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Results 1 - 10
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17,669
Approximating bounded occurrence ordering CSPs
"... A theorem of Hastad shows that for every constraint satisfaction problem (CSP) over a fixed size domain, instances where each variable appears in at most O(1) constraints admit a non-trivial approximation algorithm, in the sense that one can beat (by an additive constant) the approximation ratio ach ..."
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Cited by 2 (1 self)
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k can be approximated beyond the random ordering threshold 1/k! on bounded occurrence instances. We prove a similar result for all ordering CSPs, with arbitrary payoff functions, whose constraints have arity at most 3. Our method is based on working with a carefully defined Boolean CSP that serves
Approximation bounds for quadratic optimization with homogeneous quadratic constraints
- SIAM J. Optim
, 2007
"... Abstract. We consider the NP-hard problem of finding a minimum norm vector in n-dimensional real or complex Euclidean space, subject to m concave homogeneous quadratic constraints. We show that a semidefinite programming (SDP) relaxation for this nonconvex quadratically constrained quadratic program ..."
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Cited by 49 (24 self)
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program (QP) provides an O(m 2) approximation in the real case and an O(m) approximation in the complex case. Moreover, we show that these bounds are tight up to a constant factor. When the Hessian of each constraint function is of rank 1 (namely, outer products of some given so-called steering vectors
Approximation Bounds for Smooth Functions in by Neural and Mixture Networks
"... Abstract—We consider the approximation of smooth multivari-ate functions in C(IRd) by feedforward neural networks with a single hidden layer of nonlinear ridge functions. Under certain assumptions on the smoothness of the functions being approxi-mated and on the activation functions in the neural ne ..."
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network, we present upper bounds on the degree of approximation achieved over the domain IRd, thereby generalizing available results for compact domains. We extend the approximation results to the so-called mixture of expert architecture, which has received considerable attention in recent years, showing
Approximating Bounded Degree Instances of NP-Hard Problems
- Proc. 13th Symp. on Fundamentals of Computation Theory, LNCS 2138
, 2001
"... We present some of the recent results on computational complexity of approximating bounded degree combinatorial optimization problems. In particular, we present the best up to now known explicit nonapproximability bounds on the very small degree optimization problems which are of particular importan ..."
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Cited by 11 (4 self)
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We present some of the recent results on computational complexity of approximating bounded degree combinatorial optimization problems. In particular, we present the best up to now known explicit nonapproximability bounds on the very small degree optimization problems which are of particular
Variational algorithms for approximate Bayesian inference
, 2003
"... The Bayesian framework for machine learning allows for the incorporation of prior knowledge in a coherent way, avoids overfitting problems, and provides a principled basis for selecting between alternative models. Unfortunately the computations required are usually intractable. This thesis presents ..."
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Cited by 440 (9 self)
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a unified variational Bayesian (VB) framework which approximates these computations in models with latent variables using a lower bound on the marginal likelihood. Chapter 1 presents background material on Bayesian inference, graphical models, and propaga-tion algorithms. Chapter 2 forms
Approximation Bound for K-Means clustering of Binary Data
"... We prove that a p-swap search algorithm for the K-means clustering problem has an approximation bound 3 + 2, assuming a binary data set and Euclidean distance. This is tighter than the general bound p “ ” 2. We also present an example resulting in a cost ratio of 3 − ɛ. Thus, our bound is almost sh ..."
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We prove that a p-swap search algorithm for the K-means clustering problem has an approximation bound 3 + 2, assuming a binary data set and Euclidean distance. This is tighter than the general bound p “ ” 2. We also present an example resulting in a cost ratio of 3 − ɛ. Thus, our bound is almost
Approximation Bounds for Minimum Information Loss Microaggregation
, 2009
"... The NP-hard microaggregation problem seeks a partition of data points into groups of minimum specified size k, so as to minimize the sum of the squared euclidean distances of every point to its group’s centroid. One recent heuristic provides an Oðk 3 Þ guarantee for this objective function and an O ..."
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Cited by 1 (1 self)
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and an Oðk 2 Þ guarantee for a version of the problem that seeks to minimize the sum of the distances of the points to its group’s centroid. This paper establishes approximation bounds for another microaggregation heuristic, providing better approximation guarantees of Oðk 2 Þ for the squared distance
1 Approximation bounds for minimum information loss microaggregation
"... The NP-hard microaggregation problem seeks a partition of data points into groups of minimum specified size k, so as to minimize the sum of the squared Euclidean distances of every point to its group’s centroid. One recent heuristic provides an O(k3) guarantee for this objective function and an O(k2 ..."
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(k2) guarantee for a version of the problem that seeks to minimize the sum of the distances of the points to its group’s centroid. This paper establishes approximation bounds for another microaggregation heuristic, providing better approximation guarantees of O(k2) for the squared distance measure
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