Machine learning seeks to construct models that work with new data. Preventing model overfitting is a challenge in this strategy. In the event that it does, it finds patterns or noise in the training data that are not relevant to previously undiscovered events. To fix this problem, regularisation methods add a penalty to the model’s complexity. This makes the model want to stay simple while still fitting the data well. L2 regularization is one of the most popular ways to make things more consistent. A lot of different machine learning techniques, like neural networks, linear regression, and logistic regression, use this method.
What is L2 Regularization?
Adding a punishment term to the model’s objective function is what L2 regularization, which is also called Ridge regularization in linear regression, does. To stop overfitting, the idea behind L2 regularization is to punish the model for having big weights (coefficients). In this way, the model is told to keep the weights small, which makes it easier and more likely to work well with new data.
L2 regularization changes the loss function that the machine learning model is trying to minimise in real life. The two parts of the updated loss function are the standard error or loss term (which checks how well the model fits the data) and the regularisation term (which punishes big weights).
Why L2 Regularization Works?
Overfitting usually happens when a model is too complicated and picks up noise and complicated trends that don’t hold up in new data. Some features in a complex model might have values that are too big, which can make the model too sensitive to small changes in the training data. By making big coefficients pay a price, regularisation methods like L2 work around this problem.
L2 regularization tells the model to spread out the weights more evenly so it doesn’t depend too much on a small group of features. It moves the coefficients closer to zero, but it doesn’t set them to zero exactly. This is what makes it different from L1 regularisation, which can make sparse models with some coefficients set to zero. L2 regularisation lowers the model’s variance by lowering the size of the weights. This makes the model more flexible.
How L2 Regularization Works?
To understand how L2 regularization works, let’s look at a simple linear regression problem. The goal is to find a set of weights that makes the difference between the predicted and real values as small as possible. The goal of standard linear regression is to get the sum of squared residuals (or errors) between the expected and true values to be as small as possible.
With L2 regularization, on the other hand, we change the goal function by adding a term that punishes the sum of the squared weights. The value of this term is equal to the sum of all model weights squared. As the weights get bigger, the penalty gets bigger too, which makes the program want to keep the weights small. So, the model might have smaller weight values that make more sense, even if it has a slightly bigger error term. This would make the trade-off between bias and variance more fair.
Benefits of L2 Regularization
- Helps Prevent Overfitting: L2 regularisation controls the size of the model’s parameters, which lowers the risk of overfitting. Large weights are punished, which helps keep the model from fitting the training data too well.
- Improves Model Generalization: L2 regularisation stops big coefficients, which makes it easier for the model to adapt to new data that it hasn’t seen before. This makes it work better on test and validation samples.
- Stabilizes the Learning Process: Training a model can be unstable at times, especially when there is multicollinearity, which means that input traits are highly correlated with each other. For better results, L2 regularisation can help by making the answer more stable.
- Smooths the Model: When L2 regularisation is used, models tend to become smoother and less likely to jump around a lot when making predictions. This smoothness can help the model make more accurate guesses for things it hasn’t seen yet in spaces with a lot of dimensions.
- Works Well for Most Data: L2 regularisation works well for most datasets. It works best when the dataset has a lot of features or when most of the features are assumed to be predictive. It does not force the model to be very sparse, which makes it less likely to miss traits that could be useful.
L2 Regularization in Practice
The linear models like linear regression and logistic regression are the ones that use L2 regularisation the most. It is also used a lot in models that are more complicated, like neural networks.
Linear Regression with L2 Regularization (Ridge Regression):
Ridge Regression is a type of linear regression that uses L2 regularisation. To use L2 regularisation, an extra term is added to the loss function in linear regression. In this term, the squares of the model values are added together and given a weight by a regularisation parameter. When this regularisation parameter is set to a higher value, big weights are punished more, which makes the coefficients smaller. The goal of Ridge regression is to find the factors that make the error term and the regularisation term as small as possible.
Logistic Regression with L2 Regularization:
When you use L2 regularisation on logistic regression, you add a penalty to the loss function that is proportional to the squared values. This works in the same way. By punishing big coefficients, this keeps the model from overfitting noisy data, which could happen in classification problems otherwise.
Neural Networks with L2 Regularization:
Weights are regularised by L2 regularisation in neural networks. Neural networks have several parameters. L2 regularisation helps regulate model parameters. This helps the model handle varied networks, especially deep, overfitting networks.
Choosing the Regularization Parameter
Picking the right regularisation strength is one of the hardest parts of using L2 regularisation. This strength is set by a hyperparameter, which is usually written as alpha or lambda. This hyperparameter sets the right mix between keeping the weights small and fitting the data. The regularisation term doesn’t have much of an effect if lambda is set to a very small number, and the model may fit too well. If lambda is set too high, on the other hand, the model might be too limited, and it might not fit the data well enough by missing important connections.
Cross-validation is usually used to find the best value of lambda. This method divides the dataset into several parts, and the model is trained and tested on each part to find the lambda value that gives the best generalisation performance.
L2 vs L1 Regularization
L1 regularization and L2 regularization are often put next to each other. How they punish the model factors is what makes them different from each other. In L2 regularisation, the sum of the squared coefficients is punished. In L1 regularisation, the sum of the absolute numbers of the coefficients is punished.
When L1 regularisation is used, it can make some values equal to zero. This removes less important features from the model, which is the same thing as feature selection. This can be useful for files with a lot of dimensions, where many features might not be important. L2 regularisation, on the other hand, tends to push all coefficients towards zero without getting rid of them totally. This can be helpful when all features are thought to have some predictive value.
In real life, a lot of machine learning systems use Elastic Net regularisation, which combines L1 and L2 penalties to find the best mix between selecting features and reducing weight.
In conclusion
There is a powerful machine learning method called L2 regularization that helps make models more general by punishing models with high weights. L2 regularization lowers the risk of overfitting by pushing for simpler models with smaller coefficients. This is especially true in spaces with a lot of dimensions. It is an important part of making strong and accurate predictive models and is used in many machine learning algorithms, from linear models to neural networks.
But the level of regularisation needs to be carefully adjusted so that the model doesn’t fit the data too well or too poorly. Finally, L2 regularisation is a basic method that helps make sure that machine learning models work well on new data they haven’t seen before when it’s used correctly.