检索结果-内蒙古大学图书馆

2017年

作者： Panik Michael J.

ISBN: (数字)9781119377412

ISBN: (纸本)9781119377382

A beginner’s guide to stochastic growth modeling The chief advantage of stochastic growth models over deterministic models is that they combine both deterministic and stochastic elements of dynamic behaviors, such as weather, natural disasters, market fluctuations, and epidemics. This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of outcomes. However, the background requirements for studying SDEs can be daunting for those who lack the rigorous course of study received by math majors. Designed to be accessible to readers who have had only a few courses in calculus and statistics, this book offers a comprehensive review of the mathematical essentials needed to understand and apply stochastic growth models. In addition, the book describes deterministic and stochastic applications of population growth models including logistic, generalized logistic, Gompertz, negative exponential, and linear. Ideal for students and professionals in an array of fields including economics, population studies, environmental sciences, epidemiology, engineering, finance, and the biological sciences, stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling: • Provides precise definitions of many important terms and concepts and provides many solved example problems • Highlights the interpretation of results and does not rely on a theorem-proof approach • Features comprehensive chapters addressing any background deficiencies readers may have and offers a comprehensive review for those who need a mathematics refresher • Emphasizes solution techniques for SDEs and their practical application to the development of stochastic population models An indispensable resource for students and practitioners with limited exposure to mathematics and statistics, stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling is an excellent

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ESTIMATION OF THE QUADRATIC VARIATION OF NEARLY OBSERVED SEMIMARTINGALES WITH APPLICATION TO FILTERING

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1993年第2期31卷 494-517页

作者： PICARD, J CNRS-URA Aubiere France

Consider a filtering problem in which the available information is a noisy observation of a continuous semimartingale H(t). In the case of a high signal-to-noise ratio, it is proved that H(t) and its quadratic variation can be jointly estimated by means of a finite-dimensional filter;moreover, for this result, the observation noise and H(t) are not required to be independent. This problem can be viewed as a linear filtering problem with randomly time-varying parameters, and our filter is auto-adaptive with respect to changes of the parameters. These results are then applied to the nonlinear filtering of Markov diffusion processes when the observation function is not injective but satisfies a weaker detectability assumption. It appears that filtering such a system involves two timescales. The study is based on time discretization;the main tools are an averaging principle and an application of the asymptotic ordinary differential equation method for the study of stochastic algorithms.

关键词： NONLINEAR FILTERING SYSTEMS WITH SMALL NOISE LINEAR FILTERING WITH UNKNOWN PARAMETERS ADAPTIVE FILTERING AVERAGING PRINCIPLE stochastic algorithms

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Provable training of a ReLU gate with an iterative non-gradient algorithm

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NEURAL NETWORKS 2022年第0期151卷 264-275页

作者： Karmakar, Sayar Mukherjee, Anirbit Univ Florida Dept Stat 230 Newell Dr Gainesville FL 32611 USA Univ Manchester Dept Comp Sci Kilburn Bldg Manchester M13 9PL Lancs England

In this work, we demonstrate provable guarantees on the training of a single ReLU gate in hitherto unexplored regimes. We give a simple iterative stochastic algorithm that can train a ReLU gate in the realizable setting in linear time while using significantly milder conditions on the data distribution than previous such results.& nbsp;Leveraging certain additional moment assumptions, we also show a first-of-its-kind approximate recovery of the true label generating parameters under an (online) data-poisoning attack on the true labels, while training a ReLU gate by the same algorithm. Our guarantee is shown to be nearly optimal in the worst case and its accuracy of recovering the true weight degrades gracefully with increasing probability of attack and its magnitude.& nbsp;For both the realizable and the non-realizable cases as outlined above, our analysis allows for minibatching and computes how the convergence time scales with the mini-batch size. We corroborate our theorems with simulation results which also bring to light a striking similarity in trajectories between our algorithm and the popular S.G.D. algorithm - for which similar guarantees as here are still unknown. (C) 2022 Elsevier Ltd. All rights reserved.

