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- W2026465556 abstract "The problem of learning an integer lattice of ${bf Z}^k $ in an on-line fashion is considered. That is, the learning algorithm is given a sequence of k-tuples of integers and predicts for each tuple in the sequence whether it lies in a hidden target lattice of ${bf Z}^k $. The goal of the algorithm is to minimize the number of prediction mistakes. An efficient learning algorithm with an absolute mistake bound of $k + lfloor klog (nsqrt k ) rfloor $ is given, where n is the maximum component of any tuple seen. It is shown that this bound is approximately a $log log n$ factor larger than the lower bound on the worst case number of mistakes given by the VC dimension of lattices that are restricted to ${ - n, cdots ,0, cdots ,n }^k $. This algorithm is used to learn rational lattices, cosets of lattices, an on-line word problem for abelian groups, and a subclass of the commutative regular languages. Furthermore, by adapting the results of [D. Helmbold, R. Sloan, and M. K. Warmuth, Machine Learning..." @default.
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- W2026465556 date "1990-07-01" @default.
- W2026465556 modified "2023-09-23" @default.
- W2026465556 title "Learning integer lattices" @default.
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- W2026465556 doi "https://doi.org/10.5555/92571.92655" @default.
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