Results 1  10
of
21,300
Weierstrass and Approximation Theory
"... We discuss and examine Weierstrass' main contributions to approximation theory. ..."
Abstract

Cited by 189 (7 self)
 Add to MetaCart
We discuss and examine Weierstrass' main contributions to approximation theory.
Approximation Theory of Output Statistics
 IEEE Trans. Inform. Theory
, 1993
"... AbstractGiven a channel and an input process, the minimum randomness of those input processes whose output statistics approximate the original output statistics with arbitrary accuracy is studied. The notion of resolvability of a channel, defined as the number of random bits required per channel us ..."
Abstract

Cited by 171 (11 self)
 Add to MetaCart
AbstractGiven a channel and an input process, the minimum randomness of those input processes whose output statistics approximate the original output statistics with arbitrary accuracy is studied. The notion of resolvability of a channel, defined as the number of random bits required per channel
Approximate objects and approximate theories
 KR2000: Principles of Knowledge Representation and Reasoning,Proceedings of the Seventh International conference
, 2000
"... We propose to extend the ontology of logical AI to include approximate objects, approximate predicates and approximate theories. Besides the ontology we treat the relations among different approximate theories of the same phenomena. Approximate predicates can’t have complete ifandonlyif definitio ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
We propose to extend the ontology of logical AI to include approximate objects, approximate predicates and approximate theories. Besides the ontology we treat the relations among different approximate theories of the same phenomena. Approximate predicates can’t have complete if
Determining the Number of Factors in Approximate Factor Models
, 2000
"... In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors c ..."
Abstract

Cited by 561 (30 self)
 Add to MetaCart
In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors
Greed is Good: Algorithmic Results for Sparse Approximation
, 2004
"... This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal representa ..."
Abstract

Cited by 916 (9 self)
 Add to MetaCart
This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
Abstract

Cited by 585 (13 self)
 Add to MetaCart
Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems
Large N field theories, string theory and gravity
, 2001
"... We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Antide Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evide ..."
Abstract

Cited by 1443 (45 self)
 Add to MetaCart
and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions, but we discuss also field
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
Abstract

Cited by 907 (36 self)
 Add to MetaCart
. In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating
Density in Approximation Theory
, 2005
"... Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the possibility of approximation. Is the given family of functions from which we plan to approximate dense in the ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the possibility of approximation. Is the given family of functions from which we plan to approximate dense
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
Abstract

Cited by 475 (67 self)
 Add to MetaCart
the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
Results 1  10
of
21,300