An Equivalence Between Sparse Approximation and Support Vector Machines

In the first part of this paper we show a similarity between the principle of Structural Risk Minimization Principle (SRM) (Vapnik, 1982) and the idea of Sparse Approximation, as defined in (Chen, Donoho and Saunders, 1995) and Olshausen and Field (1996). Then we focus on two specific (approximate) implementations of SRM and Sparse Approximation, which have been used to solve the problem of function approximation. For SRM we consider the Support Vector Machine technique proposed by V. Vapnik and his team at AT&T Bell Labs, and for Sparse Approximation we consider a modification of the Basis Pursuit De-Noising algorithm proposed by Chen, Donoho and Saunders (1995). We show that, under certain conditions, these two techniques are equivalent: they give the same solution and they require the solution of the same quadratic programming problem.

Facilitation of the equivalence - equivalence responding

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Testing for multigroup equivalence of a measuring instrument : a walk through the process

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The influence of the parents??? educational level and participants??? age in the derivation of equivalence-equivalence

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Equivalence of truncated count mixture distributions and mixtures of truncated count distributions

This article is about modeling count data with zero truncation. A parametric count density family is considered. The truncated mixture of densities from this family is different from the mixture of truncated densities from the same family. Whereas the former model is more natural to formulate and to interpret, the latter model is theoretically easier to treat. It is shown that for any mixing distribution leading to a truncated mixture, a (usually different) mixing distribution can be found so. that the associated mixture of truncated densities equals the truncated mixture, and vice versa. This implies that the likelihood surfaces for both situations agree, and in this sense both models are equivalent. Zero-truncated count data models are used frequently in the capture-recapture setting to estimate population size, and it can be shown that the two Horvitz-Thompson estimators, associated with the two models, agree. In particular, it is possible to achieve strong results for mixtures of truncated Poisson densities, including reliable, global construction of the unique NPMLE (nonparametric maximum likelihood estimator) of the mixing distribution, implying a unique estimator for the population size. The benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities, which is less appealing for the practitioner but theoretically easier. Mixtures of truncated count densities form a convex linear model, for which a developed theory exists, including global maximum likelihood theory as well as algorithmic approaches. Once the problem has been solved in this class, it might readily be transformed back to the original problem by means of an explicitly given mapping. Applications of these ideas are given, particularly in the case of the truncated Poisson family.

Maximizing revenue in Grid markets using an economically enhanced resource manager

Traditional resource management has had as its main objective the optimization of throughput, based on parameters such as CPU, memory, and network bandwidth. With the appearance of Grid markets, new variables that determine economic expenditure, benefit and opportunity must be taken into account. The Self-organizing ICT Resource Management (SORMA) project aims at allowing resource owners and consumers to exploit market mechanisms to sell and buy resources across the Grid. SORMA's motivation is to achieve efficient resource utilization by maximizing revenue for resource providers and minimizing the cost of resource consumption within a market environment. An overriding factor in Grid markets is the need to ensure that the desired quality of service levels meet the expectations of market participants. This paper explains the proposed use of an economically enhanced resource manager (EERM) for resource provisioning based on economic models. In particular, this paper describes techniques used by the EERM to support revenue maximization across multiple service level agreements and provides an application scenario to demonstrate its usefulness and effectiveness. Copyright © 2008 John Wiley & Sons, Ltd.