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arXiv 2017年

作者： Litvinenko, Alexander Litvinenko, Natalya Mamyrbayev, Orken Extreme Computing Research Center Center for Uncertainty Quantification in Computational Science & Engineering King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Applied research department Institute of Mathematics and Mathematical Modeling CS MES RK Almaty Kazakhstan Institute of information and computational technologies CS MES RK Almaty Kazakhstan

An accurate qualitative and comprehensive assessment of human potential is one of the most important challenges in any company or collective. We apply Bayesian networks for developing more accurate overall estimations of psychological characteristics of an individual, based on psychological test results, which identify how much an individual possesses a certain trait. Examples of traits could be a stress resistance, the readiness to take a risk, the ability to concentrate on certain complicated work. The most common way of studying psychological characteristics of each individual is testing. Additionally, the overall estimation is usually based on personal experiences and the subjective perception of a psychologist or a group of psychologists about the investigated psychological personality traits.62C10, 62C12 Copyright © 2017, The Authors. All rights reserved.

关键词： Bayesian networks

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Advanced multilevel Monte Carlo methods

arXiv

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arXiv 2017年

作者： Jasra, Ajay Law, Kody Suciu, Carina Department of Statistics & Applied Probability National University of Singapore Singapore117546 Singapore Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37934 United States Center for Uncertainty Quantification in Computational Science & Engineering King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the discretization of a associated probability law. The MLMC approach works with a hierarchy of biased approximations which become progressively more accurate and more expensive. Using a telescoping representation of the most accurate approximation, the method is able to reduce the computational cost for a given level of error versus i.i.d. sampling from this latter approximation. All of these ideas originated for cases where exact sampling from couples in the hierarchy is possible. This article considers the case where such exact sampling is not currently possible. We consider Markov chain Monte Carlo and sequential Monte Carlo methods which have been introduced in the literature and we describe different strategies which facilitate the application of MLMC within these methods. Copyright © 2017, The Authors. All rights reserved.

关键词： Monte Carlo methods

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Multilevel monte carlo in approximate bayesian computation

arXiv

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arXiv 2017年

作者： Jasra, Ajay Jo, Seongil Nott, David Shoemaker, Christine Tempone, Raul Department of Statistics & Applied Probability & Operations Research Cluster National University of Singapore Singapore117546 Singapore Department of Civil & Environmental Engineering & Operations Research Cluster National University of Singapore Singapore119260 Singapore Center for Uncertainty Quantification in Computational Science & Engineering King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given. Copyright © 2017, The Authors. All rights reserved.

关键词： Bayesian networks

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DGTD analysis of EM interactions on microwave systems loaded with circuit interfaced thin wires

DGTD analysis of EM interactions on microwave systems loaded...

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Progress in Electromagnetic Research Symposium (PIERS)

作者： Ping Li Yifei Shi Hakan Bagci Department of Electrical and Computer Engineering Purdue University West Lafayette IN USA Division of Computer Electrical and Mathematical Sciences and Engineering King Abdullah University of Science and Technology (KAUST) Saudi Arabia Center for Uncertainty Quantification in Computational Science and Engineering King Abdullah University of Science and Technology (KAUST) Thuwal Saudi Arabia

ISBN: (纸本)9781509060948

Summary form only given. The discontinuous Galerkin time-domain (DGTD) method is gaining popularity among computational electromagnetics (CEM) practitioners. This can be attributed to the fact that it has several advantages over the classical finite element method. The DGTD method realizes “information exchange” between neighboring spatial discretization elements using numerical flux. Therefore all spatial operations are localized within a given element leading to a block-diagonal mass matrix which is inverted very efficiently only once before the time marching starts. Consequently, if an explicit time integrator is used, the DGTD method becomes high compact and efficient. Despite these advantages, the use of the DGTD method for analyzing electromagnetic field interactions on microwave systems loaded with cables/thin wires has been very limited. Direct application of the DGTD method for solving Maxwell equation on such structures will result in a rather inefficient simulation tool since the DGTD will call for a very fine discretization in the proximity of thin wires. To overcome this problem, in this work, electromagnetic field interactions on thin wires are modeled using the modified telegrapher's equation (MTEs), which describe a simplified relation between transient voltage and current distributions along a given thin wire. Like Maxwell equations, MTEs describes a hyperbolic system of equations, which are discretized using the one-dimensional (1D) DGTD method. The coupling between the two matrix systems resulting from the discretization of Maxwell equations and MTEs using 3D and 1D DGTD methods is realized by introducing equivalent source terms in each equation set. A weighted electric field obtained from the 3D discretization around the wire is introduced as a voltage source in the MTEs. A volume current density obtained from the 1D discretization on the wire is introduced as a current source in the Maxwell equation describing the Ampere's law equation, respecti

关键词： Wires Mathematical model Electromagnetics Microwave theory and techniques STEM Maxwell equations Three-dimensional displays

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A stochastic maximum principle for risk-sensitive mean-field type control

A stochastic maximum principle for risk-sensitive mean-field...

