Ridge Regression is a technique which penalizes the size of regression coefficients in order to deal with multicollinear variables or ill-posed statistical problems.

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How to interpret ridge regression plot

Following is the ridge regression example in MASS package: ...
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Plot cv.glmnet with norm in x axis [closed]

I would like to make comparable plots of Ridge coefficients and CV error, having the L1 norm on the x axis. I can do that for the ridge plot by fixing xvar="norm". Is there some equivalence for ...
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Comparing different models using LOOCV method [migrated]

I have to compare different models (OLS, BEST SUBSET, RIDGE, LASSO, PCR and PLS) using the LOO cross Validation (the criterion of comparison is the test-MSE). Could someone explain me how to do it ...
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Extremly poor polynomial fitting with SVR in sklearn

I try to fit an obvious around degree 5 polynomial function. Much to my despair, sklearn bluntly refuses to match the polynomial, and instead output a 0-degree like ...
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35 views

How to calculate predicted values using an lm.ridge object?

I've found this line of code to calculate predicted values from a ridge.lm model: ...
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Regularization for ARIMA models

I am aware of LASSO, ridge and elastic-net type of regularization in linear regression models. Question: Can this (or a similar) kind of regularization be applied to ARIMA modelling (with a ...
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Does ridge regression adequately control for regression to the mean effects in my outcome variable?

I've been asked how to control for regression to the mean effects in a difference of differences analysis on health insurance data. We're measuring a utilization outcome both pre- and ...
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Survival analysis coxph using ridge regression with 2000 variables => “Penalty terms cannot be in an interaction”

I'm doing a survival analysis using coxph function (package survival). I'm using a ridge regression model included 2000 variables but I have a type of error message "...
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1answer
33 views

Sparsity in Lasso and advantage over ridge (Statistical Learning) [duplicate]

I'm learning about the Statistical learning and in the section comparing Lasso and Ridge Regression it shows that the main difference between these two problems is the way the constraint/penalty is ...
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How do I rank coefficients returned from a ridge regression?

I am running a ridge regression using GLMNET (alpha = 0) and would like to interpret the coefficients returned. I know there isn't really a significance test for this, but can I at least rank the ...
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How to make correlated variables, uncorrelated?

I have 7 independent variables with 3 observations and they are highly(<95) correlated with each other (each of them) and my dependent variable is head count for 3 years( thus only 3 observations ) ...
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2answers
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Penalizing the Ordinary Least Squares estimation

In a regression analysis, we aim to find the best relationship between two variables (independent variable denoted $y$ and other dependent variable denoted by $x$, and which are related by: $y = ...
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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 ...
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I did ridge regression and i am confused with coefficients

ridd=lm.ridge(mariner~o1+o2+o3,q,lambda=0.001) ridd o1 o2 o3 34.7597607381 0.0001989008 0.0393011905 ...
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My Cross-validation error is always increasing with increasing regularisation parameter

I am not sure what is happening, but my cross-validaton error is always increasing with increasing alpha in ridge regression. It should technically go down and then increase. Here is what I am doing ...
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35 views

How to find the best coefficient vector using cross-validation

So basically my dataset is divided into 5 train and 5 test folds. This is how I did in scikit: ...
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Ridge Regression STATA

I used ridge regression in order to dealing with multicollinearity but there is something that i do not understand. I use STATA command: -ridgereg y x1 x2 x3 x4 x5 x6 x7 x8 x9, ...
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For a quadratic form to minimize with a L2 regularization term, is the gradient of the solution collinear to the solution?

Say you minimize a quadratic form f with a L2 regularization term (g = f + L2_term). The solution of minimizing g is x*. Is the gradient of f applied to x* collinear to x* as the figure below ...
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How I Can Apply Ridge Regression? [closed]

my model is cross-sectional with macro variables and i run it with OLS. However, I found that it suffers from multicollinearity. I tried to change some variables but multicollinearity is still there. ...
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Range of lambda in elastic net regression

$\def\l{|\!|}$ Given the elastic net regression $$\min_b \frac{1}{2}\l y - Xb \l^2 + \alpha\lambda \l b\l_2^2 + (1 - \alpha) \lambda \l b\l_1$$ how can an appropriate range of $\lambda$ be chosen ...
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Getting very small values for lambda with glmnet()?

I'm using glmnet() to analyze a weather data set of 50 variables and 240 observations. My question is pretty simple: when I run ridge regression and LASSO on the ...
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Equating the two equations of Ridge Regression

I'm studying Ridge Regression now and I'm having a bit of trouble understanding how to relate the two equations that pop up when I read about it. There is the coefficient estimate: $$\hat{\beta} = ...
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1answer
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Ridge regression in multivariate Gaussian distribution

When implementing GMM (Gaussian Mixture Model) in practice, the covariance matrix ${\Sigma}_{D\times D}$ is often singular. The reason is that we have to estimate $\frac{D(D+1)}{2}$ parameters in ...
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Hyper parameters optimization

Any one with a tip on how to define a suitable condition to find an optimal set of parameters for a combined norm regularization on a grid? Not cross validation or any related method. I am asking if ...
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Different behaviors for different Ridge implementations in R

I am having trouble reconciling the different behavior of different Ridge implementations in R. As the following code demonstrates it seems that MASS:lm.ridge ...
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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 ...
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Do mildly informative prior distributions tend to mitigate false positives (i.e. Type I error rates)?

