# How To Use Regularization In Machine Learning?

Updated: Apr 17

Biasness and Variance – These two things can render your Machine Learning model useless. The quality and type of data that you use to train your model have a huge impact on its eventual performance. If your dataset is too rigid or limited, there’s a chance that your Machine Learning model will develop a bias that can compromise its usage. Similarly, if your data set contains too much noise (outliers in the overall dataset), your model can become overly flexible.

In a Machine Learning model, biasness is referred to as overfitting, and variance is referred to as underfitting. Both of these can end up compromising your ML model. This is where regularization comes into play. Regularization is a crucial concept in Machine Learning, and it counters biasness (overfitting) as well as variance (underfitting). In this article, we are going to cover everything you need to know about regularization, including what it is, how it works, and most importantly, how you can use it in Machine Learning. So, without further ado, let’s dive into it!

## What Are Overfitting and Underfitting?

Before we take a deep dive into regularization, let's talk about overfitting and underfitting to understand the core concepts. Simply put, overfitting and underfitting are terms used to describe modeling errors caused by problems in a dataset.

Overfitting occurs when a dataset consists of data that is limited. A limited dataset results in an ML model that is fitted to a very limited set of data points. Limited data points result in a biasness that makes the model too rigid to be usable.

Underfitting is the opposite of overfitting. This happens when your dataset has too many data points that aren't relevant. Irrelevant data results in "noise" that affects your model's accuracy. A noisy dataset results in an ML model that is too flexible, making it inaccurate and unreliable when processing unseen data.

Both overfitting and underfitting compromise the usability of your ML model resulting in a high error rate when you run unseen data through it. Avoiding overfitting and underfitting can be complicated, but it's not entirely impossible. Regularization techniques can be used to manage modeling errors and develop machine learning models that are accurate in real-life applications. To avoid overfitting and underfitting, you first need to develop a thorough understanding of bias and variance in machine learning.

## What are Bias and Variance?

In order to train a machine learning model, you need to feed it with complex datasets. Ideally, a dataset should have data points that train an ML model to have low bias and low variance. Unfortunately, this isn't entirely possible. When it comes to datasets, variance and bias are inversely proportional. This means a dataset that has high bias will have low variation and vice versa.

A high bias dataset consists of data points that are limited. This means it consists of data that isn't diverse enough to train an ML model to easily match unseen data. It results in a rigid model that is incapable of processing data in the real world.

A high variance dataset has a diverse set of data points. These diverse data points result in an ML model that fits different datasets easily but has a higher chance of making inaccurate predictions. Too much variance results in ML models that are too flexible, making them inaccurate.

When training an ML model, it's important to come up with training data that maintains a fine balance between bias and variance. However, even the most well-made dataset will end up producing some degree of bias and variance. So. in order to fine-tune your machine learning model, you need to counter these errors with regularization techniques.

## What Is Regularization in Machine Learning?

Regularization is a term used to describe the fine-tuning of a machine learning function. As we've discussed above, variance and bias lead to margins of error in an ML model. These errors make your model less accurate and less reliable when processing unseen data. In order to fully understand regularization, we need to look at it from a mathematical point of view. Basically, regularization is a form of regression that fine-tunes an existing equation. It does this by limiting (or regularizing) a coefficient in order to bring it closer to zero.

There are many regularization techniques used to fine-tune machine learning equations. The most popular are:

Ridge regression (L2 regression)

Lasso regression (L1 regression)

Ensemble learning

K-Fold Cross-Validation

We’re going to take a detailed look at each of these regularization techniques and see how they work. However, before we get into the details of regularization techniques, let's understand how regularization works in Machine Learning.

## How Does Regularization Work in Machine Learning?

We feed training data to a machine learning model in order to prepare it for processing unseen data. Machine learning models process training data and discover patterns by processing and generalizing data. If training data has noise in it (which it usually does), an ML model can get thrown off while discovering patterns. This can lead to its accuracy being compromised.

Regularization techniques are used in machine learning to counter noise in datasets and ensure that a machine learning model stays accurate. Here's an equation to demonstrate what regularization is.

**Y ≈ β0 + β1X1 + β2X2 + …+ βpXp**

In the equation above, Y is the learned relation, and β denotes the coefficient estimates for various variables (denoted by X). In order to fine-tune the equation, a Residual Sum of Squares (RSS) is introduced into the mix.

The RSS works by adjusting your coefficients based on the training data that you feed your ML model. It constrains estimates and brings them closer to zero, reducing noise from your data and preventing inaccuracies from forming in your machine learning model.

Regularization can greatly improve the accuracy of your machine learning model, especially when it’s combined with increasing the size of your training dataset. It should be noted that increasing the size of your training dataset doesn’t mean increasing the diversity of variables in your data. It means increasing the quantity of the same types of variables. This gives your model more data to process and generalize.

## Regularization Techniques in Machine Learning

As we mentioned above, there are different types of regularization techniques. Each technique has its own advantages, drawbacks, and use cases. For this discussion, we're going to focus on the following regularization techniques:

Ridge regression (L2 regression)

Lasso regression (L1 regression)

Ensemble learning

K-Fold Cross-Validation

### Regularization Through the Cost Function

The cost function (also known as the loss function) is used in machine learning to define the difference between an actual value and a predicted value. The cost function can be further categorized into two forms:

Cost function

Loss function

Some people use these terms interchangeably; however, there is a difference between the two. The former describes the median (or average) of the loss function across a complete set of training data. The latter describes an error in a single training data example.

