Estimating with support vector regression

As the name implies, SVR is part of the support vector family and a sibling of the support vector machine (SVM) for classification (or we can just call it SVC) that you learned about in Chapter 3, Recognizing Faces with Support Vector Machine.

To recap, SVC seeks an optimal hyperplane that best segregates observations from different classes. Suppose a hyperplane is determined by a slope vector w and intercept b, and the optimal hyperplane is picked so that the distance (which can be expressed as ) from the nearest points in each of the segregated spaces to the hyperplane is maximized. The optimal w and b can be learned and solved with the following optimization problem:

• Minimizing ||w||
• Subject to y⁽ⁱ⁾(wx⁽ⁱ⁾ + b) ≥ 1, for a training set of (x⁽¹⁾, y⁽¹⁾), (x⁽²⁾, y⁽²⁾), … (x⁽ⁱ⁾, y⁽ⁱ⁾)…, (x^(m), y^(m))

In SVR, our goal is to find...