Measuring Learning Complexity with Criteria Epitomizers

John Case (1) , Timo Kötzing (2)

1 CIS - Department of Computer and Information Sciences [Newark]
2 MPII - Max-Planck-Institut für Informatik

In prior papers, beginning with the seminal work by Freivalds et~al.~1995, the notion of \emph{intrinsic complexity} is used to analyze the learning complexity of sets of functions in a Gold-style learning setting. Herein are pointed out some weaknesses of this notion. Offered is an alternative based on \emph{epitomizing sets} of functions -- sets, which are learnable under a given learning criterion, but not under other criteria which are not at least as powerful. To capture the idea of epitomizing sets, new reducibility notions are given based on \emph{robust learning} (closure of learning under certain classes of operators). Various degrees of epitomizing sets are \emph{characterized} as the sets complete with respect to corresponding reducibility notions! These characterizations also provide an easy method for showing sets to be epitomizers, and they are, then, employed to prove several sets to be epitomizing. Furthermore, a scheme is provided to generate easily \emph{very strong} epitomizers for a multitude of learning criteria. These strong epitomizers are so-called \emph{self-learning} sets, previously applied by Case and Kötzing, 2010. These strong epitomizers can be generated and employed in a myriad of settings to witness the strict separation in learning power between the criteria so epitomized and other not as powerful criteria!

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

John Case, Timo Kötzing. Measuring Learning Complexity with Criteria Epitomizers. Symposium on Theoretical Aspects of Computer Science (STACS2011), Mar 2011, Dortmund, Germany. pp.320-331. ⟨hal-00573633⟩