Linked Questions

19 votes
2 answers
40k 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 ...
  • 341
0 votes
1 answer
995 views

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

Looking for an intuitive explanation, thanks.
0 votes
0 answers
797 views

Ridge regression is similar to Linear regression [duplicate]

I can not see any difference between Ridge Regression and Linear Regression MY understanding, The point of ridge Regression is based on the training data we find the best line that fits training ...
  • 261
1 vote
0 answers
37 views

Ridge regression algorithm [duplicate]

Could someone explain how ridge regression algorithm works, step by step? Without focusing too much on formulas but rather how the mechanism works.
  • 131
68 votes
3 answers
15k views

Why does ridge estimate become better than OLS by adding a constant to the diagonal?

I understand that the ridge regression estimate is the $\beta$ that minimizes residual sum of square and a penalty on the size of $\beta$ $$\beta_\mathrm{ridge} = (\lambda I_D + X'X)^{-1}X'y = \...
  • 4,369
23 votes
2 answers
2k views

The limit of "unit-variance" ridge regression estimator when $\lambda\to\infty$

Consider ridge regression with an additional constraint requiring that $\hat{\mathbf y}$ has unit sum of squares (equivalently, unit variance); if needed, one can assume that $\mathbf y$ has unit sum ...
  • 98.3k
23 votes
3 answers
22k views

Can there be multiple local optimum solutions when we solve a linear regression?

I read this statement on one old true/false exam: We can get multiple local optimum solutions if we solve a linear regression problem by minimizing the sum of squared errors using gradient ...
13 votes
1 answer
15k 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 got is about Bayesian Linear Regression. I wonder if it's both the same things because the formula look quite similar
  • 195
6 votes
3 answers
2k 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-...
10 votes
2 answers
3k views

Bias / variance tradeoff math

I understand the matter in the underfitting / overfitting terms but I still struggle to grasp the exact math behind it. I've checked several sources (here, here, here, here and here) but I still don't ...
  • 281
12 votes
2 answers
3k views

Ridge penalized GLMs using row augmentation?

I've read that ridge regression could be achieved by simply adding rows of data to the original data matrix, where each row is constructed using 0 for the dependent variables and the square root of $k$...
  • 1,135
10 votes
1 answer
990 views

Why is Elastic Net called Elastic Net?

What is the etymology of "Elastic Net" in Elastic Net Regularization? Does it have anything to do with the name of "lasso"? Related: Why is ridge regression called "ridge&...
6 votes
1 answer
788 views

Why is bridge regression called "bridge"?

Bridge regression coefficient estimate $\hat{β}^{br}$ are the values that minimize the \begin{equation} \text{RSS} + \lambda \sum_{j=1}^p|\beta_j|^q , \end{equation} where $q \in \mathbb{R}$ and $q &...
3 votes
0 answers
2k 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? ...
0 votes
1 answer
766 views

Derivation of ridge regression for multi-value-target vectors

At university, I learned with these slides about ridge regression and its derivation with the assumption that the target- and predicted values have the dimensions $1\times1$. However, now I need to ...
  • 145

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