On learning discretized geometric concepts
Bshouty, N.H.; Zhixiang Chen; Homer, S.
Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on
Volume , Issue , 20-22 Nov 1994 Page(s):54 - 63
Digital Object Identifier 10.1109/SFCS.1994.365705
Summary:We present a polynomial time online learning algorithm that learns
any discretized geometric concept generated from any number of
halfspaces with any number of known (to the learner) slopes in a
constant dimensional space. In particular, our algorithm learns (from
equivalence queries only) unions of discretized axis-parallel rectangles
in a constant dimensional space in polynomial time. The algorithm also
runs in polynomial time in l if the teacher lies on l counterexamples.
We then show a PAC-learning algorithm for the above discretized
geometric concept when the example oracle lies on the labels of the
examples with a fixed probability p⩽½-1/r that runs in
polynomial time also with r. We use these methods, as well as a bounded
version of the finite injury priority method, to construct algorithms
for learning several classes of rectangles. In particular we design
efficient algorithms for learning several classes of unions of
discretized axis-parallel rectangles in either arbitrary dimensional
spaces or constant dimensional spaces
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