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Learning to predict by the methods of temporal differences
 MACHINE LEARNING
, 1988
"... This article introduces a class of incremental learning procedures specialized for prediction – that is, for using past experience with an incompletely known system to predict its future behavior. Whereas conventional predictionlearning methods assign credit by means of the difference between predi ..."
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Cited by 1433 (55 self)
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This article introduces a class of incremental learning procedures specialized for prediction – that is, for using past experience with an incompletely known system to predict its future behavior. Whereas conventional predictionlearning methods assign credit by means of the difference between predicted and actual outcomes, the new methods assign credit by means of the difference between temporally successive predictions. Although such temporaldifference methods have been used in Samuel's checker player, Holland's bucket brigade, and the author's Adaptive Heuristic Critic, they have remained poorly understood. Here we prove their convergence and optimality for special cases and relate them to supervisedlearning methods. For most realworld prediction problems, temporaldifference methods require less memory and less peak computation than conventional methods and they produce more accurate predictions. We argue that most problems to which supervised learning is currently applied are really prediction problems of the sort to which temporaldifference methods can be applied to advantage.
A simple distributed autonomous power control algorithm and its convergence
 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY
, 1993
"... For wireless cellular communication systems, one seeks a simple effective means of power control of signals associated with randomly dispersed users that are reusing a single channel in different cells. By effecting the lowest interference environment, in meeting a required minimum signaltointerf ..."
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Cited by 418 (3 self)
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For wireless cellular communication systems, one seeks a simple effective means of power control of signals associated with randomly dispersed users that are reusing a single channel in different cells. By effecting the lowest interference environment, in meeting a required minimum signaltointerference ratio of p per user, channel reuse is maximized. Distributed procedures for doing this are of special interest, since the centrally administered alternative requires added infrastructure, latency, and network vulnerability. Successful distributed powering entails guiding the evolution of the transmitted power level of each of the signals, using only local measurements, so that eventually all users meet the p requirement. The local per channel power measurements include that of the intended signal as well as the undesired interference from other users (plus receiver noise). For a certain simple distributed type of algorithm, whenever power settings exist for which all users meet the p requirement, we demonstrate exponentially fast convergence to these settings.
A class of generalized stochastic petri nets for the performance evaluation of multiprocessor systems
 ACM Transactions on Computer Systems
, 1984
"... Generalized Stochastic Petri Nets (GSPNs) are presented and are applied to the performance evaluation of multiprocessor systems. GSPNs are derived from standard Petri nets by partitioning the set of transitions into two subsets comprising timed and immediate transitions. An exponentially distributed ..."
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Cited by 292 (4 self)
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Generalized Stochastic Petri Nets (GSPNs) are presented and are applied to the performance evaluation of multiprocessor systems. GSPNs are derived from standard Petri nets by partitioning the set of transitions into two subsets comprising timed and immediate transitions. An exponentially distributed random firing time is associated with each timed transition, whereas immediate transitions fire in zero time. It is shown that GSPNs are equivalent to continuoustime stochastic processes, and solution methods for the derivation of the steady state probability distribution are presented. Examples of application of GSPN models to the performance evaluation of multiprocessor systems show the usefulness and the effectiveness of this modeling tool. 1.
Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods
, 1994
"... This document is the electronic version of the 2nd edition of the Templates book, which is available for purchase from the Society for Industrial and Applied ..."
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Cited by 236 (5 self)
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This document is the electronic version of the 2nd edition of the Templates book, which is available for purchase from the Society for Industrial and Applied
Efficient and Reliable Schemes for Nonlinear Diffusion Filtering
 IEEE Transactions on Image Processing
, 1998
"... Nonlinear diffusion filtering is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a recent discrete nonlinear diffusion scalespace framework we present semiimplicit schemes which are sta ..."
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Cited by 218 (22 self)
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Nonlinear diffusion filtering is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a recent discrete nonlinear diffusion scalespace framework we present semiimplicit schemes which are stable for all time steps. These novel schemes use an additive operator splitting (AOS) which guarantees equal treatment of all coordinate axes. They can be implemented easily in arbitrary dimensions, have good rotational invariance and reveal a computational complexity and memory requirement which is linear in the number of pixels. Examples demonstrate that, under typical accuracy requirements, AOS schemes are at least ten times more efficient than the widelyused explicit schemes.
A sparse approximate inverse preconditioner for nonsymmetric linear systems
 SIAM J. SCI. COMPUT
, 1998
"... This paper is concerned with a new approach to preconditioning for large, sparse linear systems. A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner f ..."
