Questions tagged [ridge-regression]

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

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Should Kernel Ridge Regression with linear kernel yield same results as Ridge regression?

I'm comparing the performance of different regressors from scikit-learn for fitting some data. I would have expected that Ridge regression and Kernel Ridge regression both yield the same model/...
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What is the impact of the weight decay on self normalizing neural network with selu activations?

So there is a regularization technique called weight decay performing thikonov regularization (or in statistics community ridge regression). There is also a (lets say new) approach for neural ...
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How should I consider the signs of the beta weights in a composite?

I had covariates (say, $X_1$) and some biomarkers ($X_2, \ldots, X_5$) and I wanted to model an outcome ($Y$) using these biomarkers. The biomarkers are correlated. So I decided to use a ridge ...
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Is there a canonical example of when ridge outperforms lasso?

Can someone please give me an example of when ridge would out perform lasso? Won't lasso do better in most circumstances? If a regressor has a large coefficient, that means the regressor is a good ...
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Effect of log transformation or standardization of a regressor in the filtering step

We are working with a dataset that has hundreds of biomarkers (many of which are correlated) and often they have many missing values. Our initial goal was to use an elastic net but that would require ...
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1answer
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What is the difference between “variables of interest” and “variables from which lasso selects” in Lasso?

I'm getting started with regularization models and I notice that Lasso requires three inputs, a dependent variable and then two sets of what I assume as independent variables, one which are of ...
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Getting started with regularization (Lasso)

I've got a small data set of 55 observations with a binary outcome variable of which only 11 are 1's and the rest are 0's. I was wondering if Lasso was a useful tool to predict my outcome here and if ...
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How to consider interaction terms in the ridge / lasso / elastic net?

I would like to ask a question about how to consider interaction terms in my penalized regression? My primary goal is to build the model to predict. I think in the conventional GLM, we run the model ...
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1answer
23 views

Comparison of regression models in terms of the importance of variables

I would like to compare models (multiple regression, LASSO, Ridge, GBM) in terms of the importance of variables. But I'm not sure if the procedure is correct, because the values ​​obtained are not on ...
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1k views

In regression, why not use regularization by default?

I remember reading somewhere in another post about the different viewpoints between people from statistics and from machine learning or neural networks, where one user was mentioning this idea as an ...
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What are the available method that can alleviate the overfitting problem in traditional OLS problem, but still can get a linear fitting?

Recently, I have read the paper https://static1.squarespace.com/static/56def54a45bf21f27e160072/t/5a0d0673419202ef1b2259f2/1510803060244/The_Sampling_Error_in_Estimates_of_Mean-...
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1answer
63 views

AIC and its degrees of freedom for linear regression models

I have a dataset $S$ with $D$ features and three fitted linear regression models: Model1. Ridge regression that is fitted on all $D$ features from $S$. Model2. Ridge regression that is fitted on some $...
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1answer
32 views

False positive/negative rate in ridge and lasso regressions

I have a confusion matrix of true and estimated $\boldsymbol{\beta}$ vectors of lasso and ridge models from a replicate of a simulation study, say. The following tables illustrate the scenario. $$\...
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Results of cv.glmnet in R versus RidgeCV in scikit-learn

I'm having trouble reconciling different values for the ridge parameter that minimizes mean squared error when using RidgeCV in scikit-learn (Python) and cv.glmnet (R). First a few things to note: ...
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Getting different values for MSE using anova(lm(y~.)) and mean(residuals(fit)^2)

Using this dataset of gas mileage for different cars I've been asked to run a ridge regression using $\frac{p*\sigma^2}{\beta'\beta}$ as the k-value. I've been told $\sigma^2 = MSE$ $p =$ ...
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1answer
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Robust regression with M-estimators

I have a couple of question regarding robust regression with M-estimators, such as Huber estimator or Tukey biweight estimator: Is it possible/common to combine these with regularization terms, such ...
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25 views

Ridge Regression worse results with more feature. Does it make sense?

PREMISE I am dealing with a regression problem with time-series data (of option prices data). In my setup, I need to use only piece-wise linear models or linear transformations of data. I took care ...
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1answer
46 views

Poor performance on Regularized models

I'm trying to build a simple model to predict the price of a cab ride, using features such as hour, source, destination, car model, distance, and weather features such as pressure and humidity. I've ...
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Efficiency of ridge regression in under determined systems

Imagine an underdetermined linear system, composed of N (continuous) labels and N samples, each have P features (with N < P): $$\hat{\textbf{Y}}_{N \times 1} = \textbf{X}_{N \times P} \textbf{W}_{...
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1answer
106 views

Why cant Ridge Regression benift from negative lamda? [duplicate]

in Rigid regression, we generally set a positive Lambda for regularization to get a less Residual. Why cant we have a negative Lambda in a regularization if we can benefit from it?
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17 views

Estimating coefficients of a linear model with collinear dependent variables that have errors with known variances

I want to estimate the coefficients $\beta$ of the linear model $Y=\beta X$ from observations of $(Y_i,X_i), i=1\ldots n$, where $X$ is multidimensional. Two problems: All variables have been ...
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1answer
60 views

Statistical library for orthogonal distance regression with a ridge penalty?

There are many libraries in R and python for doing orthogonal distance regression and for doing ridge regression separately. Is there one for doing them at the same time?
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Variance of ridge regression estimator under perturbed data

In section 1.3 Ridge Regression as Perturbation of the notes the author comes up with the following ridge estimator $$ \widehat{\boldsymbol{\beta}}=\left[(\mathbf{X}+\mathbf{W})^{T}(\mathbf{X}+\mathbf{...
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Regression training and testing error

Let’s say we fit a linear regression. What does the correlation between its training error and testing error say about the model, its performance or the data? What does a very low or very high ...
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1answer
30 views

l2 lambdas in Keras.regularizers [closed]

Is the value supplied to the shrinkage regularizers (l1 and l2) in Keras the inverse of the lambda coefficient? e.g. ...
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How to do cross validation in ODE models with more predicted than measured time courses?

