# Linked Questions

1answer
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### 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 ...
0answers
90 views

### Is there difference between “spectral decomposition” and “singular value decomposition”? [duplicate]

Am I right that "spectral decomposition" for symmetric matrix and "singular value decomposition" for non square matrix? Any clarification would be appreciated.
0answers
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### $L^2$ Regularization and Hessian Matrix [duplicate]

In the second paragraph it is mentioned that eigenvector of $H$ is rescaled by a factor of $\frac{\lambda_i} {\lambda_i +\alpha}$ What exactly meant by that ?
0answers
23 views

### How to prove biased estimator with SVD of X [duplicate]

Hi guys, I'm assuming that I am able to use SVD of X to solve this question. So, X = UΣV where U and V are nxn and pxp orthogonal matrices respectively and Σ is an nxp matrix containing the singular ...
0answers
18 views

### Penalized Regression: “ridge” RMSE and coefficients larger than those for plain “lm” [duplicate]

Working with the "prostate" dataset in "ElemStatLearn" package. ...
3answers
5k views

### Ridge Regression -Increase in $\lambda$ leads to a decrease in flexibilty

In Introduction to Statistical Learning, in the part where ridge regression is explained, the authors say that As $\lambda$ increases, the flexibility of the ridge regression fit decreases, ...
3answers
2k views

I'm trying to learn some basic Machine Learning and some basic R. I have made a very naive implementation of $L_2$ regularization in R based on the formula: $\hat w^{ridge} = (X^TX +\lambda I)^{-1} X^... 1answer 652 views ### Reversing ridge regression: given response matrix and regression coefficients, find suitable predictors Consider a standard OLS regression problem$\newcommand{\Y}{\mathbf Y}\newcommand{\X}{\mathbf X}\newcommand{\B}{\boldsymbol\beta}\DeclareMathOperator*{argmin}{argmin}$: I have matrices$\Y$and$\X$... 2answers 1k views ### Maximum penalty for ridge regression Consider a regression model $$y = X \beta + \varepsilon.$$ I will use ridge regression to estimate$\beta$. Ridge regression contains a tuning parameter (the penalty intensity)$\lambda$. If I ... 2answers 855 views ### How to derive the covariance matrix of$\hat\beta$in linear regression? I just read this very insightful post about ridge regression, where the author stated that the variance of$\hat\beta$is: $$\text{var}(\hat\beta) = \sigma^2(\textbf{X}^\prime \textbf{X})^{-1}.$$ I ... 2answers 562 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 ... 1answer 199 views ### Why does sklearn Ridge not accept warm start? I am experimenting with some regularized linear regression methods using sklearn and noticed that Ridge does not accept warm start. I found it odd as many other methods do accept like Lasso, ... 1answer 119 views ### why ridge regression only decreases slope and not increases it? I was following the below example from 'StatQuest with Josh Starmer' youtube channel. The example is pretty simple: red line is the usual 'least squares' (for the red points), and the blue one is ... 1answer 64 views ### What is the relationship between the sum of squares of all weights and lambda in the ridge regression [duplicate] Currently I am reading chapter 8, regression. And I feel quite confused about the following paragraph(see picture below), does it mean in ridge algorithm, the sum of all weights will be less than ... 0answers 87 views ### How can$X^TX$be decomposed? Nikolaenko et al. claims that in ridge regression$A\beta=b$, where$A=X^TX+\lambda I \in R^{d\times d}$and$b=X^Ty \in R^d$(page 3), it can be decomposed into:$\$A=\sum\limits_{i=1}^{n}A_i+\...

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