  For a wide variety of regularization methods, algorithms computing the entire
solution path have been developed recently. Solution path algorithms do not
only compute the solution for one particular value of the regularization
parameter but the entire path of solutions, making the selection of an optimal
parameter much easier. Most of the currently used algorithms are not robust in
the sense that they cannot deal with general or degenerate input. Here we
present a new robust, generic method for parametric quadratic programming. Our
algorithm directly applies to nearly all machine learning applications, where
so far every application required its own different algorithm.
  We illustrate the usefulness of our method by applying it to a very low rank
problem which could not be solved by existing path tracking methods, namely to
compute part-worth values in choice based conjoint analysis, a popular
technique from market research to estimate consumers preferences on a class of
parameterized options.
