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Добірка наукової літератури з теми "Stochastic approximation techniques"

Автор: Grafiati

Опубліковано: 15 лютого 2025

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Статті в журналах з теми "Stochastic approximation techniques"

Worden, Lee, Ira B. Schwartz, Simone Bianco, Sarah F. Ackley, Thomas M. Lietman, and Travis C. Porco. "Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics." Computational and Mathematical Methods in Medicine 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/4253167.

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We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics.

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Bosch, Paul. "A Numerical Method for Two-Stage Stochastic Programs under Uncertainty." Mathematical Problems in Engineering 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/840137.

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Motivated by problems coming from planning and operational management in power generation companies, this work extends the traditional two-stage linear stochastic program by adding probabilistic constraints in the second stage. In this work we describe, under special assumptions, how the two-stage stochastic programs with mixed probabilities can be treated computationally. We obtain a convex conservative approximations of the chance constraints defined in second stage of our model and use Monte Carlo simulation techniques for approximating the expectation function in the first stage by the average. This approach raises with another question: how to solve the linear program with the convex conservative approximation (nonlinear constrains) for each scenario?

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Sengul, Suleyman, Zafer Bekiryazici, and Mehmet Merdan. "Wong-Zakai method for stochastic differential equations in engineering." Thermal Science 25, Spec. issue 1 (2021): 131–42. http://dx.doi.org/10.2298/tsci200528014s.

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In this paper, Wong-Zakai approximation methods are presented for some stochastic differential equations in engineering sciences. Wong-Zakai approximate solutions of the equations are analyzed and the numerical results are compared with results from popular approximation schemes for stochastic differential equations such as Euler-Maruyama and Milstein methods. Several differential equations from engineering problems containing stochastic noise are investigated as numerical examples. Results show that Wong-Zakai method is a reliable tool for studying stochastic differential equations and can be used as an alternative for the known approximation techniques for stochastic models.

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Capobianco, Enrico. "Computationally Efficient Atomic Representations for Nonstationary Stochastic Processes." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 03 (September 2003): 325–51. http://dx.doi.org/10.1142/s0219691303000177.

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Function approximation methods based on frames or other overcomplete dictionaries of approximating functions offer advantages over the orthogonal schemes due to the fact that the associated redundancy may lead to better de-noising and reconstruction power. Wavelet packets represent special wavelet frames; they combine overcompleteness with high time-frequency localization power through an optimal frequency-then-time segmentation. Compared to cosine packets, which enable optimal adaptation through time-then-frequency segmentation, wavelet packets show a different time-frequency resolution trade-off that might be useful for analyzing some kinds of non-stationary phenomena. We study the properties of covariance non-stationary stochastic processes whose realizations are observed at very high frequencies; the data are supplied by time series of a stock market return index. For these complex processes the effectiveness of wavelet and cosine packets is explored by implementing entropic optimization, greedy approximation techniques and dimension reduction methods.

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Najim, K., and E. Ikonen. "Distributed logic processors trained under constraints using stochastic approximation techniques." IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 29, no. 4 (July 1999): 421–26. http://dx.doi.org/10.1109/3468.769763.

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Vande Wouwer, A., C. Renotte, and M. Remy. "Application of stochastic approximation techniques in neural modelling and control." International Journal of Systems Science 34, no. 14-15 (November 2003): 851–63. http://dx.doi.org/10.1080/00207720310001640296.

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Jaakkola, Tommi, Michael I. Jordan, and Satinder P. Singh. "On the Convergence of Stochastic Iterative Dynamic Programming Algorithms." Neural Computation 6, no. 6 (November 1994): 1185–201. http://dx.doi.org/10.1162/neco.1994.6.6.1185.

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Recent developments in the area of reinforcement learning have yielded a number of new algorithms for the prediction and control of Markovian environments. These algorithms, including the TD(λ) algorithm of Sutton (1988) and the Q-learning algorithm of Watkins (1989), can be motivated heuristically as approximations to dynamic programming (DP). In this paper we provide a rigorous proof of convergence of these DP-based learning algorithms by relating them to the powerful techniques of stochastic approximation theory via a new convergence theorem. The theorem establishes a general class of convergent algorithms to which both TD(λ) and Q-learning belong.

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Montes, Francisco, and Jorge Mateu. "On the MLE for a spatial point pattern." Advances in Applied Probability 28, no. 2 (June 1996): 339. http://dx.doi.org/10.1017/s0001867800048382.

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Parameter estimation for a two-dimensional point pattern is difficult because most of the available stochastic models have intractable likelihoods ([2]). An exception is the class of Gibbs or Markov point processes ([1], [5]), where the likelihood typically forms an exponential family and is given explicitly up to a normalising constant. However, the latter is not known analytically, so parameter estimates must be based on approximations ([3], [6], [7]). In this paper we present comparisons amongst the different techniques available in the literature to obtain an approximation of the maximum likelihood estimate (MLE). Two stochastic methods are specifically illustrated: a Newton-Raphson algorithm ([7]) and the Robbins-Monro procedure ([8]). We use a very simple point process model, the Strauss process ([4]), to test and compare those approximations.

