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What is the role of regularization in regression model selection?

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Regression is a powerful technique for finding the relationship between a set of variables and a target outcome. However, when you have many variables or a complex relationship, you may face some challenges, such as overfitting, multicollinearity, or high variance. How can you overcome these issues and select the best regression model for your data? One possible solution is regularization.

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Asad Ali

Data Science & Analytics Leader | Strategic Consultant to Fortune 100 Organizations

1 What is regularization?

Regularization is a method of adding a penalty term to the regression equation, which reduces the magnitude of the coefficients or shrinks them to zero. This helps to avoid overfitting, which occurs when the model fits the training data too well and fails to generalize to new data. Regularization also helps to deal with multicollinearity, which occurs when some variables are highly correlated and cause instability in the estimates. By shrinking the coefficients, regularization reduces the variance of the model and improves its performance.

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Asad Ali

Data Science & Analytics Leader | Strategic Consultant to Fortune 100 Organizations
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While developing broadcast ratings prediction models, my team encountered the challenge of limited records (around 500 broadcasts). This constraint posed difficulties in feature curation, particularly as the models needed to be linear regression-based for explainability. Implementing Ridge regression proved instrumental in mitigating overfitting, enabling the incorporation of more features. This not only enhanced overall accuracy but also facilitated the measurement of the impact of multiple regressors which had significant business importance

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2 Types of regularization

There are different types of regularization, depending on how the penalty term is calculated and applied. The most common ones are ridge regression, lasso regression, and elastic net regression. Let's see how they differ and when to use them.

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Muhammad Hassan Bin Afzal

Lifelong Learner | Researcher & Educator | Bridging Data and Policy for Meaningful Change
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In my research, regularization is vital for regression model selection, particularly with high-dimensional data. It mitigates overfitting by adding a penalty to coefficients. I use L1 (Lasso) for feature selection, as it shrinks irrelevant predictors to zero, and L2 (Ridge) to reduce the impact of less critical predictors in scenarios where all have relevance. Optimizing the regularization parameter through cross-validation is crucial to balance model complexity and enhance generalizability, a consistent theme in my analyses.

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3 Ridge regression

Ridge regression adds a penalty term that is proportional to the square of the coefficients. This means that it reduces all the coefficients by the same amount, but does not eliminate any of them. Ridge regression is useful when you have many variables that contribute to the outcome, but none of them is dominant. It also works well when you have multicollinearity, as it stabilizes the estimates and reduces the variance.

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4 Lasso regression

Lasso regression adds a penalty term that is proportional to the absolute value of the coefficients. This means that it reduces some of the coefficients to zero, effectively removing them from the model. Lasso regression is useful when you have many variables, but only a few of them are relevant to the outcome. It also works well when you want to perform feature selection, as it identifies the most important variables and discards the rest.

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5 Elastic net regression

Elastic net regression combines the features of ridge and lasso regression, by adding a penalty term that is a weighted average of the square and the absolute value of the coefficients. This means that it reduces some of the coefficients to zero, but not all of them. Elastic net regression is useful when you have many variables, some of them are correlated, and some of them are important to the outcome. It also works well when you want to balance between feature selection and variance reduction.

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6 How to choose regularization

Regularization is a powerful tool for improving your regression model, but how do you choose the best type and amount of regularization for your data? There are two main factors to consider: the complexity of the model and the bias-variance trade-off. The complexity of the model depends on the number and nature of the variables, and the relationship between them and the outcome. The bias-variance trade-off refers to the trade-off between underfitting and overfitting, or between having a low or high error on new data. You can use cross-validation, a technique that splits the data into multiple subsets and evaluates the model on each subset, to compare different regularization methods and parameters, and select the one that minimizes the error on new data.

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What is the role of regularization in regression model selection?

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3

4

5

6

7

1 What is regularization?

2 Types of regularization

3 Ridge regression

4 Lasso regression

5 Elastic net regression

6 How to choose regularization

7 Here’s what else to consider

Statistics

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What is the role of regularization in regression model selection?

1

2

3

4

5

6

7

1 What is regularization?

2 Types of regularization

3 Ridge regression

4 Lasso regression

5 Elastic net regression

6 How to choose regularization

7 Here’s what else to consider

Statistics

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