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The Semi-stochastic Ski-rental Problem

31st IARCS Annual International Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)

作者： Madry, Aleksander Panigrahi, Debmalya Microsoft Res New England Cambridge MA 02142 USA MIT Comp Sci & Artificial Intelligence Lab Cambridge MA 02139 USA

ISBN: (纸本)9783939897347

In this paper, we introduce the semi-stochastic model for dealing with input uncertainty in optimization problems. This model is a hybrid between the overly pessimistic online model and the highly optimistic stochastic (or Bayesian) model. In this model, the algorithm can obtain only limited stochastic information about the future (i.e. about the input distribution)-as the amount of stochastic information we make available to the algorithm grows from no information to full information, we interpolate between the online and stochastic models. The central question in this framework is the trade-off between the performance of an algorithm, and the stochastic information that it can access. As a first step towards understanding this trade-off, we consider the ski-rental problem in the semi-stochastic setting. More precisely, given a desired competitive ratio, we give upper and lower bounds on the amount of stochastic information required by a deterministic algorithm for the ski-rental problem to achieve that competitive ratio.

关键词： online optimization stochastic algorithm

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stochastic PREDICTION AND FEEDBACK CONTROL OF ROUTER QUEUE SIZE IN A VIRTUAL NETWORK ENVIRONMENT

STOCHASTIC PREDICTION AND FEEDBACK CONTROL OF ROUTER QUEUE S...

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作者： Muflih Alqahtani Air Force Institute of Technology

学位级别：硕士

Modern congestion and routing management algorithms work well for networks with static topologies and moderate QoS requirements. However, these algorithms may not be suitable for modern military networks with fluid dynamic topologies and traffic demands that include mobile networks with many assets. These secure networks require a high level of Quality of Service (QoS) that must adapt to changing demands with no service interruptions. The idea of a network weatherman was developed by Stuckey to predict router queue size by using an extended Kalman filter [2]. He modeled and exercised his design in OPNET with positive results. The goal of this research is to investigate the use of queue size predictions and network weatherman and to determine the effectiveness of three types of filters to predict future traffic demand in a virtual network environment. These filters are an extended Kalman filter, an unscented Kalman filter, and a basic filter. These queue size predictions will be used to implement a network controller to improve the performance of information technology (IT) networks and formulate some type of context awareness and cognitive process in the management of networks by reducing packet loss.

关键词： Kalman filter stochastic algorithm MATLAB VMware Workstation Queue Prediction of Queue Size Queue Controller

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Increasing the efficiency of existing complex downstream processes by plant-wide retrofit

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CHEMICAL ENGINEERING RESEARCH & DESIGN 2015年 99卷 199-207页

作者： Lorenz, Hilke-Marie Otte, Daniel Staak, Daniel Repke, Jens-Uwe TU Bergahademie Freiberg Inst Thermal Environm & Nat Prod Proc Engn D-09596 Freiberg Germany Lonza Ltd CH-3930 Visp Switzerland

The economic feasibility of processes in the chemical industry is often determined by the energy and raw material demand, hence process efficiency is crucial. Most published methods to increase the efficiency of industrial processes are limited by a maximum possible degree of complexity of the respective processes. Thus, a systematic approach for the retrofit of existing processes is developed in the presented work, particularly for processes with industrial relevant complexity. The hybrid approach combines heuristic and mathematical methods. Due to recycle streams in the processes, retrofit modifications can affect the entire process, thus the operating points of all units have to be adapted. Therefore, a mathematical optimisation problem is formulated and a method based on the global optimisation algorithm molecular inspired parallel tempering (MIPT) is developed. In order to solve the optimisation problem, MATLAB (TM) and Chemcad (TM) are linked via an OPC interface. The developed method is successfully applied to an existing complex industrial world-scale process, which comprises a large number of components, including 18 unit operations and a considerable number of recycle streams. The presented retrofit leads to an increase of the efficiency of this complex process. (C) 2015 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

关键词： Retrofit MINLP Multicomponent mixtures Global optimisation Sensitivity study stochastic algorithm

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A sum-over-paths algorithm for third-order impulse-response moment extraction within RC IC-interconnect networks

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SOLID-STATE ELECTRONICS 2015年第Jul.期109卷 63-71页

作者： Wojcik, E. A. Ni, D. Lam, T. M. Le Coz, Y. L. Rensselaer Polytech Inst ECSE Dept Troy NY 12180 USA

