منابع مشابه
Labeled Compression Schemes for Extremal Classes
It is a long-standing open problem whether there exists a compression scheme whose size is of the order of the VapnikChervonienkis (VC) dimension d. Recently compression schemes of size exponential in d have been found for any concept class of VC dimension d. Previously, compression schemes of size d have been given for maximum classes, which are special concept classes whose size equals an upp...
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Maximum classes of domain size n and VC dimension d have ( n ≤d ) concepts, and this is an upper bound on the size of any such class. We give a compression scheme for any maximum class that represents each concept by a subset of up to d unlabeled domain points and has the property that for any sample of a concept in the class, the representative of exactly one of the concepts consistent with th...
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This paper studies labeled sample compression for multi-label concept classes. For a specific extension of the notion of VC-dimension to multi-label classes, we prove that every maximum multilabel class of dimension d has a sample compression scheme in which every sample is compressed to a subset of size at most d. We further show that every multi-label class of dimension 1 has a sample compres...
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This paper is concerned with various combinatorial parameters of classes that can be learned from a small set of examples. We show that the recursive teaching dimension, recently introduced by Zilles et al. (2008), is strongly connected to known complexity notions in machine learning, e.g., the self-directed learning complexity and the VC-dimension. To the best of our knowledge these are the fi...
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where we use c |X to denote the projection of c on X. The teaching dimension of C is the smallest number t such that every c ∈ C has a teaching set of size no more than t [GK95]. However, teaching dimension does not always capture the cooperation in teaching and learning, and the notion of recursive teaching dimension has been introduced and studied extensively in the literature [Kuh99, DSZ10, ...
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ژورنال
عنوان ژورنال: Journal of the ACM
سال: 2016
ISSN: 0004-5411,1557-735X
DOI: 10.1145/2890490