关键词： Neural nets Non-gradient iterative algorithms stochastic algorithms Non-smooth non-convex optimization

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Approximate inference in Bayesian networks: Parameterized complexity results

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2018年 93卷 119-131页

作者： Kwisthout, Johan Radboud Univ Nijmegen Donders Inst Brain Cognit & Behav Montessorilaan 3 NL-6525 HR Nijmegen Netherlands

Computing posterior and marginal probabilities constitutes the backbone of almost all inferences in Bayesian networks. These computations are known to be intractable in general, both to compute exactly and to approximate (e.g., by sampling algorithms). While it is well known under what constraints exact computation can be rendered tractable (viz., bounding tree-width of the moralized network and bounding the cardinality of the variables) it is less known under what constraints approximate Bayesian inference can be tractable. Here, we extend the existing formal framework of fixed-error randomized tractability (a randomized analogue of fixed-parameter tractability), and use it to address this problem, both by re-interpreting known results from the literature and by providing some additional new results, including results on fixed parameter tractable de-randomization of approximate inference. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Approximate inference Sampling Bayesian networks Parameterized complexity stochastic algorithms De-randomization

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LINEAR CONVERGENCE OF COMPARISON-BASED STEP-SIZE ADAPTIVE RANDOMIZED SEARCH VIA STABILITY OF MARKOV CHAINS

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SIAM JOURNAL ON OPTIMIZATION 2016年第3期26卷 1589-1624页

作者： Auger, Anne Hansen, Nikolaus Univ Paris 11 LRI Inria Bat 660 F-91405 Orsay France

In this paper, we consider comparison-based adaptive stochastic algorithms for solving numerical optimization problems. We consider a specific subclass of algorithms that we call comparison-based step-size adaptive randomized search (CB-SARS), where the state variables at a given iteration are a vector of the search space and a positive parameter, the step-size, typically control's the overall standard deviation of the underlying search distribution. We investigate the linear convergence of CB-SARS on scaling-invariant objective functions. Scaling-invariant functions preserve the ordering of points w.r.t. their function value when the points are scaled with the same positive parameter (the scaling is done w.r.t. a fixed reference point). This class of functions includes norms composed with strictly increasing functions as well as many non-quasi-convex and noncontinuous functions. On scaling-invariant functions, we show the existence of a homogeneous Markov chain, as a consequence of natural invariance properties of CB-SARS (essentially scale-invariance and invariance to strictly increasing transformation of the objective function). We then derive sufficient conditions for global linear convergence of CB-SARS, expressed in terms of different stability conditions of the normalized homogeneous Markov chain (irreducibility, positivity, Harris recurrence, geometric ergodicity) and thus define a general methodology for proving global linear convergence of CB-SARS algorithms on scaling-invariant functions. As a by-product we provide a connexion between comparison-based adaptive stochastic algorithms and Markov chain Monte Carlo algorithms.

关键词： stochastic algorithms numerical optimization Markov chains Markov chain Monte Carlo comparison-based linear convergence invariance adaptive randomized search adaptive algorithms derivative-free optimization

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Ordinal hill climbing algorithms for discrete manufacturing process design optimization problems

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DISCRETE EVENT DYNAMIC SYSTEMS-THEORY AND APPLICATIONS 2000年第4期10卷 307-324页

作者： Sullivan, KA Jacobson, SH United Airlines Inc Chicago IL 60666 USA Univ Illinois Dept Mech & Ind Engn Urbana IL 61801 USA

This paper introduces ordinal hill climbing algorithms for addressing discrete manufacturing process design optimization problems using computer simulation models. Ordinal hill climbing algorithms combine the search space reduction feature of ordinal optimization with the global search feature of generalized hill climbing algorithms. By iteratively applying the ordinal optimization strategy within the generalized hill climbing algorithm framework, the resulting hybrid algorithm can be applied to intractable discrete optimization problems. Computational results on an integrated blade rotor manufacturing process design problem are presented to illustrate the application of the ordinal hill climbing algorithm. The relationship between ordinal hill climbing algorithms and genetic algorithms is also discussed. This discussion provides a framework for how the ordinal hill climbing algorithm fits into currently applied algorithms, as well as to introduce a bridge between the two algorithms.

