N entries containing the bounds for each dimension
Dimension-adaptive bounds on compressive FLD Classification
... target dimension grows only as the log of the number of classes and is not adversely affected by the number of projected data ...these bounds depend on the dimension- ality d of the original data ...
15
Dimension-Free Error Bounds from Random Projections
... Learning from high dimensional data is challenging in gen- eral – however, often the data is not truly high dimensional in the sense that it may have some hidden low complex- ity geometry. We give new, user-friendly ...
8
Dimension-free Concentration Bounds on Hankel Matrices for Spectral Learning
... our dimension-free bounds are quite tight (except the subexponential bound for the prefix variant) and significantly more accurate than the bounds provided by classically used ...
33
Tight Lower Bounds on the VC-dimension of Geometric Set Systems
... Its importance derives from the fact that it is the set system underlying the construction of cuttings via random sampling (see Chazelle and Friedman 1990 as well as the recent survey of Mustafa and Varadarajan 2017, to ...
8
Dimension-free Concentration Bounds on Hankel Matrices for Spectral Learning
... these dimension-free inequalities is that the spectral learning algorithm is consistent, even if the whole empirical Hankel matrix is used, suggesting that the choice of relevant sets of rows and columns is maybe ...
32
Bounds on the domination number and the metric dimension of co normal product of graphs
... give bounds on the domination number of the co-normal product of ...give bounds on the metric dimension of the co-normal product of ...metric dimension of some families of ...
12
Rigorous effective bounds on the Hausdorff dimension of continued fraction Cantor sets : a hundred decimal digits for the dimension of E2
... T n (z) = 1/(z + n), n ∈ A, are contained in ...those bounds derived from Banach space ...T n (z) = 1/(n + z), n ∈ A, prompts the introduction of the contraction ratio, ...
30
Nearly-tight VC-dimension and Pseudodimension Bounds for Piecewise Linear Neural Networks
... upper bounds were O(W 2 ) (see Goldberg and Jerrum, 1995, Section ...upper bounds (except the O(W 2 ) upper bound of Goldberg and Jerrum) using a unified technique, and gives a slightly more refined picture ...
17
Nonlinear Estimators and Tail Bounds for Dimension Reduction in l1 Using Cauchy Random Projections
... In this paper, we study three types of nonlinear estimators: the sample median estimators, the geometric mean estimators, and the maximum likelihood estimators (MLE). The sample median and the geometric mean estimators ...
36
ABSTRACT In this paper, we present some bounds for metric dimension of a graph G in terms of order and
... 1 SSM College of Engineering and Technology, Department of Mathematics, Dindigul, Tamil nadu, India. 2 DMI-St.Eugene University, Department of Science and Humanities, Chibombo, Zambia. Corresponding Author: K.Renganathan ...
7
Bounds on the hausdorff dimension of a renormalisation map arising from an excitable reaction-diffusion system on a fractal lattice
... Anthony J. Mulholland 1 Department of Mathematics, University of Strathclyde, Glasgow, U.K. Abstract A renormalisation approach to investigate travelling wave solutions of an excitable reaction- diffusion system on a ...
20
Bounds on the Metric Dimension of Graphs
... metric dimension, rather than location ...metric dimension or, more simply, the dimension dim (G) of a connected graph G is the cardinality of a minimum resolving ...
7
Bounds on the Hausdorff dimension of random attractors
... Hausdorff dimension of the random ...Hausdorff dimension brings us closer to the true value of the Hausdorff ...Hausdorff dimension means firstly that the dimension is finite, but the true ...
118
Diophantine approximation on manifolds and lower bounds for Hausdorff dimension
... R n of interest are of dependent variables, which reflects the fact that y ∈ M, introduces major difficulties in attempting to describe the measure theoretic structure of S n (ψ) ∩ ...R n is called ...
21
Randomized Online PCA Algorithms with Regret Bounds that are Logarithmic in the Dimension
... regret bounds against the best fixed subspace chosen offline (based on the entire data ...for each of the s ...regret bounds against the best partition of size s (see, ...regret bounds grow ...
34
RSA Cryptanalysis with Increased Bounds on the Secret Exponent using Less Lattice Dimension
... Given that 9 MSBs of p will be known with success probability 1%, this requires a cluster of 2 13 machines for little more than a year. – Now we consider δ = 0.3 for m = 11, t = 5 following Table 4. Here the lattice ...
14
On the Calculation of Uncertainty Statistics with Error Bounds for CFD Calculations Containing Random Parameters and Fields
... for each dimension, examine integrand data to determine ...a dimension, use hierarchical multi-level Clenshaw-Curtis or Gauss-Patterson ...that dimension using data at the Clenshaw-Curtis or ...
40
Lexical Annotation for Multi-word Entries Containing Nominalizations
... whose entries capture the relationship of the nominaliza- tion with its associated ...some entries for nominalizations and their co-occurring verbs. These entries are much more complex than NOMLEX ...
6
New upper bounds of n!
... √ 2πn n n = 1. (2) This formula provides an extremely accurate approximation of n! for large values of n. The first proofs of Stirling ’ s formula was given by De Moivre (1730) [1] and ...
9
DIMENSION CHANGES IN A SOLID CONTAINING ANISOTROPIC DEFECTS
... We have shown that the anisotropic changes in external dimensions of a solid due to the presence of aligned anisotropic defects can be written as simple functio[r] ...
6