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SUN, XU, XINGYE KAN, and JINQIAO DUAN. "APPROXIMATION OF INVARIANT FOLIATIONS FOR STOCHASTIC DYNAMICAL SYSTEMS." Stochastics and Dynamics 12, no. 01 (March 2012): 1150011. http://dx.doi.org/10.1142/s0219493712003614.

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Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random sets. Thus it is desirable to have some techniques to approximate random invariant foliations. In this paper, invariant foliations are approximated for dynamical systems with small noisy perturbations, via asymptotic analysis. Namely, random invariant foliations are represented as a perturbation of the deterministic invariant foliations, with deviation errors estimated.

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Schweiger, Regev, Eyal Fisher, Elior Rahmani, Liat Shenhav, Saharon Rosset, and Eran Halperin. "Using Stochastic Approximation Techniques to Efficiently Construct Confidence Intervals for Heritability." Journal of Computational Biology 25, no. 7 (July 2018): 794–808. http://dx.doi.org/10.1089/cmb.2018.0047.

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Дисертації з теми "Stochastic approximation techniques"

Krishnaswamy, Ravishankar. "Approximation Techniques for Stochastic Combinatorial Optimization Problems." Research Showcase @ CMU, 2012. http://repository.cmu.edu/dissertations/157.

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The focus of this thesis is on the design and analysis of algorithms for basic problems in Stochastic Optimization, specifically a class of fundamental combinatorial optimization problems where there is some form of uncertainty in the input. Since many interesting optimization problems are computationally intractable (NP-Hard), we resort to designing approximation algorithms which provably output good solutions. However, a common assumption in traditional algorithms is that the exact input is known in advance. What if this is not the case? What if there is uncertainty in the input? With the growing size of input data and their typically distributed nature (e.g., cloud computing), it has become imperative for algorithms to handle varying forms of input uncertainty. Current techniques, however, are not robust enough to deal with many of these problems, thus necessitating the need for new algorithmic tools. Answering such questions, and more generally identifying the tools for solving such problems, is the focus of this thesis. The exact problems we study in this thesis are the following: (a) the Survivable Network Design problem where the collection of (source,sink) pairs is drawn randomly from a known distribution, (b) the Stochastic Knapsack problem with random sizes/rewards for jobs, (c) the Multi-Armed Bandits problem, where the individual Markov Chains make random transitions, and finally (d) the Stochastic Orienteering problem, where the random tasks/jobs are located at different vertices on a metric. We explore different techniques for solving these problems and present algorithms for all the above problems with near-optimal approximation guarantees. We also believe that the techniques are fairly general and have wider applicability than the context in which they are used in this thesis.

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Mhanna, Elissa. "Beyond gradients : zero-order approaches to optimization and learning in multi-agent environments." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASG123.