We have created the first stochastic SoP (Sum-over-Paths) algorithm to extract third-order impulse-response (IR) moment within RC IC interconnects. It employs a newly discovered Feynman SoP Postulate. Importantly, our algorithm maintains computational efficiency and full parallelism. Our approach begins with generation of s-domain nodal-voltage equations. We then perform a Taylor-series expansion of the circuit transfer function. These expansions yield transition diagrams involving mathematical coupling constants, or weight factors, in integral powers of complex frequency s. Our SoP Postulate enables stochastic evaluation of path sums within the circuit transition diagram to order s(3)-corresponding to the order of IR moment (m(3)) we seek here. We furnish, for the first time, an informal algebraic proof independently validating our SoP Postulate and algorithm. We list, as well, detailed procedural steps, suitable for coding, that define an efficient stochastic algorithm for m3 IR extraction. Origins of the algorithm's statistical "capacitor-number cubed" correction and "double-counting" weight factors are explained, for completeness. Our algorithm was coded and successfully tested against exact analytical solutions for 3-, 5-, and 10-stage RC lines. We achieved better than 0.65% 1-sigma error convergence, after only 10K statistical samples, in less than 1 s of 2-GHz Pentium (R) execution time. These results continue to suggest that stochastic SoP algorithms may find useful application in circuit analysis of massively coupled networks, such as those encountered in high-end digital IC-interconnect CAD. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： RC-circuits Moments Path sum stochastic algorithm

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Nonlinear methods for inverse statistical problems

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2011年第1期55卷 132-142页

作者： Barbillon, Pierre Celeux, Gilles Grimaud, Agnes Lefebvre, Yannick De Rocquigny, Etienne Univ Paris 11 INRIA Saclay Orsay France Ecole Cent Paris Paris France

In the uncertainty treatment framework considered, the intrinsic variability of the inputs of a physical simulation model is modelled by a multivariate probability distribution. The objective is to identify this probability distribution - the dispersion of which is independent of the sample size since intrinsic variability is at stake - based on observation of some model outputs. Moreover, in order to limit the number of (usually burdensome) physical model runs inside the inversion algorithm to a reasonable level, a nonlinear approximation methodology making use of Kriging and a stochastic EM algorithm is presented. It is compared with iterated linear approximation on the basis of numerical experiments on simulated data sets coming from a simplified but realistic modelling of a dyke overflow. Situations where this nonlinear approach is to be preferred to linearisation are highlighted. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Uncertainty modelling Nonlinear approximation Kriging stochastic algorithm

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Prediction under uncertainty in reservoir modeling

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2004年第1-2期44卷 143-153页

作者： Subbey, S Christie, M Sambridge, M Heriot Watt Univ Inst Petr Engn Edinburgh EH14 4AS Midlothian Scotland Australian Natl Univ Inst Adv Studies Res Sch Earth Sci Canberra ACT 0200 Australia

Reservoir simulation is routinely employed in the prediction of reservoir performance under different depletion and operating scenarios. Usually, a single history-matched model, conditioned to production data, is obtained. The model is then used to forecast future production profiles. Because the history match is non-unique, the forecast production profiles are therefore uncertain, although this uncertainty is not usually quantified. This paper presents a new approach for generating uncertain reservoir performance predictions and quantifying the uncertainty associated with forecasting future performance. Firstly, multiple reservoir realizations are generated using a new stochastic algorithm. This involves adaptively sampling the model parameter space using an algorithm, which biases the sampling towards regions of good fit. Using the complete ensemble of models generated, the posterior distribution is resampled in order to quantify the uncertainty associated with forecasting reservoir performance in a Bayesian framework. The strength of the method in performance prediction is demonstrated by using an upscaled model to history match fine scale data. The maximum likelihood model is then used in forecasting the fine grid performance, and the uncertainty associated with the predictions is quantified. It is demonstrated that the maximum likelihood model is highly accurate in reservoir performance prediction. (C) 2004 Published by Elsevier B.V.

关键词： uncertainty history matching stochastic algorithm Bayesian framework maximum likelihood prediction

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Unsupervised Nearest Neighbors Clustering With Application to Hyperspectral Images

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IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING 2015年第6期9卷 1105-1116页

作者： Cariou, Claude Chehdi, Kacem Univ Rennes 1 IETR TSI2M Team CNRS UMR 6164 F-22300 Lannion France

We address the problem of unsupervised clustering of multidimensional data when the number of clusters is not known a priori. The proposed iterative approach is a stochastic extension of the kNN density-based clustering (KNNCLUST) method which randomly assigns objects to clusters by sampling a posterior class label distribution. In our approach, contextual class-conditional distributions are estimated based on a k nearest neighbors graph, and are iteratively modified to account for current cluster labeling. Posterior probabilities are also slightly reinforced to accelerate convergence to a stationary labeling. A stopping criterion based on the measure of clustering entropy is defined thanks to the Kozachenko-Leonenko differential entropy estimator, computed from current class-conditional entropies. One major advantage of our approach relies in its ability to provide an estimate of the number of clusters present in the data set. The application of our approach to the clustering of real hyperspectral image data is considered. Our algorithm is compared with other unsupervised clustering approaches, namely affinity propagation (AP), KNNCLUST and Non Parametric stochastic Expectation Maximization (NPSEM), and is shown to improve the correct classification rate in most experiments.

