Linked Questions

59
votes
3answers
7k 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 = \...
22
votes
2answers
792 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 ...
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
1answer
2k views

Phoney data and ridge regression are the same?

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 $k$...
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
7
votes
2answers
1k 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 ...
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-...
3
votes
0answers
153 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 &...
2
votes
1answer
80 views

What modeling problem does ridge regression solve?

If your modeling problem is that you have too many features, a solution to this problem is LASSO regularization. By forcing some feature coefficients to be zero, you remove them, thus reducing the ...
2
votes
0answers
473 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
1answer
31 views

OLS loss function 3-d surface plot

I was trying to plot the OLS loss function as a function of coefficients $\beta_0$, $\beta_1$. As far as I know it should be a convex function with one local minimum which is also a global minimum. I'...
1
vote
0answers
28 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.
0
votes
1answer
43 views

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

Looking for an intuitive explanation, thanks.