# Questions tagged [ridge-regression]

A regularization method for regression models that shrinks coefficients towards zero.

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### Interpreting the biased coefficients of a ridge or LASSO regression model [duplicate]

In a recent conversation with one of the colleagues I was presented with a view that LASSO/Ridge regularization (trading bias for variance) renders coefficient estimates useless for interpretation, i....
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### Question about retraining a regression model

Exercise. Suppose you train a Ridge model to a regression problem that has a normalized perfomance measure (say K) that attains a value in the interval [0,1], where 0 means that the model is terrible ...
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### Ridge Estimator in Summation Form

I am trying to derive $\widehat{\beta}$ in summation form from the following: $$\text{argmin } \sum_{i=1}^{N}(y_i - X_i^{T}\beta)^2 + \lambda \sum_{k=1}^{K}{\beta}_k^2$$ I do not want to resort to ...
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### glmnet Ridge Regression Plot makes no sense (to me at least)

I have a data set with around 50 variables and I am applying ridge and lasso on this data set. What I´ve noticed is, that the plot for the lambda values does differ from the mean values I get when ...
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### Geometric intuition for how ridge ($L_2$) regularization helps under multicollinearity

We have some nice posts (1, 2 and likely more) illustrating multicollinearity geometrically. Now, ridge regression ($L_2$ regularization) is known to be a remedy of multicollinearity. What is the ...
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### If L2-Regularization includes no bias, why do many images show a circle as the constraint region?

I got a little bit (massively, to be honest), confused by the following apparent misconceptions I have learned recently. Looking for information about L2-Regularization, the following image is one of ...
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### What does size of coefficients have to do with multicollinearity or overfitting?

In the section on Ridge Regression (source: Elements of Statistical Learning by Hastie, Tibshirani, Friedman) : When there are many correlated variables in a linear regression model, their ...
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### Why don't Lasso and Ridge Coefficients Correlate in Penalized Linear Regression? [duplicate]

I have fitted Lasso and Ridge regressions on the same training data and having checked the training MSE error seems more-less the same: ...
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### Variance in Generalized Ridge Regression/Weighted Least Squares

I'm following this collection of papers regarding ridge regression, https://arxiv.org/pdf/1509.09169.pdf , and I ran into this section on the mentioning of generalizing ridge regression. And when ...
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### Elastic net can be seen as lasso

Let $y \in \Bbb R^n$, $\Bbb 1$ be an n-vector with all its entries equal to $1$, and $Z \in \Bbb R^{n×p}$ with columns of unit norm and such that $Z^T \Bbb 1 = 0$. The elastic net is a penalized ...
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### practical way to run statistical test on the coefficients obtained from ridge or lasso

In the OLS, we can run t-tests on the coefficients obtained from linear regression, but how can we test on the coefficients we obtained in the case of lasso or ridge? What's the common practice in ...
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### Double-layered optimization to find optimal regularization parameter lambda for Ridge/LASSO

I have an overdetermined system of equations problem where n >> m and the OLS almost always finds an approximation instead of an exact solution. I already ...
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### Multicollinearity Market mix modeling

I want to know what can be the best approach to handle multicollinearity. I am building a regression model with just 4 independent but all important variables and am not able to control the VIF. ...
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1 vote
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### How do the ridge or lasso coefficient changes when we add more variables

Suppose we run ridge or lasso regression over a bunch of features. And now suppose we add one more feature into the regressions. What will happen to the coefficients of the "old" features? I ...
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### Is it possible to create a 0 intercept ridge regression model?

I am working on implementing ridge regression for market mix modeling where I wish to use my own create base(UCM) instead of intercept, I had been using linear regression for this purpose but now my ...
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### Ridge and Lasso regression coefficient change when we change the scales of the variables

I am interested in the following question: suppose we run a ridge of a lasso model on a bunch of variables. Now if we multiple one of the variables $x_1$ by 2, what happens to the coefficients. Some ...
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### Centering vs standardizing in ridge regression

I have read that to apply ridge regression, we first need to standardize the predictive variables. That is because the variables should be in a homogenous scale so that lambda has an effect of the ...
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### How does ridge regression reduce the variance of the estimates of $\beta$

In the scikit-learn library, Ridge class, there is a note that reads: "Regularization improves the conditioning of the problem and reduces the variance of the estimates." Given the ...
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### Is standarization necessary for ridge regression?

Is variable normalization necessary in Ridge regression (for both X and y)? If so, what happens (mathematically) if we don't do it?
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### What does it say about the data if ridge regression is not reducing multicollinearity?

I am predicting the salary to be offered to a new candidate for which I am concentrating on just continuous (9 in number) variables. Variables are as attached. When I ran OLS the coefficient for total ...