I am curious if others have sources that speak to the matter that providing informative and/or mildly informative prior distributions on a parameter tend to mitigate false alarm rates? I know from the ...
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Why intercept term out of penalty term in Ridge regression

I am reading about ridge regression in Elements of Statistical Learning. In the ridge regression, we don not include intercept term $\beta_0$ in the penalty term. The book says, penalization of the ...
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Variance Inflation Factor less than 1 in ridge regression?

I was trying to determine the biasing constant in ridge regression when I came across a phenonomenon that seems quite puzzling, to me at least. I let the GCV criterion choose a constant for me and ...
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Interpretation of ridge regularization in regression

I have several questions regarding the ridge penalty in the least squares context: $$\beta_{ridge} = (\lambda I_D + X'X)^{-1}X'y$$ 1) The expression suggests that the covariance matrix of X is ...
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Why is glmnet giving me different answers than ridge estimation

I'm using glmnet to calculate ridge regression estimates. I got some results that made me suspicious in that glmnet is really doing what I think it does. To check this I wrote a simple R script where ...
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Finding standard error of beta coefficients in ridge regression using lambda

I need to get the standard errors of coefficients with Ridge Regression, by calculating the SE of the beta estimates after I choose the right lambda. ...
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Have difficulty understanding Matlab's Ridge regression

I am confused by Matlab's documentation of Ridge regression at http://www.mathworks.com/help/stats/ridge-regression.html and couldn't figure it out by myself. On that page, the Introduction to Ridge ...
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Under exactly what conditions is ridge regression able to provide an improvement over ordinary least squares regression?

Ridge regression estimates parameters $\boldsymbol \beta$ in a linear model $\mathbf y = \mathbf X \boldsymbol \beta$ by $$\hat{\boldsymbol \beta}_\lambda = (\mathbf X^\top \mathbf X + \lambda \mathbf ...
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questions on glmnet result

I am trying to experiment with glmnet for a data set, which has 41 independent variables is 41. There are 80 data points in total. ...
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Unified view on shrinkage: what is the relation (if any) between Stein's paradox, ridge regression, and random effects in mixed models?

Consider the following three phenomena. Stein's paradox: given some data from multivariate normal distribution in $\mathbb R^n, \: n\ge 3$, sample mean is not a very good estimator of the true mean. ...
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1answer
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Effective degrees of freedom for regularized regression

If I have a quadratic programming problem $$\min_b \frac{1}{2} b^tX^tXb - b^t(X^tY)$$ which I regularize by adding a multiple of the identity$\lambda I$ to $X^tX$, then the effective degrees of ...
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1answer
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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 ...
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What criterion are used to accept/reject hypotheses in ridge regression?

On what basis might one accept/reject a hypothesis when running ridge regression? For example, if I have five predictor variables as part of a ridge regression... what criterion would I use to accept ...
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1answer
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Ridge regression - what is k=0?

I'm getting to know ridge regression and what to check my understanding quickly. I understand that k is the shrinkage parameter. If I'm reading off coefficients where k=0, is that equivalent to an ...
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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 l2-norm (euclidean ...
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Support vector regression versus kernel ridge regression

I have a question concerning the difference between support vector regression and kernel regression. I will try to write down all the math so no misunderstandings arise (hopefully). Let's begin with ...
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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_{ridge} = (\lambda I_D + X'X)^{-1}X'y = ...
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1answer
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Linear Regression with $L_2$: Different penalty strengths yield the same parameters?

Suppose I have model 1: $$Y=aX$$ where $X$ is $n\times1$, consisting of a single feature. suppose I fit this model with $L_2$ penalty with coefficient $\lambda=1$ : $$ \underset{a}{\min} ...
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What's the typical range of possible values for the shrinkage parameter in penalized regression?

In lasso or ridge regression, one has to specify a shrinkage parameter, often called by $\lambda$ or $\alpha$. This value is often chosen via cross validation by checking a bunch of different values ...
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Bias correction of ridge regression

I'm using ridge regression for estimating the fair value of variable $Y$ against a vector of correlated predictor variables $X_i$, based on past observations of both $Y$ and $X_i$. Let's assume that ...
2
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1answer
284 views

How to Find Adjusted $R^2$ or $R^2$ from Lasso and Ridge regression model

How do I find the adjusted $R^2$ (or $r^2$) from Lasso and Ridge regression? I used the glmnet package. For instance if I have this code so far.... ...
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Explicit optimization of RIDGE penalization parameter

I work with a very simple setup: I have two possibly very correlated features $x_{1,2}$, with normaliazation such as $\text{var}(x_{1,2}) = 1$, $Ey = Ex_{1,2} = 0$ (for the empirical distribution). I ...
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Calculated breeding values using markers using animal model in R

Animal model (frequently used in animal science and sometime in human or plants) is mixed model with: $y$ = $X$$b$ + $Z$$u$ + $e$ y is observed values for any quantitative variable, $Xb$ is fixed ...