What is Kernel Linear and Multiclass ridge regression in shogun?

This recipe will help us understand what shogun's kernel linear and multiclass ridge regression are and the differences between them.

Recipe Objective: What is Kernel, Linear, and Multiclass ridge regression in shogun? What is the difference between them?

This recipe explains what Kernel, Linear, and Multiclass ridge regression in shogun is, the difference between them, and explains each with an example.
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Kernel Ridge Regression

Kernel ridge regression is a non-parametric form of ridge regression. The aim is to learn a function in the space induced by the respective kernel k by minimizing a squared loss with a squared norm regularization term.

# Kernel Ridge Regression
x_train = RealFeatures(feats_train)
x_test = RealFeatures(feats_test)
y_train = RegressionLabels(labels_train)
y_test = RegressionLabels(labels_test)

z = GaussianKernel(x_train, x_train, 1.0)
k = KernelRidgeRegression(0.001, z, y_train)

k.train()
predict = k.apply_regression(x_test)

eva = MeanSquaredError()
mse = eva.evaluate(predict, y_test)

Linear Ridge Regression

Linear Ridge Regression can be represented in numerical form as "y = (w^t) (x)" where w is the weight vector, x is a feature vector, and y is the predicted value. We aim to minimize the squared loss; to do so, we find the linear function that best explains the data.

# Linear Ridge Regression
x_train = RealFeatures(feats_train)
x_test = RealFeatures(feats_test)
y_train = RegressionLabels(labels_train)
y_test = RegressionLabels(labels_test)

l = LinearRidgeRegression(0.001, x_train, y_train)
l.train()
predict = l.apply_regression(x_test)

eva = MeanSquaredError()
mse = eva.evaluate(predict, y_test)

Multiple Kernel Learning

Multiple kernel learning (MKL) is based on convex combinations of arbitrary kernels over potentially different domains.

# Multiple Kernel Learning
x_train = RealFeatures(feats_train)
x_test = RealFeatures(feats_test)
y_train = RegressionLabels(labels_train)
y_test = RegressionLabels(labels_test)

poly = PolyKernel(10, 2)
gauss_1 = GaussianKernel(2.0)
gauss_2 = GaussianKernel(3.0)

kernel = CombinedKernel()
kernel.append_kernel(poly)
kernel.append_kernel(gauss_1)
kernel.append_kernel(gauss_2)
kernel.init(x_train, x_train)

svm_solver = SVRLight()
m = MKLRegression(svm_solver)
m.set_kernel(kernel)
m.set_labels(y_train)
m.train()

beta = kernel.get_subkernel_weights()
alpha = mkl.get_alphas()

kernel.init(x_train, x_test)
predict = m.apply_regression()

res = MeanSquaredError()
mse = res.evaluate(predict, y_test)

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