关键词： Bayes' decision rule data clustering differential entropy estimation hyperspectral images nearest neighbors pixel classification stochastic algorithm

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Approximation of exit times for one-dimensional linear diffusion processes

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2020年第6期80卷 1668-1682页

作者： Herrmann, Samuel Massin, Nicolas Univ Bourgogne Franche Comte CNRS UMR 5584 Inst Math Bourgogne IMB F-21000 Dijon France

In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and the Ornstein-Uhlenbeck context, that is for particular time-homogeneous diffusion processes. Here the aim is therefore to generalize this efficient numerical approach in order to obtain an approximation of both the exit time and position for a general linear diffusion. The main challenge of such a generalization is to handle with time-inhomogeneous diffusions. The efficiency of the method is described with particular care through theoretical results and numerical examples. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Exit time Linear diffusion Random walk Generalized spheroids stochastic algorithm

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Bayesian Mixed Effect Atlas Estimation with a Diffeomorphic Deformation Model

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SIAM JOURNAL ON IMAGING SCIENCES 2015年第3期8卷 1367-1395页

作者： Allassonniere, S. Durrleman, S. Kuhn, E. Ecole Polytech CMAP F-91128 Palaiseau France INRIA Paris Roquencourt Aramis Lab F-75013 Paris France Univ Paris 06 Sorbonne Univ UMR 1127 F-75013 Paris France CNRS UMR 7225 F-75013 Paris France ICM F-75013 Paris France INRA Unite MIA F-78352 Jouy En Josas France

In this paper we introduce a diffeomorphic constraint on the deformations considered in the deformable Bayesian mixed effect template model. Our approach is built on a generic group of diffeomorphisms, which is parameterized by an arbitrary set of control point positions and momentum vectors. This enables us to estimate the optimal positions of control points together with a template image and parameters of the deformation distribution which compose the atlas. We propose to use a stochastic version of the expectation-maximization algorithm where the simulation is performed using the anisotropic Metropolis adjusted Langevin algorithm. We propose also an extension of the model including a sparsity constraint to select an optimal number of control points with relevant positions. Experiments are carried out on the United States Postal Service database, on mandibles of mice, and on three-dimensional murine dendrite spine images.

关键词： deformable template model atlas estimation diffeomorphic deformations stochastic algorithm anisotropic MALA control point optimization sparsity

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A sum-over-paths impulse-response moment-extraction algorithm for RLCM IC-interconnect networks

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SOLID-STATE ELECTRONICS 2007年第8期51卷 1109-1123页

作者： Le Coz, Y. L. Krishna, D. Petranovic, D. M. Rensselaer Polytech Inst ECSE Dept Troy NY 12180 USA Mentor Graph Corp Wilsonville OR 97070 USA

We have created a new impulse-response (IR) moment-extraction algorithm for RLCM circuit networks. It employs a Feynman sumover-paths postulate. Our approach begins with generation of s-domain nodal-voltage equations. We then perform a Taylor-series expansion of the circuit transfer function. These expansions yield transition diagrams involving mathematical coupling constants, or weight factors, in integral powers of complex frequency s. Our sum-over-paths postulate supports stochastic evaluation of path sums within the circuit transition diagram to any desired order of s. The specific order of s in the sum corresponds, as well, to the order of IR moment we seek to extract. In developing the algorithm, importantly, we maintain computational efficiency and full parallelism. Initial verification studies of uncoupled and coupled RLCM lines furnished promising results: less than 10% 1-sigma error for m(1) or m(2) moment, after 10 K sampled path-sum terms. In addition, we observed excellent convergence to exact, analytical moment values with increasing number of samples. Our sum-over-paths postulate, in fact, implies generality for arbitrary RLCM-interconnect network topologies, beyond those specific examples presented in this work. We believe, in conclusion, that this type of IR-moment extraction algorithm may find useful application in a massively coupled electrical system, such as a high-end digital-IC interconnect network. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： feynman sum over paths IC-interconnect modeling Impulse response Moment extraction RLCM circuit networks stochastic algorithm

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