I have an ODE model of biochemical reactions with 37 state variables and 88 strictly positive parameters. Unfortunately, I can only expect to get time course measurements of about 10 state variables (...
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1answer
62 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 ...
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How To Feed Un-Scaled Data Into a Model That Was Trained on Scaled Data

I have a data frame that contains time series data. I split the dataframe into test and train. I want to prevent leakage so I split the data frame before doing any scaling. On the train data set, I ...
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1answer
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Why glmnet 's $\lambda$ value is so small? Does it strictly implement the loss function under the hood?

I am running a glmnet fit with 1200000 samples. According to the glmnet doc, $\lambda$ value is the coefficient controlling how much the regularization term contributes to the total loss function. ...
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23 views

Estimate variance of parameters in non-linear ridge regression

I am basically estimating the shape of an unknown function f(x) from multi-dimensional chemical reaction data by estimating the most likely function values $f$ on a grid $x$ with kernel regression. To ...
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43 views

Solving ridge regression for p >> n case using dual algorithm with or without nonnegativity constraints

I was reading the paper "Efficient Regularized Regression with L0 Penalty for Variable Selection and Network Construction" in which iterated ridge regression is used to solve L0 penalized regression ...
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1answer
33 views

High odds ratio for composite score created by ridge regression

This question is a follow up to one of my previous questions asked on this site. The goal was to create a composite score for biomarkers related to a binary outcome and then use that in a regression ...
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43 views

Comparing Ridge and Lasso Regression [duplicate]

I was thinking about main differences between ridge and lasso introducing a $\ell^2$ and $\ell^1$ penalty term respectively. The main thing is that with ridge I will keep all my features in the end ...
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Shapley value vs ridge regression

My goal is to get the feature importance for multiple regression. I have a data set with some multicollinearity. I found two methods to solve this problem. The first one is the Shapley value. ...
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1answer
194 views

L1 and L2 regularization showing increased MSE with added vars (that eventually decreases)

I am attempting to run Ridge, LASSO, and Elastic Net regression as the regularization approaches are commonly used in the problem I'm working to solve. I have successfully run both glmnet() and cv....
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74 views

Mathematical proof of how L1 and L2 regularization work [duplicate]

How do you mathematically prove that L1 regularization makes weights sparse but L2 regularization does not?
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417 views

Implementing ridge regression in python

I was trying to implement ridge regression in python. I implemented the following code: ...
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What is the meaning of assuming a special prior on regularization method

I have heard/read that L1 regularization assumes Laplacian prior, however L2 regularization assumes Gaussian prior. But what exactly "assume" mean here? How does it work? How do each of these ...
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Does the initial distribution of data have any affect on which regularization parameter can work well?

In scenarios when we want to know why performance of a predicting linear regression model when using L1 regularization has outperformed with the case that we have used L2 regularization, I wonder ...
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48 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 ...
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1answer
56 views

Understanding concepts of regularization

I am trying to understand regularization in machine learning. But, I do not understand some fundamental concepts in this topic, could you please explain? A model that has high variance, captures ...
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1answer
681 views

R Ridge Regression: Choosing best lambda

I am doing ridge regression with Mass package and stuck with the problem trying to find the best lambda. I know that it should look somehow like thi ...
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Intuition for nonmonotonicity of coefficient paths in ridge regression

Intuitively, why may some of the slope coefficients in ridge regression increase in magnitude when the penalty parameter $\lambda$ is increased? Or in other words, why are the coefficient paths ...
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Variance of $\hat{\beta}$ in Ridge Regression

If you are using ridge regression, what happens to the variance of your parameter estimates relative to regular regression? My intuition is telling me that it would decrease because you are doing a ...
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Equivalence of two optimization problems [duplicate]

Ridge regression problem: $\sum_i^n(y_i-\beta_0-\beta_{1i}-\beta_{2i})^2 \longrightarrow min_{\beta}$ $s.t. \sum_i^p\beta_i^2 \leq c$ $\sum_i^n(y_i-\beta_0-\beta_{1i}-\beta_{2i})^2 + \lambda(\sum_i^...
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2answers
66 views

variance of the square of the bias on linear regression

Basic setting let the linear model be: $$ \mathbf{y}=\mathbf{X\beta}+\epsilon $$ where $\epsilon \sim N(0,\sigma^2\mathbf{I}_n)$ $n$ is the number of samples $p$ is the number of attributes. $\...
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3answers
65 views

Should one drop independent variables if they don't have linear relationship with the response variable?

I am building a linear regression model using Ridge regression. Some of the independent variables don't have linear relationships with the dependent variable. I've tried to do data transformations on ...
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Elastic net regression with uneven penalties for predictors

For a regression model where you are certain that y that depends on some predictors but are agnostic about whether some other predictors should enter, how should you incorporate this prior information?...
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32 views

Data normalization in ridge regression when there is no intercept

I would like to have a linear model without an intercept and also without the target being centered. How should my data then be normalized when using ridge regression? If I standardized the variables ...
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63 views

Should we penalize dummy variables? [duplicate]

Using glmnet we run the following regression cvfit = cv.glmnet(x,y, alpha = 0, intercept = FALSE) where $y$ is the response variable and $x$ is the input matrix....