Abstract
We study the problem of proper learning of unions of two discretized axis-parallel rectangles over the domain {0,n−1}d in the on-line model with equivalence and membership queries. An obvious approach to this problem would use two equivalence queries to find one example in each of the two rectangles contained in the target concept and then use membership queries to find end points of the rectangles. However, there is one substantial difficulty: For any two end points, how to decide whether they belong to the same rectangle? In this paper, we develop some strategies to overcome the above difficulties and construct an algorithm that properly learns unions of two rectangles over the domain {0,n−1}d with at most two equivalence queries and at most (11d+2) log n+d+3 membership queries. We also show that this algorithm is optimal in terms of query complexity
The author was supported by NSF grants CCR-9103055 and CCR-9400229.
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© 1995 Springer-Verlag Berlin Heidelberg
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Chen, Z. (1995). An optimal algorithm for proper learning of unions of two rectangles with queries. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030848
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DOI: https://doi.org/10.1007/BFb0030848
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