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Numerical solution of saddle point problems
 ACTA NUMERICA
, 2005
"... Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has b ..."
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Cited by 178 (27 self)
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Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for solving this type of systems. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.
Regression Models for Ordinal Data: A Machine Learning Approach
, 1999
"... In contrast to the standard machine learning tasks of classification and metric regression we investigate the problem of predicting variables of ordinal scale, a setting referred to as ordinal regression. The task of ordinal regression arises frequently in the social sciences and in information retr ..."
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Cited by 15 (3 self)
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In contrast to the standard machine learning tasks of classification and metric regression we investigate the problem of predicting variables of ordinal scale, a setting referred to as ordinal regression. The task of ordinal regression arises frequently in the social sciences and in information retrieval where human preferences play a major role. Also many multiclass problems are really problems of ordinal regression due to an ordering of the classes. Although the problem is rather novel to the Machine Learning Community it has been widely considered in Statistics before. All the statistical methods rely on a probability model of a latent (unobserved) variable and on the condition of stochastic ordering. In this paper we develop a distribution independent formulation of the problem and give uniform bounds for our risk functional. The main difference to classification is the restriction that the mapping of objects to ranks must be transitive and asymmetric. Combining our theoretical framework with results from measurement theory we present an approach that is based on a mapping from objects to scalar utility values and thus guarantees transitivity and asymmetry. Applying the principle of Structural Risk Minimization as employed in Support Vector Machines we derive a new learning algorithm based on large margin rank boundaries for the task of ordinal regression. Our method is easily extended to nonlinear utility functions. We give experimental results for an Information Retrieval task of learning the order of documents with respect to an initial query. Moreover, we show that our algorithm outperforms more naive approaches to ordinal regression such as Support Vector Classification and Support Vector Regression in the case of more than two ranks.
Placing Registration Marks
 In Proceedings of 1993 IEEE International Conference on Robotics and Automation
, 1993
"... In industrial assembly, a registration mark can be placed on parts to aid a computer vision system in determining the position and orientation (pose) of parts. However, when sensor noise and limits on resolution introduce errors in the measured location of the registration mark, these errors can pro ..."
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Cited by 14 (2 self)
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In industrial assembly, a registration mark can be placed on parts to aid a computer vision system in determining the position and orientation (pose) of parts. However, when sensor noise and limits on resolution introduce errors in the measured location of the registration mark, these errors can propagate into the measurement of part pose. In this paper we define the Registration Mark Problem: given an nsided rigid planar polygonal part and a set of k poses for the part, locate a point on the surface of the part that maximizes the minimum distance between transformed points. A registration mark at this point will be maximally robust to sensor imperfections. We give an O(n log n + k 4 log k log k) time algorithm to solve this planar problem using a result from Schwartz and Sharir [22] and demonstrate the algorithm using a commercial vision system. Our results extend to classes of curved planar parts and polyhedral parts. 1 Introduction Determining the precise position and orient...
Compression, Information Theory and Grammars: A Unified Approach
 ACM Trans. on Information Systems
, 1990
"... : Text compression is of considerable theoretical and practical interest. It is, for example, becoming increasingly important for satisfying the requirements of fitting a large database onto a single CDROM. Many of the compression techniques discussed in the literature are model based. We here prop ..."
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Cited by 9 (5 self)
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: Text compression is of considerable theoretical and practical interest. It is, for example, becoming increasingly important for satisfying the requirements of fitting a large database onto a single CDROM. Many of the compression techniques discussed in the literature are model based. We here propose the notion of a formal grammar as a flexible model of text generation that encompasses most of the models offered before as well as, in principle, extending the possibility of compression to a much more general class of languages. Assuming a general model of text generation, a derivation is given of the well known Shannon entropy formula, making possible a theory of information based upon text representation rather than on communication. The ideas are shown to apply to a number of commonly used text models. Finally, we focus on a Markov model of text generation, suggest an information theoretic measure of similarity between two probability distributions, and develop a clustering algorith...