L1 and L2 regularization techniques regularize machine learning models by affecting the cost/loss function. Let’s take a detailed look at each of these regularization techniques and talk about their differences.

#### 1- Ridge Regression or L2 Regularization

The simplest way to describe ridge (L2) regularization is that it attempts to estimate the mean of a dataset in order to avoid inaccuracies. L2 regularization works by adding a squared value of weights to a loss function.

Ridge regression minimizes inaccuracies by forcefully keeping weights small without turning them into absolute zeros. To make this easier to understand, let's take a look at an example.

If you’re using a machine learning model to make predictions of housing prices, you can use L2 regularization to counter overfitting or underfitting. L2 regularization can be performed by adding the squared value of all the feature weights to your loss function. This squared value of weights will result in less important variables having a minor impact on the overall prediction. L2 regularization also uses a lambda to control the amount of regularization being applied to a given machine learning model.

**Usage of Ridge Regression:**

Works by estimating the mean of a given dataset.

L2 regularization adds a squared value of weights to a loss function.

The squared value in ridge regression is close to zero but not an absolute zero.

Ridge regression returns non-sparse solutions due to the fact that weights are non-zero values but very close to zero.

L2 regularization uses a lambda to control the amount of regularization being applied to a machine learning model.

**Limitation of Ridge Regression:**

L2 regularization is not suitable for feature reduction since it doesn’t reduce the overall number of variables.

Ridge regression doesn’t hold up well against outliers. The difference caused by outliers can grow out of control when it gets squared.

#### 2- Lasso Regression or L1 Regularization

L1 (lasso regression) regularization works by making an attempt to estimate the median of given data. A major aspect of L1 regularization is to minimize errors by reducing variables to zero. By doing so, feature reduction takes place.

Lasso regression can be thought of as a function that allows you to select particular features in your dataset. In L1 regularization, you assign a weight of zero to selected features. This weight is multiplied with features in order to convert those features to zero as well. This results in the eradication of the influence of these selected features. Features that you don’t want to reduce can be assigned with weights that are non-zero values close to zero.

Similar to L2 regularization, L1 also uses a lambda to control the amount of regularization being applied in a function.

**Usage of Lasso Regression:**

L1 regularization works by reducing selected features to 0 (feature reduction). It makes training datasets less complex.

Lasso regression assigns zero weights to features that are to be reduced and non-zero weights to features that must remain relevant.

L1 regularization is suitable for taking non-related features and reducing their influence in a dataset.

Lasso regression uses a lambda to control the amount of regularization being applied to a machine learning model.

**Limitation of Lasso Regression:**

Lasso regression can perform poorly if the number of predictors in a dataset exceeds the number of observations.

If a dataset has more than two highly related variables, lasso regression can randomize their selection, leading to improper data interpretation.

#### Difference Between L1 And L2 Regularization (Ridge vs Lasso Regression):

L1 and L2 regularization both work by assigning weights to features in a loss function; however, there are a few key differences between both types of regularization.

L1 regularization focuses on estimating the median of a dataset, while L2 regularization estimates the mean of a dataset.

L2 regularization doesn’t cause feature reduction, meaning it doesn’t decrease the complexity of a dataset.

L1 regularization produces non-sparse results while L1 produces spare results.

L2 regularization does not perform well in datasets with outliers, while L1 does.

Ridge (L2) and lasso (L1) regression are regularization techniques that work best in different use cases. When applying regularization to a machine learning model, you need to know what type of data is present in your training data. Ultimately, your training data plays a detrimental role in deciding what type of regularization you should go for.

### Other Regularization Methods

Ridge and Lasso regression aren’t the only regularization techniques out there. There might be times when L1 and L2 regularization aren’t suitable. This can be due to features in your data that these two types of regularization may not be able to handle. So, let’s take a look at two other types of regularization that can be used to train machine learning models with greater accuracy.

#### Ensemble Learning

Ensemble learning is a type of machine learning regularization that fine-tunes your ML model’s performance by taking predictions from multiple models and merging them.

Ensemble learning has three main approaches: boosting, bagging, and stacking. Each method revolves around taking multiple models and combining their predictions. The concept is that by combining multiple models, generalization can be improved, leading to an ML model becoming more accurate. It goes without saying that in order to perform ensemble learning, you need to have access to multiple machine learning models.

#### K-Fold Cross-Validation

K-fold cross-validation is a regularization technique used to predict the overall skill of a specific machine learning model. This regularization technique makes use of statistics and is used quite frequently because of how easy it is. K-fold cross-validation is easy to execute and produces results that tend to have lower bias levels than other regularization techniques.

## How can we help?

Regularization is a core aspect of machine learning. Without regularization techniques, machine learning models simply cannot be accurate enough to be usable in real-world scenarios. Hopefully, by the end of this article, you'll have a far better idea of what regularization is, how it works, and what's the difference between L1 and L2 regularization.

It goes without saying that regularization can be tricky. Once you get into the math and begin working on algorithms, its application and fine-tuning can take a lot of time. Most importantly, it takes just one wrong step to mess it all up to the core. So, if you want to implement regularization in your Machine Learning model, it's best to get it done by a highly professional and qualified Machine Learning expert. That's where we come in.

Here at IIInigence, we stand proud as the best Artificial Intelligence and Machine Learning development company offering regularization, data modeling, model training, and several other services. So, if you have any confusion about how you can implement regularization techniques, feel free to get in touch with our experts. We have a dedicated team of machine learning experts who can help you improve workflows and develop ML models with greater accuracy.