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作者： Djehiche, Boualem Tembine, Hamidou Tempone, Raul Department of Mathematics KTH Royal Institute of Technology Stockholm100 44 Sweden Center for Interdisciplinary Studies in Security and Privacy Electrical and Computer Engineering Polytechnic School of Engineering New York University NY10003 United States Division of Engineering Saadiyat Island New York University Abu Dhabi Abu Dhabi United Arab Emirates SRI Uncertainty Quantification Center in Computational Science and Engineering CEMSE King Abdullah University of Science and Technology Thuwai Jeddah23955-6900 Saudi Arabia

In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng's type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models. © 1963-2012 IEEE.

关键词： Maximum principle

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Exponential stability of shallow water equations with arbitrary time dependent action

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International Journal of Dynamics and Control 2014年第3期2卷 247-253页

作者： Dia, Ben Mansour SRI Center for Uncertainty Quantification in Computational Science and Engineering CEMSE King Abdullah University of Sciences and Technology Thuwal23955-6900 Saudi Arabia

In this paper, we examine an exponential stability result in L2- norm of the classical solution of shallow water equations. By using Riemann analysis with sub-critical flow condition, we show that only one boundary control law suffices to achieve the exponential stability. For that, we provide a sufficient dissipative condition as second order polynomial inequality with respect to the boundary control law which relies on the setting of a non-increasing arbitrary action. © 2014, Springer-Verlag Berlin Heidelberg.

关键词： Equations of motion

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Cooperative mean-field type games 19

Cooperative mean-field type games

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19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014

作者： Cissé, Abdoul Karim Tembine, Hamidou GrIIsG - ISG International Business School Paris France SRI - Center for Uncertainty Quantification in Computational Science and Engineering CEMSE KAUST Saudi Arabia

ISBN: (纸本)9783902823625

In the standard formulation of a game, a player's payoff function depends on the states and actions of all the players. Yet, real world applications suggest to consider also a functional of the probability measure of states and actions of all the players. In this paper, we consider cooperative mean-field type games in which the state dynamics and the payoffs depend not only on the state and actions but also on their probability measure. We establish stochastic maximum principle and provide a time-dependent payoff allocation procedure for coalitions. The allocated payoff considers not only fairness property but also the cost of making the coalition. Finally, time consistency and subgame perfectness solution concept equations are established. © IFAC.

关键词： Stochastic systems

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Nonasymptotic mean-field games 19

Nonasymptotic mean-field games

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19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014

作者： Tembine, Hamidou KAUST Strategic Research Initiative Center for Uncertainty Quantification in Computational Science and Engineering CEMSE KAUST Saudi Arabia

ISBN: (纸本)9783902823625

Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networked systems with few entities. In this paper we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions. © IFAC.

关键词： Game theory

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Fast distributed strategic learning for global optima in queueing access games 19

Fast distributed strategic learning for global optima in que...

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19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014

作者： Tembine, Hamidou KAUST Strategic Research Initiative Center for Uncertainty Quantification in Computational Science and Engineering CEMSE KAUST Saudi Arabia

ISBN: (纸本)9783902823625

In this paper we examine combined fully distributed payoff and strategy learning (CODIPAS) in a queue-aware access game over a graph. The classical strategic learning analysis relies on vanishing or small learning rate and uses stochastic approximation tool to derive steady states and invariant sets of the underlying learning process. Here, the stochastic approximation framework does not apply due to non-vanishing learning rate. We propose a direct proof of convergence of the process. Interestingly, the convergence time to one of the global optima is almost surely finite and we explicitly characterize the convergence time. We show that pursuit-based CODIPAS learning is much faster than the classical learning algorithms in games. We extend the methodology to coalitional learning and proves a very fast formation of coalitions for queue-aware access games where the action space is dynamically changing depending on the location of the user over a graph. © IFAC.

关键词： Learning algorithms

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Cooperative Mean-Field Type Games

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IFAC Proceedings Volumes 2014年第3期47卷 8995-9000页

作者： Abdoul Karim Cissé Hamidou Tembine GrIIsG - ISG International Business School Paris France SRI – Center for Uncertainty Quantification in Computational Science & Engineering CEMSE KAUST

关键词： Mean-field type cooperation stochastic maximum principle subgame perfection

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