CIXL2: A Crossover Operator for Evolutionary Algorithms Based on Population Features
 Journal of Artificial Intelligence Research (JAIR
, 2005
"... In this paper we propose a crossover operator for evolutionary algorithms with real values that is based on the statistical theory of population distributions. The operator is based on the theoretical distribution of the values of the genes of the best individuals in the population. The proposed ope ..."
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Cited by 7 (2 self)
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In this paper we propose a crossover operator for evolutionary algorithms with real values that is based on the statistical theory of population distributions. The operator is based on the theoretical distribution of the values of the genes of the best individuals in the population. The proposed operator takes into account the localization and dispersion features of the best individuals of the population with the objective that these features would be inherited by the offspring. Our aim is the optimization of the balance between exploration and exploitation in the search process. In order to test the efficiency and robustness of this crossover, we have used a set of functions to be optimized with regard to different criteria, such as, multimodality, separability, regularity and epistasis. With this set of functions we can extract conclusions in function of the problem at hand. We analyze the results using ANOVA and multiple comparison statistical tests. As an example of how our crossover can be used to solve artificial intelligence problems, we have applied the proposed model to the problem of obtaining the weight of each network in a ensemble of neural networks. The results obtained are above the performance of standard methods. 1.
Controlling Networks with Collaborative Nets
, 2000
"... Networks, such as the electric grid, are operated by sets of agents that are heterogeneous, local and distributed. (By "heterogeneous" we mean that the agents can range from simple devices, like relays, to very intelligent entities, like committees of humans. By "local and distributed" we mean th ..."
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Cited by 6 (4 self)
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Networks, such as the electric grid, are operated by sets of agents that are heterogeneous, local and distributed. (By "heterogeneous" we mean that the agents can range from simple devices, like relays, to very intelligent entities, like committees of humans. By "local and distributed" we mean that each agent can sense only a few of the network's state variables and influence only a few of its control variables.) We are concerned with two issues: the quality and speed of decisionmaking by heterogeneous, local and distributed agents. For quality, our standard of comparison is an ideal, centralized agent, which senses the state of the entire network and makes globally optimal decisions. (Of course, such a centralized agent is impractical for large networks.
Nearly Optimal Competitive Online Replacement
"... This paper studies the following online replacement problem. There is a real function f(t), called the flow rate, defined over a finite time horizon [0; T ]. It is known that m f(t) M for some reals 0 m ! M . At time 0 an online player starts to pay money at the rate f(0). At each time 0 ! t T ..."
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Cited by 5 (2 self)
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This paper studies the following online replacement problem. There is a real function f(t), called the flow rate, defined over a finite time horizon [0; T ]. It is known that m f(t) M for some reals 0 m ! M . At time 0 an online player starts to pay money at the rate f(0). At each time 0 ! t T the player may changeover and continue paying money at the rate f(t). The complication is that each such changeover incurs some fixed penalty. The player is called online as at each time t the player knows f only over the time interval [0; t]. The goal of the player is to minimize the total cost comprised of cumulative payment flow plus changeover costs. This formulation of the replacement problem has various interesting applications among which are: equipment replacement, supplier replacement, the menu cost problem and mortgage refinancing.
Textbook notes of herd management: Dynamic programming and Markov decision processes
, 1996
"... ..."
Techniques For Solving General KKT Systems
, 2000
"... We consider techniques for solving general KKT systems. In particular, we address the situation of a singular (1,1) block, and focus on ways to eliminate the singularity, either by reducing the system size or by employing an augmented Lagrangian technique. The latter is a parameterdependent approac ..."
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Cited by 3 (2 self)
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We consider techniques for solving general KKT systems. In particular, we address the situation of a singular (1,1) block, and focus on ways to eliminate the singularity, either by reducing the system size or by employing an augmented Lagrangian technique. The latter is a parameterdependent approach. We provide some observations regarding the condition number, the spectrum, and a sensible choice of the parameter. The analysis demonstrates how the case of a singular (1,1) block is different from other cases. We also present a few general results regarding inversion of certain KKT matrices, the spectra of their associated Schur complements, and error estimates for regularized systems. Finally, we present a parameterdependent preconditioning technique, and discuss its spectral properties.