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Weierstrass and Approximation Theory
"... We discuss and examine Weierstrass' main contributions to approximation theory. ..."
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Cited by 190 (9 self)
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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 ..."
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Cited by 170 (11 self)
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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 Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a
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 ..."
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Cited by 9 (2 self)
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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
The space complexity of approximating the frequency moments
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1996
"... The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, ..."
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Cited by 855 (12 self)
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The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly
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 ..."
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Cited by 538 (29 self)
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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
APPROXIMATION THEORY AND APPROXIMATION PRACTICE
"... — the constructive approximation of functions. ..."
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 ..."
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Cited by 916 (8 self)
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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
Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality
, 1998
"... The nearest neighbor problem is the following: Given a set of n points P = fp 1 ; : : : ; png in some metric space X, preprocess P so as to efficiently answer queries which require finding the point in P closest to a query point q 2 X. We focus on the particularly interesting case of the ddimens ..."
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Cited by 1017 (40 self)
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dimensional Euclidean space where X = ! d under some l p norm. Despite decades of effort, the current solutions are far from satisfactory; in fact, for large d, in theory or in practice, they provide little improvement over the bruteforce algorithm which compares the query point to each data point. Of late
Results 1  10
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