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要旨:
In prior papers, beginning with the seminal work by Freivalds et al. 1995, the
notion of 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 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 robust
learning (closure of learning under certain classes of operators). Various
degrees of epitomizing sets are 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 very strong epitomizers for a multitude of learning criteria.
These strong epitomizers are so-called self-learning sets, previously applied
by Case & Koetzing, 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!
