Physical Sciences and Mathematics Commons^™

Intrinsic Complexity Of Learning Geometrical Concepts From Positive Data, Sanjay Jain, Efim Kinber

School of Computer Science & Engineering Faculty Publications

Intrinsic complexity is used to measure the complexity of learning areas limited by broken-straight lines (called open semi-hulls) and intersections of such areas. Any strategy learning such geometrical concepts can be viewed as a sequence of primitive basic strategies. Thus, the length of such a sequence together with the complexities of the primitive strategies used can be regarded as the complexity of learning the concepts in question. We obtained the best possible lower and upper bounds on learning open semi-hulls, as well as matching upper and lower bounds on the complexity of learning intersections of such areas. Surprisingly, upper …