difference between LinearRegression and svm.SVR(kernel=“linear”)

Question

First there are questions on this forum very similar to this one but trust me none matches so no duplicating please.

I have encountered two methods of linear regression using scikit's sklearn and I am failing to understand the difference between the two, especially where in first code there's a method train_test_split() called while in the other one directly fit method is called.

I am studying with multiple resources and this single issue is very confusing to me.

First which uses SVR

X = np.array(df.drop(['label'], 1))

X = preprocessing.scale(X)

y = np.array(df['label'])

X_train, X_test, y_train, y_test = cross_validation.train_test_split(X, y, test_size=0.2)

clf = svm.SVR(kernel='linear')

clf.fit(X_train, y_train)

confidence = clf.score(X_test, y_test)

And second is this one

# Split the data into training/testing sets
diabetes_X_train = diabetes_X[:-20]
diabetes_X_test = diabetes_X[-20:]

# Split the targets into training/testing sets
diabetes_y_train = diabetes.target[:-20]
diabetes_y_test = diabetes.target[-20:]

# Create linear regression object
regr = linear_model.LinearRegression()

# Train the model using the training sets
regr.fit(diabetes_X_train, diabetes_y_train)

# Make predictions using the testing set
diabetes_y_pred = regr.predict(diabetes_X_test)

So my main focus is the difference between using svr(kernel="linear") and using LinearRegression()

Answer 1

cross_validation.train_test_split : Splits arrays or matrices into random train and test subsets.

In second code, splitting is not random.

svm.SVR: The Support Vector Regression (SVR) uses the same principles as the SVM for classification, with only a few minor differences. First of all, because output is a real number it becomes very difficult to predict the information at hand, which has infinite possibilities. In the case of regression, a margin of tolerance (epsilon) is set in approximation to the SVM which would have already requested from the problem. But besides this fact, there is also a more complicated reason, the algorithm is more complicated therefore to be taken in consideration. However, the main idea is always the same: to minimize error, individualizing the hyperplane which maximizes the margin, keeping in mind that part of the error is tolerated.

Linear Regression: In statistics, linear regression is a linear approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variables) denoted X. The case of one explanatory variable is called simple linear regression.

Reference: https://cs.adelaide.edu.au/~chhshen/teaching/ML_SVR.pdf

Answer 2

This is what I found:

Intuitively, as all regressors it tries to fit a line to data by minimising a cost function. However, the interesting part about SVR is that you can deploy a non-linear kernel. In this case you end making non-linear regression, i.e. fitting a curve rather than a line. This process is based on the kernel trick and the representation of the solution/model in the dual rather than in the primal. That is, the model is represented as combinations of the training points rather than a function of the features and some weights. At the same time the basic algorithm remains the same: the only real change in the process of going non-linear is the kernel function, which changes from a simple inner product to some non linear function.

So SVR allows non linear fitting problems as well while LinearRegression() is only for simple linear regression with straight line (may contain any number of features in both cases).