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5,532
On the Size of HigherDimensional Triangulations
, 2005
"... I show that there are sets of n points in three dimensions, in general position, such that any triangulation of these points has only O(n 5/3) simplices. This is the first nontrivial upper bound on the MinMax triangulation problem posed by Edelsbrunner, Preparata and West in 1990: What is the mini ..."
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Cited by 1 (0 self)
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I show that there are sets of n points in three dimensions, in general position, such that any triangulation of these points has only O(n 5/3) simplices. This is the first nontrivial upper bound on the MinMax triangulation problem posed by Edelsbrunner, Preparata and West in 1990: What
Convexity, Classification, and Risk Bounds
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2003
"... Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 01 loss function. The convexity makes these algorithms computationally efficien ..."
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Cited by 181 (15 self)
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nonnegative surrogate loss function. We show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function: that it satisfy a pointwise form of Fisher consistency for classification. The relationship is based on a simple variational
Randomized Competitive Analysis for TwoServer Problems
"... Abstract. We prove that there exits a randomized online algorithm for the 2server 3point problem whose expected competitive ratio is at most 1.5897. This is the first nontrivial upper bound for randomized kserver algorithms in a general metric space whose competitive ratio is well below the corre ..."
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Abstract. We prove that there exits a randomized online algorithm for the 2server 3point problem whose expected competitive ratio is at most 1.5897. This is the first nontrivial upper bound for randomized kserver algorithms in a general metric space whose competitive ratio is well below
unknown title
"... We prove that any language in ACC can be approximately computed by twolevel circuits of size 2('Ogn)', with a symmetricfunction gate at the top and only AND gates on the first level. This implies that any language in ACC can be recognized by depth3 threshold circuits of size 2('&a ..."
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;"gn)'. This result gives the first nontrivial upper bound on the computing power of ACC circuits. 1
A dynamic programming solution to the nqueens problem
, 1992
"... The nqueens problem is to determine in how many ways n queens may be placed on an nbyn chessboard so that no two queens attack each other under the rules of chess. We describe a simple O ( f(n)8”) solution to this problem that is based on dynamic programming, where f(n) is a loworder polynomial. ..."
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Cited by 3 (0 self)
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. This appears to be the first nontrivial upper bound for the problem.
Languages That Capture Complexity Classes
 SIAM Journal of Computing
, 1987
"... this paper a series of languages adequate for expressing exactly those properties checkable in a series of computational complexity classes. For example, we show that a property of graphs (respectively groups, binary strings, etc.) is in polynomial time if and only if it is expressible in the first ..."
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Cited by 245 (21 self)
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more than machine dependent issues. Furthermore a whole new approach is suggested. Upper bounds (algorithms) can be produced by expressing the property of interest in one of our languages. Lower bounds may be demonstrated by showing that such expression is impossible.
Efficient SVM training using lowrank kernel representations
 Journal of Machine Learning Research
, 2001
"... SVM training is a convex optimization problem which scales with the training set size rather than the feature space dimension. While this is usually considered to be a desired quality, in large scale problems it may cause training to be impractical. The common techniques to handle this difficulty ba ..."
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Cited by 240 (3 self)
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method (IPM) in terms of storage requirements as well as computational complexity. We then suggest an efficient use of a known factorization technique to approximate a given kernel matrix by a low rank matrix, which in turn will be used to feed the optimizer. Finally, we derive an upper bound
Robustness of simple monetary policy rules under model uncertainty
 MONETARY POLICY RULES
, 1999
"... In this paper, we investigate the properties of alternative monetary policy rules using four structural macroeconometric models: the FuhrerMoore model, Taylor’s MultiCountry Model, the MSR model of Orphanides and Wieland, and the FRB staff model. All four models incorporate the assumptions of rat ..."
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Cited by 240 (31 self)
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to an upper bound on nominal interest rate volatility. Our analysis provides strong support for rules in which the firstdifference of the federal funds rate responds to the current output gap and the deviation of the oneyear average inflation rate from a specified target. In all four models, first
Sparse multinomial logistic regression: fast algorithms and generalization bounds
 IEEE Trans. on Pattern Analysis and Machine Intelligence
"... Abstract—Recently developed methods for learning sparse classifiers are among the stateoftheart in supervised learning. These methods learn classifiers that incorporate weighted sums of basis functions with sparsitypromoting priors encouraging the weight estimates to be either significantly larg ..."
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Cited by 190 (1 self)
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and the feature dimensionality, making them applicable even to large data sets in highdimensional feature spaces. To the best of our knowledge, these are the first algorithms to perform exact multinomial logistic regression with a sparsitypromoting prior. Third, we show how nontrivial generalization bounds can
On the bichromatic kset problem
 Proc. 19th ACMSIAM Sympos. Discrete Algorithms
, 2008
"... Abstract We study a bichromatic version of the wellknown kset problem: given two sets R and B of points of total size n and an integer k, how many subsets of the form (R " h) [ (B n h) can have size exactly k over all halfspaces h? In the dual, the problem is asymptotically equivalent to ..."
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Cited by 5 (1 self)
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to determining the worstcase combinatorial complexity of the klevel in an arrangement of n halfspaces. Disproving an earlier conjecture by Linhart (1993), we present the first nontrivial upper bound for all k o / n in two dimensions: O(nk
Results 11  20
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5,532