منابع مشابه
On the VC-dimension of uniform hypergraphs
Let F be a k-uniform hypergraph on [n] where k − 1 is a power of some prime p and n ≥ n0(k). Our main result says that if |F | > ( n k−1 ) − logp n + k!kk , then there exists E0 ∈ F such that {E ∩ E0 : E ∈ F} contains all subsets of E0. This improves a longstanding bound of ( n k−1 ) due to Frankl and Pach [7].
متن کاملHitting Set for Hypergraphs of Low VC-dimension
We study the complexity of the Hitting Set problem in set systems (hypergraphs) that avoid certain sub-structures. In particular, we characterize the classical and parameterized complexity of the problem when the Vapnik-Chervonenkis dimension (VC-dimension) of the input is small. VC-dimension is a natural measure of complexity of set systems. Several tractable instances of Hitting Set with a ge...
متن کاملOn the Eeective Vc Dimension
The very idea of an \EEective Vapnik Chervonenkis (VC) dimension" (Vapnik, Levin and Le Cun, 1993) relies on the hypothesis that the relation between the generalization error and the number of training examples can be expressed by a formula algebraically similar to the VC bound. This hypothesis calls for a serious discussion since the traditional VC bound widely overestimates the generalization...
متن کاملOn the Approximability of Partial VC Dimension
We introduce the problem Partial VC Dimension that asks, given a hypergraph H = (X,E) and integers k and l, whether one can select a set C ⊆ X of k vertices of H such that the set {e ∩ C, e ∈ E} of distinct hyperedge-intersections with C has size at least l. The sets e ∩ C define equivalence classes over E. Partial VC Dimension is a generalization of VC Dimension, which corresponds to the case ...
متن کاملVC dimension of ellipsoids
We will establish that the vc dimension of the class of d-dimensional ellipsoids is (d +3d)/2, and that maximum likelihood estimate with N -component d-dimensional Gaussian mixture models induces a geometric class having vc dimension at least N(d + 3d)/2.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2006
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-006-0025-4