Which hyperparameter controls the width of the hyperplane in SVMs for linear regression?

In support vector machines (SVMs) used for regression tasks, the hyperparameter that controls the width of the hyperplane is known as epsilon (ε). This parameter defines the margin of tolerance where no penalty is given to errors in predictions. Essentially, it specifies a tube around the regression line within which predictions can vary without incurring a loss.

When epsilon is set to a smaller value, the tube also becomes narrower, which means the model will aim to fit the training data closely, potentially leading to a more complex model that may overfit the training data. Conversely, if epsilon is set to a larger value, the tube widens, allowing for greater flexibility and potentially resulting in a simpler model that might underfit.

The other parameters mentioned serve different roles within the SVM framework. For example, the regularization penalty (C) influences the trade-off between maximizing the margin and minimizing classification error, while gamma (γ) impacts the influence of individual training examples in kernel-based SVMs. Alpha (α) typically relates to learning rates in other optimization contexts, but it is not a hyperparameter for controlling the width of the hyperplane in SVM regression.