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L'essor des dispositifs connectés et des données qu'ils génèrent a stimulé le développement d'applications à grande échelle. Ces dispositifs forment des réseaux distribués avec un traitement de données décentralisé. À mesure que leur nombre augmente, des défis comme la surcharge de communication et les coûts computationnels se présentent, nécessitant des méthodes d'optimisation adaptées à des contraintes de ressources strictes, surtout lorsque les dérivées sont coûteuses ou indisponibles. Cette thèse se concentre sur les méthodes d'optimisation sans dérivées, qui sont idéales quand les dérivées des fonctions sont inaccessibles. Ces méthodes estiment les gradients à partir des évaluations de fonction, ce qui les rend adaptées à l'apprentissage distribué et fédéré, où les dispositifs collaborent pour résoudre des tâches d'optimisation avec peu d'informations et des données bruitées. Dans le premier chapitre, nous traitons de l'optimisation distribuée sans dérivées pour des fonctions fortement convexes sur plusieurs agents. Nous proposons un algorithme distribué de descente de gradient projete sans dérivées, qui utilise des estimations de gradient à un point, où la fonction est interrogée une seule fois par réalisation stochastique, et les évaluations sont bruitées. Ce chapitre démontre la convergence presque sûre de l'algorithme et fournit des bornes théoriques sur le taux de convergence. Avec des pas constants, l'algorithme atteint un taux de convergence linéaire. C'est la première fois que ce taux est établi pour des estimations de gradient à un point (voire même pour des estimations de gradient à deux points) pour des fonctions stochastiques. Nous analysons aussi les effets des pas décroissants, établissant un taux de convergence correspondant aux méthodes centralisées sans dérivées. Le deuxième chapitre se penche sur les défis de l'apprentissage fédéré qui est limité par le coût élevé de la transmission de données sur des réseaux à bande passante restreinte. Pour y répondre, nous proposons un nouvel algorithme qui réduit la surcharge de communication en utilisant des estimations de gradient à un point. Les dispositifs transmettent des valeurs scalaires plutôt que de grands vecteurs de gradient, réduisant ainsi la quantité de données envoyées. L'algorithme intègre aussi directement les perturbations des communications sans fil dans l'optimisation, éliminant le besoin de connaître explicitement l'état du canal. C'est la première approche à inclure les propriétés du canal sans fil dans un algorithme d'apprentissage, le rendant résilient aux problèmes de communication réels. Nous prouvons la convergence presque sûre de cette méthode dans des environnements non convexes et validons son efficacité à travers des expériences. Le dernier chapitre étend l'algorithme précédent au cas des estimations de gradient à deux points. Contrairement aux estimations à un point, les estimations à deux points interrogent la fonction deux fois, fournissant une approximation plus précise du gradient et améliorant le taux de convergence. Cette méthode conserve l'efficacité de communication des estimations à un point, avec uniquement des valeurs scalaires transmises, et assouplit l'hypothèse de bornitude de la fonction objective. Nous prouvons des taux de convergence linéaires pour des fonctions fortement convexes et lisses. Pour les problèmes non convexes, nous montrons une amélioration notable du taux de convergence, en particulier pour les fonctions dominées par le gradient K, atteignant également un taux linéaire. Nous fournissons aussi des résultats montrant l'efficacité de communication par rapport à d'autres techniques d'apprentissage fédéré
The rise of connected devices and the data they produce has driven the development of large-scale applications. These devices form distributed networks with decentralized data processing. As the number of devices grows, challenges like communication overhead and computational costs increase, requiring optimization methods that work under strict resource constraints, especially where derivatives are unavailable or costly. This thesis focuses on zero-order (ZO) optimization methods are ideal for scenarios where explicit function derivatives are inaccessible. ZO methods estimate gradients based only on function evaluations, making them highly suitable for distributed and federated learning environments where devices collaborate to solve global optimization tasks with limited information and noisy data. In the first chapter, we address distributed ZO optimization for strongly convex functions across multiple agents in a network. We propose a distributed zero-order projected gradient descent algorithm that uses one-point gradient estimates, where the function is queried only once per stochastic realization, and noisy function evaluations estimate the gradient. The chapter establishes the almost sure convergence of the algorithm and derives theoretical upper bounds on the convergence rate. With constant step sizes, the algorithm achieves a linear convergence rate. This is the first time this rate has been established for one-point (and even two-point) gradient estimates. We also analyze the effects of diminishing step sizes, establishing a convergence rate that matches centralized ZO methods' lower bounds. The second chapter addresses the challenges of federated learning (FL) which is often hindered by the communication bottleneck—the high cost of transmitting large amounts of data over limited-bandwidth networks. To address this, we propose a novel zero-order federated learning (ZOFL) algorithm that reduces communication overhead using one-point gradient estimates. Devices transmit scalar values instead of large gradient vectors, lowering the data sent over the network. Moreover, the algorithm incorporates wireless communication disturbances directly into the optimization process, eliminating the need for explicit knowledge of the channel state. This approach is the first to integrate wireless channel properties into a learning algorithm, making it resilient to real-world communication issues. We prove the almost sure convergence of this method in nonconvex optimization settings, establish its convergence rate, and validate its effectiveness through experiments. In the final chapter, we extend the ZOFL algorithm to include two-point gradient estimates. Unlike one-point estimates, which rely on a single function evaluation, two-point estimates query the function twice, providing a more accurate gradient approximation and enhancing the convergence rate. This method maintains the communication efficiency of one-point estimates, where only scalar values are transmitted, and relaxes the assumption that the objective function must be bounded. The chapter demonstrates that the proposed two-point ZO method achieves linear convergence rates for strongly convex and smooth objective functions. For nonconvex problems, the method shows improved convergence speed, particularly when the objective function is smooth and K-gradient-dominated, where a linear rate is also achieved. We also analyze the impact of constant versus diminishing step sizes and provide numerical results showing the method's communication efficiency compared to other federated learning techniques

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Bakhous, Christine. "Modèles d'encodage parcimonieux de l'activité cérébrale mesurée par IRM fonctionnelle." Phd thesis, Université de Grenoble, 2013. http://tel.archives-ouvertes.fr/tel-00933426.