关键词： stochastic algorithms ordinal optimization optimization hill climbing genetic algorithms manufacturing process design

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Efficient algorithms for large scale global optimization: Lennard-Jones clusters

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2003年第2期26卷 173-190页

作者： Locatelli, M Schoen, F Univ Turin Dipartimento Informat I-10124 Turin Italy Univ Florence Dipartimento Sistemi & Informat I-50121 Florence Italy

A stochastic global optimization method is applied to the challenging problem of finding the minimum energy conformation of a cluster of identical atoms interacting through the Lennard-Jones potential. The method proposed incorporates within an already existing and quite successful method, monotonic basin hopping, a two-phase local search procedure which is capable of significantly enlarging the basin of attraction of the global optimum. The experiments reported confirm the considerable advantages of this approach, in particular for all those cases which are considered in the literature as the most challenging ones, namely 75, 98, 102 atoms. While being capable of discovering all putative global optima in the range considered, the method proposed improves by more than two orders of magnitude the speed and the percentage of success in finding the global optima of clusters of 75, 98, 102 atoms.

关键词： global optimization Lennard-Jones clusters stochastic algorithms molecular conformation monotonic basin hopping multistart

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Performance of soft limiters in the LMS algorithm for cyclostationary white Gaussian inputs

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SIGNAL PROCESSING 2018年 152卷 197-205页

作者： Bershad, Neil J. Eweda, Eweda Bermudez, Jose C. M. Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92660 USA C4 Adv Solut Abu Dhabi U Arab Emirates Univ Fed Santa Catarina Dept Elect & Elect Engn BR-88040970 Florianopolis SC Brazil

The analysis of saturation-type nonlinearities on the input and the error in the weight update equation for LMS adaptation were obtained for a stationary white Gaussian data model in [28] for system identification. Here the input signal is modeled by a cyclostationary white Gaussian random process with periodically time-varying power. The system parameters vary according to a random-walk. Using the previous analysis results, nonlinear recursions are presented for the transient and steady-state weight first and second moments that include the effect of the soft limiters. Monte Carlo simulations of the algorithms provide strong support for the theory. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Adaptive filters Analysis Signed LMS algorithms stochastic algorithms

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SOME INSIGHTS ON THE OPTIMAL SCHEMES OF TALL GUYED MASTS

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JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 2013年第5期19卷 749-758页

作者： Belevicius, Rimantas Jatulis, Donatas Sesok, Dmitrij Vilnius Gediminas Tech Univ Dept Engn Mech LT-10223 Vilnius Lithuania Vilnius Gediminas Tech Univ Dept Bridges & Special Struct LT-10223 Vilnius Lithuania Vilnius State Univ Inst Math & Informat LT-08663 Vilnius Lithuania

The article presents the technique for simultaneous topology, shape and sizing optimisation of tall guyed masts under wind loadings and self-weight using simulated annealing. The objective function is the mass of the mast structure including guys, while the set of design parameters may consist of up to 10 parameters of different nature. The constraints are assessed according to Eurocodes and include the local and global stability constraints, limitations on the slenderness in mast elements, and strength constraints. The proposed optimisation technique covers three independent parts: the optimisation algorithm, meshing pre-processor that yields computational scheme of mast depending on the design parameters, and finite element program evaluating the objective function and constraints via penalisation technique. As an example the results of optimisation of a typical 60 m tall guyed telecommunication mast with different antenna areas are presented. On the basis of these results, the authors try ascertaining the approximate optimal diapasons of geometry and topology parameters such as the width of the shaft, distance of the guy foundation from the mast axis, heights of the guy attachment levels and so on. The authors hope, this will be helpful for constructors as an initial design of mast topology, shape and element sizing.

关键词： tall guyed mast global optimisation stochastic algorithms optimal ranges of geometry topology parameters

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Mean-square stability of the Normalized Least-Mean Fourth algorithm for white Gaussian inputs

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DIGITAL SIGNAL PROCESSING 2011年第6期21卷 694-700页

作者： Bershad, Neil J. Bermudez, Jose C. M. Univ Fed Santa Catarina Dept Elect Engn BR-88040900 Florianopolis SC Brazil

Normalized forms of adaptive algorithms are usually sought in order to obtain convergence properties independent of the input signal power. Such is the case of the well-known Normalized LMS (NLMS) algorithm. The Least-Mean Fourth (LMF) adaptive algorithm has been shown to outperform LMS in different situations. However, the LMF stability is dependent on both the signal power and on the adaptive weights initialization. This paper studies the behavior of two normalized forms of the LMF algorithm for Gaussian inputs. Contrary to what could be expected, the mean-square stability of both normalized algorithms is shown to be dependent upon the input signal power. Thus, the usefulness of the NLMF algorithm is open to question. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Adaptive filters Analysis Normalized Least-Mean Fourth stochastic algorithms

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