Regression: Regularization parameter 0

In summary, the conversation discusses the use of ScikitLearn's Elastic Net implementation for regression with a data set where the number of data points is larger than the number of features. The routine uses crossvalidation to find two hyperparameters, ##\alpha## and ##c##, and minimizes the expression ##\frac {1}{2N} ||y-Xw||^2 + \alpha c ||w||_1 + \frac 1 2 \alpha (1-c) ||w||_2^2 ##. The person speaking obtains a hyperparameter of ##\alpha=0##, which means no regularization is preferred. They question what this implies and if overfitting is an issue in this
  • #1
SchroedingersLion
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TL;DR Summary
ScikitLearn Elastic Net regression gives a hyperparameter of 0, implying that ordinary least squares is the best method.
Hi guys,

I am using ScikitLearn's Elastic Net implementation to perform regression on a data set where number of data points is larger than number of features. The routine uses crossvalidation to find the two hyperparameters: ElasticNetCV
The elastic net minimizes ##\frac {1}{2N} ||y-Xw||^2 + \alpha c ||w||_1 + \frac 1 2 \alpha (1-c) ||w||_2^2 ##, where ##\alpha## and ##c## are the hyperparameters.

However, I obtain a hyperparameter of ##\alpha=0##, which means the routine prefers no regularization at all. I was wondering what this means. The regularization is done in order to decrease overfitting on test data. What does a parameter of 0 imply? Does it mean I cannot have overfitting in this case?SL
 
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  • #2
Generally, if the number of features <<< data points and there is little correlation between them, then OLS is the best method
 
  • #3
So overfitting is not an issue when I have more data points than features?
Makes somewhat sense, because if I want to fit a line with n parameters, and I have N>>n data points, I can not hit each data point as good as I want, not even in the training data. So overfitting is suppressed.
 
  • #4
The elastic net is a combination of lasso and ridge and will penalize collinear and low t-stat variables - so if you get the same results as an OLS your predictors are fine
 
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  • #5
Thank you!
 
  • #6
Should add that none of these methods deal well with autocorellation - need GLS or GMM for that
 

FAQ: Regression: Regularization parameter 0

1. What is the purpose of the regularization parameter in regression?

The regularization parameter in regression is used to control the complexity of the model and prevent overfitting. It penalizes large coefficients and helps to find a balance between the model's ability to fit the training data and its ability to generalize to new data.

2. How does a regularization parameter of 0 affect the regression model?

A regularization parameter of 0 means that no penalty is applied to the model's coefficients. This can lead to overfitting, as the model will try to fit the training data as closely as possible without considering the complexity of the model.

3. Can a regularization parameter of 0 be used for all types of regression?

Yes, a regularization parameter of 0 can be used for all types of regression, including linear regression, logistic regression, and polynomial regression. However, it is important to note that the optimal value of the regularization parameter may vary depending on the type of regression and the dataset.

4. How do you determine the optimal value for the regularization parameter in regression?

The optimal value for the regularization parameter can be determined by using techniques such as cross-validation or grid search. These methods involve testing different values for the regularization parameter and selecting the one that results in the best performance on a validation dataset.

5. Is a higher or lower value for the regularization parameter better?

The optimal value for the regularization parameter depends on the dataset and the complexity of the model. In general, a higher value for the regularization parameter will result in a simpler model with smaller coefficients, while a lower value will result in a more complex model with larger coefficients. It is important to find the right balance between model complexity and performance on new data.

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