Difference Between Ridge Regression and SVM Regressor in Scikit Learn

• Last Updated : 30 Dec, 2022

In this article, we will learn what is the difference between the two most common regression algorithms that is kernel Ridge Regression and SVR. And then we will move on to its code implementation using scikit learn in Python.

What is Kernel ridge regression?

Kernel ridge regression is a variant of ridge regression, which uses the kernel trick to learn a linear function in the high-dimensional feature space. This allows it to perform well on nonlinear data, without the need to explicitly transform the input into a higher-dimensional space.

SVR (Support Vector regression):

Support vector regression (SVR) is another type of regression algorithm that uses support vector machines (SVMs) to learn a function that best fits the data. Like kernel ridge regression, it can be used to learn nonlinear functions, but it does so by trying to fit a regression function that is as flat as possible while still adequately fitting the data.

Both kernel ridge regression and SVR can be useful for regression tasks, and the choice between them may depend on the specific characteristics of the data and the desired performance of the model. In general, kernel ridge regression can be more computationally efficient and easier to tune, but SVR may be able to learn more complex functions. In Scikit-Learn, both algorithms can be implemented using the KernelRidge and SVR classes, respectively.

Which is better?

You can compare the MSE of the kernel ridge regression model (kr) and the support vector regression model (svr) on the test data to see which model performs better. If the MSE of the kernel ridge regression model is lower, it may indicate that the model is better able to capture the patterns in the data and make more accurate predictions. On the other hand, if the MSE of the support vector regression model is lower, it may indicate that the model is more robust and generalizes better to new data.

In Scikit-Learn, both kernel ridge regression and support vector regression (SVR) can be implemented using the KernelRidge and SVR classes, respectively. These classes provide a number of hyperparameters that can be tuned to customize the behavior of the model, such as the type of kernel to use, the regularization strength, and the size of the margin in SVR.

To use these classes, you will first need to import them from sklearn.kernel_ridge and sklearn.svm modules, respectively. Then, you can create an instance of the KernelRidge or SVR class and specify the hyperparameters that you want to use. For example:

Python3

 `from` `sklearn.model_selection ``import` `train_test_split``from` `sklearn.metrics ``import` `mean_absolute_error``from` `sklearn.kernel_ridge ``import` `KernelRidge``from` `sklearn.svm ``import` `SVR``from` `sklearn ``import` `datasets``# Load the data from a dataset in Scikit-learn``data ``=` `datasets.load_boston()`` ` `# Split the data into training and test sets``X_train, X_test,\``    ``y_train, y_test ``=` `train_test_split(data.data,``                                       ``data.target)`` ` `# Kernel ridge regression with a polynomial kernel``kr ``=` `KernelRidge()`` ` `# Support vector regression with a linear kernel``svr ``=` `SVR()`

Once you have created an instance of the KernelRidge or SVR class, you can use it to fit a regression model to your data by calling the fit method and passing it the training data and the corresponding targets. For example:

Python3

 `# Fit the kernel ridge regression model``kr.fit(X_train, y_train)`` ` `# Fit the support vector regression model``svr.fit(X_train, y_train)`

After fitting the model, you can use it to make predictions on new data by calling the prediction method and passing it the data that you want to make predictions for. For example:

Python3

 `# Use the kernel ridge regression``# model to make predictions``y_pred_kr ``=` `kr.predict(X_test)`` ` `# Use the support vector regression``# model to make predictions``y_pred_svr ``=` `svr.predict(X_test)`

After using the kernel ridge regression model and support vector regression model to make predictions now compute the mean squared error for each model

Python3

 `# Compute the mean squared error for each model``mse_kr ``=` `((y_pred_kr ``-` `y_test) ``*``*` `2``).mean()``mse_svr ``=` `((y_pred_svr ``-` `y_test) ``*``*` `2``).mean()`` ` `# Print the mean squared error for each model``print``(f``"Mean squared error (KR): {mse_kr:.2f}"``)``print``(f``"Mean squared error (SVR): {mse_svr:.2f}"``)`

Output :

```Mean squared error (KR): 20.09
Mean squared error (SVR): 48.18```

Note that the mean squared errors for the two models are the same because the code is using the same data for both models. The values may vary slightly if you run the code yourself, due to the randomness in the data generation process.

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