Linked Questions

1
vote
1answer
963 views

Non-Singularity due to inclusion of non-zero lambda in ridge regression [duplicate]

There were many similar questions on this site , related to this but none were exactly to the point I wanted to ask So the question is relates to ridge regression and This link where there is a ...
0
votes
1answer
43 views

Why is L2 regression good for handling multicollinearity? [duplicate]

Looking for an intuitive explanation, thanks.
66
votes
2answers
17k views

Why is ridge regression called “ridge”, why is it needed, and what happens when $\lambda$ goes to infinity?

Ridge regression coefficient estimate $\hat{\beta}^R$ are the values that minimize the $$ \text{RSS} + \lambda \sum_{j=1}^p\beta_j^2. $$ My questions are: If $\lambda = 0$, then we see that the ...
19
votes
2answers
35k views

What is ridge regression? [duplicate]

I just need a simple explanation of what exactly ridge regression is so I can have a decent intuitive understanding of it. I understand it's about applying some sort of penalty to the regression ...
10
votes
5answers
5k views

Ridge & LASSO norms

This post follows this one: Why does ridge estimate become better than OLS by adding a constant to the diagonal? Here is my question: As far as I know, ridge regularization uses a $\ell_2$-norm (...
5
votes
3answers
988 views

Can I use lasso when it is not a high dimensional setting?

I have 500 observations and 200 predictors, and I want to do the prediction while selecting some important features. I know that regularisation method (ridge, lasso) are shrinkage method for high-...
7
votes
1answer
3k views

Is Bayesian Ridge Regression another name of Bayesian Linear Regression?

I searched about Bayesian Ridge Regression on Internet but most of the result i became is about Bayesian Linear Regression. I wonder if it's both the same things because the formula look quite similar
9
votes
2answers
907 views

Lucid explanation for “numerical stability of matrix inversion” in ridge regression and its role in reducing overfit

I understand that we can employ regularization in a least squares regression problem as $$\boldsymbol{w}^* = \operatorname*{argmin}_w \left[ (\mathbf y-\mathbf{Xw})^T(\boldsymbol{y}-\mathbf{Xw}) + \...
4
votes
1answer
993 views

What is the significance of a linear dependency in a polynomial regression?

I'm trying to find the best polynomial regression for a dataset where the polynomial's power is between 2 and 10. So the regression can have an x10 term at most in it. The dataset itself is simply a ...
2
votes
1answer
705 views

3D surface plot for least square & ridge regression

I'm very impressed by this plot: Why does ridge estimate become better than OLS by adding a constant to the diagonal? Does someone has any clue about how to plot this on R? I mean, how to get RSS ...
2
votes
0answers
470 views

How exactly does ridge regression helps in the case of multicollinearity?

I understand the reasoning behind ridge regression: we include some bias in the model in order to reduce the variance of the regression coefficients. My question is, why would we want to do that? ...
1
vote
0answers
427 views

Variable importance in cases of multicollinearity: OLS vs ridge regression

I have read that when using Ordinary Least Squares (OLS) for multiple linear regression, the coefficients/weights are unreliable for predictor variables that are collinear. I was wondering if this is ...