Linked Questions

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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 ...
1
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0answers
41 views

LASSO method. Intuitively how does it select variables? [duplicate]

Intuitively how does the LASSO method select its variables? Is it based on standard econometrics?
2
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0answers
311 views

Implementing Lasso Regression in Numpy

I'm doing a little self study project, and am trying to implement OLS, Ridge, and Lasso regression from scratch using just Numpy, and am having problems getting this to work with Lasso regression. ...
2
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1answer
1k views

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 ...
3
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1answer
1k views

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 ...
2
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2answers
191 views

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 ...
6
votes
3answers
480 views

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 ...
1
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1answer
86 views

Can lasso and ridge regressions theoretically have exact same solution?

Intuitively lasso leads more sparsity, but is that theoretically possible they have exact same solution vector?
2
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2answers
348 views

Binary outcome prediction with binary data

I am new to R programming and although I searched through the community, I couldn't find a similar topic, although it has to be somewhere. So a link to a similar case would be sufficient. I have a ...
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1answer
1k views

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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2answers
738 views

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 $\...
6
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2answers
599 views

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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0answers
241 views
0
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1answer
143 views

$L^1$ Regularization

Let $J(w)$ be some cost function. By adding $L^1$ regularization we get $$ \tilde{J}(w) = J(w) + \beta\sum_i|w_i| $$ To study the effect of $L^1$ regularization on the optimum weights, we can ...
16
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2answers
10k views

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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