv.glmnet solving for?

This is my understanding of glmnet: if OLS is minimizing RSS, where $RSS = \sum(y-\beta x)^2$ I believe glmnet is minimizing: $RSS - \sum(\alpha |\beta_j| + (1-\alpha) \beta_j^2)$ where \$\...
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### Does the order of models (and so variables) matter in nested models?

I am trying to use nested models to investigate the influence of 5 factors on my dependent variable. I am not interested in interactions, only the influence of each variable taken separately. My ...