4、 midterm 2009 problem 4
6、Consider two classifiers: 1) an SVM with a quadratic (second order polynomial) kernel function and 2) an unconstrained mixture of two Gaussians model, one Gaussian per class label. These classifiers try to map examples in R2 to binary labels. We assume that the problem is separable, no slack penalties are added to the SVM classifier, and that we have sufficiently many training examples to estimate the covariance matrices of the two Gaussian components. (1) The two classifiers have the same VC-dimension. (T)
(2) Suppose we evaluated the structural risk minimization score for the two classifiers. The score is
the bound on the expected loss of the classifier, when the classifier is estimated on the basis of n training examples. Which of the two classifiers might yield the better (lower) score? Provide a brief justification.
The SVM would probably get a better score. Both classifiers have the same complexity penalty but SVM would better optimize the training error resulting in a lower (or equal) overall score.