Test your knowledge 

In this blog post, we will go through every aspect of Regularization for Linear regression models by answering the following 5 questions:
What is Regularization?
When to use Regularization?
Where to use Regularization?
How to use Regularization?
Why does Regularization work?
a bonus,
Other regularization techniques
and lastly,
Conclusion.
Literally, Regularization means making something more regular. It is somehow true even in the sense of Machine learning.
In Machine learning, Regularization is a process of making your predictive model more “regular” – that is, more natural, more simple, more “real“.
For example, making all the weights ( for ) more equal to each other. This is analogous to making a shape more regular by tweaking so that all the edges have the same length, right?
Regularization is a technique used to combat the problem of overfitting, so we are using it in case our model seems to overfit the data.
We use Regularization in the objective function (or we can say the cost function).
To apply Regularization, we just need to modify the cost function, by adding a regularization function at the end of it.
New cost function = Original cost function + regularization function.
Then, we optimize the New cost function instead of the Original cost function.
There are several Regularization methods for Linear regression. We are going to examine each of them:
Lasso (also called L1)
New cost function = Original cost function + ,
where:
 is the rate of Regularization. This parameter controls if regularization’s influence on your model is high or low. Higher means higher the influence of regularization. .
 is the Lasso regularization function.
For example, if you originally use MAE as your cost function, then after applying Lasso, your new cost function will be:
New cost function = .
Ridge (also called L2)
New cost function = Original cost function + ,
Interpretation of the parameters is very similar to above:
 is the rate of Regularization. This parameter controls if regularization’s influence on your model is high or low. Higher means higher the influence of regularization. .
 is the Ridge regularization function.
For example, if you originally use MSE as your cost function, then after applying Ridge, your new cost function will be:
New cost function = .
Note that the value of is your choice. When you feel that your model is still overfitting, increase . On the other hand, if you think your model escaped from overfitting but is now underfitting, just decrease .
Elastic Net
New cost function = Original cost function + ,
where:
 is regularization rate of Lasso,
 is regularization rate of Ridge.
Elastic Net Regularization is simply a combination of Lasso and Ridge. You can customize the effect of Lasso and Ridge separately using and .
What Regularization actually does is to reduce the magnitude of the weights (, with ) while keeping the original cost small enough. Hence, we shift our question to Why reducing the weights helps with the problem of overfitting?
To answer this question, we can look at it from either of the below 2 viewpoints:
Viewpoint 1: overfitting is that you emphasize on the wrong predictors. And the only way for you to emphasize a predictor is putting more weight on it. Hence, by reducing the weights, you also reduce your emphasis, or says, reduce your overfitting.
Viewpoint 2: Look at this picture of overfitting:
I bet you already saw some similar pictures like this (but probably more beautiful ones) if you have ever tried to find out some information about overfitting. But if you haven’t, let me introduce: the red points are response values of data, while the blue line is the regression model. We clearly see that the line (the model) is overfitting the data.
Notice that the slope of the line changes fiercely to match the data points. A line can have its slope changing like that if and only if the magnitudes of parameters (the weights) are large and have high variance. Hence, by reducing the magnitudes of the weights, we flatten the line and help it less overfit the data.
Other regularization techniques
Some other techniques for preventing overfitting are:
Test your understanding 

Above, we learned about the 5 aspects of Regularization.
Essentially, Regularization is a technique to deal with overfitting by reducing the weights of linear regression models.
Lasso tries to decrease the absolute value of the weights. Hence, some features with little or no effect on the model will get eliminated (i.e. weight equals 0).
Ridge, on the other hand, decreases the squared value of the weight. Hence, features with larger weights will be punished more heavily than features with smaller weights. In the end, usually, there are no features that have weights equal to 0. Instead, bad features will still have weight, although very very small. The weights after applying Ridge will be like the edges of regular shape (i.e. having comparable values) if the features’ influence on the model is quite comparable to each other.
Elastic net, as the combination of Lasso and Ridge, is in the middle of the 2. Elastic Net will be more like Lasso or more like Ridge depends on the values of and .
Regularization, especially Lasso, can also help in feature selection.
Beside L1, L2 and Elastic Net, some other techniques for fighting overfitting are: collecting more data, noise addition, and early stopping.
An important note: remember to scale all the features (the predictors) before applying Linear regression with Regularization (L1, L2, ElasticNet), because this will make the Regularization Function treat the predictors equally.
You can find the full series of blogs on Linear regression here.