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Cited by 183 (22 self)
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This paper is concerned with a new approach to preconditioning for large, sparse linear systems. A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient–type methods. Some theoretical properties of the preconditioner are discussed, and numerical experiments on test matrices from the Harwell–Boeing collection and from Tim Davis’s collection are presented. Our results indicate that the new preconditioner is cheaper to construct than other approximate inverse preconditioners. Furthermore, the new technique insures convergence rates of the preconditioned iteration which are comparable with those obtained with standard implicit preconditioners.
ImplicitExplicit Methods For TimeDependent PDEs
 SIAM J. NUMER. ANAL
, 1997
"... Implicitexplicit (IMEX) schemes have been widely used, especially in conjunction with spectral methods, for the time integration of spatially discretized PDEs of diffusionconvection type. Typically, an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection ..."
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Cited by 150 (6 self)
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Implicitexplicit (IMEX) schemes have been widely used, especially in conjunction with spectral methods, for the time integration of spatially discretized PDEs of diffusionconvection type. Typically, an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection term. Reactiondiffusion problems can also be approximated in this manner. In this work we systematically analyze the performance of such schemes, propose improved new schemes and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods. For the prototype linear advectiondiffusion equation, a stability analysis for first, second, third and fourth order multistep IMEX schemes is performed. Stable schemes permitting large time steps for a wide variety of problems and yielding appropriate decay of high frequency error modes are identified. Numerical experiments demonstrate that weak decay of high freque...
Block preconditioning for the conjugate gradient method
, 1982
"... Abstract. Block preconditionings for the conjugate gradient method are investigated for solving positive definite block tridiagonal systems of linear equations arising from discretization of boundary value problems for elliptic partial differential equations. The preconditionings rest on the use of ..."
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Cited by 96 (5 self)
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Abstract. Block preconditionings for the conjugate gradient method are investigated for solving positive definite block tridiagonal systems of linear equations arising from discretization of boundary value problems for elliptic partial differential equations. The preconditionings rest on the use of sparse approximate matrix inverses to generate incomplete block Cholesky factorizations. Carrying out of the factorizations can be guaranteed under suitable conditions. Numerical experiments on test problems for two dimensions indicate that a particularly attractive preconditioning, which uses special properties of tridiagonal matrix inverses, can be computationally more efficient for the same computer storage than other preconditionings, including the popular point incomplete Cholesky factorization. Key words, conjugate gradient method, elliptic partial differential equations, incomplete factorization, iterative methods, preconditioning, sparse matrices 1. Introduction. In
WalkSums and Belief Propagation in Gaussian Graphical Models
 Journal of Machine Learning Research
, 2006
"... We present a new framework based on walks in a graph for analysis and inference in Gaussian graphical models. The key idea is to decompose the correlation between each pair of variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edg ..."
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Cited by 95 (15 self)
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We present a new framework based on walks in a graph for analysis and inference in Gaussian graphical models. The key idea is to decompose the correlation between each pair of variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edgewise partial correlation coefficients. This representation holds for a large class of Gaussian graphical models which we call walksummable. We give a precise characterization of this class of models, and relate it to other classes including diagonally dominant, attractive, nonfrustrated, and pairwisenormalizable. We provide a walksum interpretation of Gaussian belief propagation in trees and of the approximate method of loopy belief propagation in graphs with cycles. The walksum perspective leads to a better understanding of Gaussian belief propagation and to stronger results for its convergence in loopy graphs.
Efficient numerical methods in nonuniform sampling theory
, 1995
"... We present a new “second generation” reconstruction algorithm for irregular sampling, i.e. for the problem of recovering a bandlimited function from its nonuniformly sampled values. The efficient new method is a combination of the adaptive weights method which was developed by the two first named ..."
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Cited by 94 (10 self)
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We present a new “second generation” reconstruction algorithm for irregular sampling, i.e. for the problem of recovering a bandlimited function from its nonuniformly sampled values. The efficient new method is a combination of the adaptive weights method which was developed by the two first named authors and the method of conjugate gradients for the solution of positive definite linear systems. The choice of ”adaptive weights” can be seen as a simple but very efficient method of preconditioning. Further substantial acceleration is achieved by utilizing the Toeplitztype structure of the system matrix. This new algorithm can handle problems of much larger dimension and condition number than have been accessible so far. Furthermore, if some gaps between samples are large, then the algorithm can still be used as a very efficient extrapolation method across the gaps.