5. Parsimonious core methods

There are various ways of introducing parsimony. In particular, it is always possible to directly impose that the solution depends only on a small number of non-zero coefficients. But it is more elegant to formulate criteria to be minimized so that the solution is naturally parsimonious. This is the case of support vector machines (SVMs), which we'll be looking at next.

In the SVM framework, we search in an EHNR $\mathcal{H}$ of kernel k the minimal norm function best discriminating a set of observations of two classes (x _i , y _i ) _{i = 1, n} with $y_i\in \left\{-\mathrm{1,}1\right\}$...