  Given a hypothesis space, the large volume principle by Vladimir Vapnik
prioritizes equivalence classes according to their volume in the hypothesis
space. The volume approximation has hitherto been successfully applied to
binary learning problems. In this paper, we extend it naturally to a more
general definition which can be applied to several transductive problem
settings, such as multi-class, multi-label and serendipitous learning. Even
though the resultant learning method involves a non-convex optimization
problem, the globally optimal solution is almost surely unique and can be
obtained in O(n^3) time. We theoretically provide stability and error analyses
for the proposed method, and then experimentally show that it is promising.
