منابع مشابه
Some new maximum VC classes
Set systems of finite VC dimension are frequently used in applications relating to machine learning theory and statistics. Two simple types of VC classes which have been widely studied are the maximum classes (those which are extremal with respect to Sauer’s lemma) and so-called Dudley classes, which arise as sets of positivity for linearly parameterized functions. These two types of VC class w...
متن کاملBounding Embeddings of VC Classes into Maximum Classes
One of the earliest conjectures in computational learning theory—the Sample Compression conjecture—asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes—those that possess maximum cardinality for their VC dimension. The most promising approach to positively resolving ...
متن کاملComplexity of Constrained VC-Classes
Let F be a class of n-dimensional binary vectors, i.e., functions f : X → {0, 1} where X = [n] ≡ {1, . . . , n} with a VC-dimension V C(F) = d. The classical result of Sauer says that the complexity of F is bounded as |F| ≤ d i=0 n i ≡ S(d, n). How does the complexity decrease as one further constrains the subset of allowed functions in F ? The paper defines a constraining parameter for binary ...
متن کاملA Note on Teaching for VC Classes
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, ...
متن کاملOn the complexity of constrained VC-classes
Sauer’s Lemma is extended to classes HN of binary-valued functions h on [n] = {1, . . . , n} which have a margin less than or equal to N on all x ∈ [n] with h(x) = 1, where the margin μh(x) of h at x ∈ [n] is defined as the largest non-negative integer a such that h is constant on the interval Ia(x) = [x− a, x+ a] ⊆ [n]. Estimates are obtained for the cardinality of classes of binary valued fun...
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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2014
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2014.01.006