Question

Given that I have already trained an SVM regressor with data generated in the sinc function, sinc(x)=sinπx/πx. What would be the the potential use of the regressor?

Answer 1

The basic idea in SVR is to map an input data x into a higher dimensional feature space F via a nonlinear mapping φ and then a linear regression problem is obtained and solved in the feature space. Therefore, the regression approximation addresses the problem of estimating a function based on a given data set G = {(xi, yi)}m i=1 (xi ∈ Rn is the input vector, yi ∈ R is the desired real-value). In SVM method, the regression function is approximated by

f(x) = ω, φ(x) + b (1)

where {φi(x)}m i=1 are the features of inputs, ω and b are coefficients. The coefficients are estimated by minimizing the regularized risk function:   

R(ω) = 1/2 ||ω||² + Cm i=1 L (f(xi), yi)

where regularized term 1 2 ω 2 is used as a flatness measurement of function , C is a fixed constant determining the tradeoff between the training error and the model complexity, and L(·) is the e-insensitive loss function defined by Vapnik:

L(f(x), y) = max{|f(x) − y| − e, 0}

where e is a prescribed parameter