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L'imagerie par résonance magnétique fonctionnelle (IRMf) est une technique non invasive permettant l'étude de l'activité cérébrale au travers des changements hémodynamiques associés. Récemment, une technique de détection-estimation conjointe (DEC) a été développée permettant d'alterner (1) la détection de l'activité cérébrale induite par une stimulation ainsi que (2) l'estimation de la fonction de réponse hémodynamique caractérisant la dynamique vasculaire; deux problèmes qui sont généralement traités indépendamment. Cette approche considère une parcellisation a priori du cerveau en zones fonctionnellement homogènes et alterne (1) et (2) sur chacune d'entre elles séparément. De manière standard, l'analyse DEC suppose que le cerveau entier peut être activé par tous les types de stimuli (visuel, auditif, etc.). Cependant la spécialisation fonctionnelle des régions cérébrales montre que l'activité d'une région n'est due qu'à certains types de stimuli. La prise en compte de stimuli non pertinents dans l'analyse, peut dégrader les résultats. La sous-famille des types de stimuli pertinents n'étant pas la même à travers le cerveau une procédure de sélection de modèles serait très coûteuse en temps de calcul. De plus, une telle sélection a priori n'est pas toujours possible surtout dans les cas pathologiques. Ce travail de thèse propose une extension de l'approche DEC permettant la sélection automatique des conditions (types de stimuli) pertinentes selon l'activité cérébrale qu'elles suscitent, cela simultanément à l'analyse et adaptativement à travers les régions cérébrales. Des exemples d'analyses sur des jeux de données simulés et réels, illustrent la capacité de l'approche DEC parcimonieuse proposée à sélectionner les conditions pertinentes ainsi que son intérêt par rapport à l'approche DEC standard.

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Manganas, Spyridon. "A Novel Methodology for Timely Brain Formations of 3D Spatial Information with Application to Visually Impaired Navigation." Wright State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=wright1567452284983244.

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Ben, Hammouda Chiheb. "Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks." Diss., 2020. http://hdl.handle.net/10754/664348.

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In biochemically reactive systems with small copy numbers of one or more reactant molecules, stochastic effects dominate the dynamics. In the first part of this thesis, we design novel efficient simulation techniques for a reliable and fast estimation of various statistical quantities for stochastic biological and chemical systems under the framework of Stochastic Reaction Networks. In the first work, we propose a novel hybrid multilevel Monte Carlo (MLMC) estimator, for systems characterized by having simultaneously fast and slow timescales. Our hybrid multilevel estimator uses a novel split-step implicit tau-leap scheme at the coarse levels, where the explicit tau-leap method is not applicable due to numerical instability issues. In a second work, we address another challenge present in this context called the high kurtosis phenomenon, observed at the deep levels of the MLMC estimator. We propose a novel approach that combines the MLMC method with a pathwise-dependent importance sampling technique for simulating the coupled paths. Our theoretical estimates and numerical analysis show that our method improves the robustness and complexity of the multilevel estimator, with a negligible additional cost. In the second part of this thesis, we design novel methods for pricing financial derivatives. Option pricing is usually challenging due to: 1) The high dimensionality of the input space, and 2) The low regularity of the integrand on the input parameters. We address these challenges by developing different techniques for smoothing the integrand to uncover the available regularity. Then, we approximate the resulting integrals using hierarchical quadrature methods combined with Brownian bridge construction and Richardson extrapolation. In the first work, we apply our approach to efficiently price options under the rough Bergomi model. This model exhibits several numerical and theoretical challenges, implying classical numerical methods for pricing being either inapplicable or computationally expensive. In a second work, we design a numerical smoothing technique for cases where analytic smoothing is impossible. Our analysis shows that adaptive sparse grids’ quadrature combined with numerical smoothing outperforms the Monte Carlo approach. Furthermore, our numerical smoothing improves the robustness and the complexity of the MLMC estimator, particularly when estimating density functions.

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Psaros, Andriopoulos Apostolos. "Sparse representations and quadratic approximations in path integral techniques for stochastic response analysis of diverse systems/structures." Thesis, 2019. https://doi.org/10.7916/d8-xcxx-my55.

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Uncertainty propagation in engineering mechanics and dynamics is a highly challenging problem that requires development of analytical/numerical techniques for determining the stochastic response of complex engineering systems. In this regard, although Monte Carlo simulation (MCS) has been the most versatile technique for addressing the above problem, it can become computationally daunting when faced with high-dimensional systems or with computing very low probability events. Thus, there is a demand for pursuing more computationally efficient methodologies. Recently, a Wiener path integral (WPI) technique, whose origins can be found in theoretical physics, has been developed in the field of engineering dynamics for determining the response transition probability density function (PDF) of nonlinear oscillators subject to non-white, non-Gaussian and non-stationary excitation processes. In the present work, the Wiener path integral technique is enhanced, extended and generalized with respect to three main aspects; namely, versatility, computational efficiency and accuracy. Specifically, the need for increasingly sophisticated modeling of excitations has led recently to the utilization of fractional calculus, which can be construed as a generalization of classical calculus. Motivated by the above developments, the WPI technique is extended herein to account for stochastic excitations modeled via fractional-order filters. To this aim, relying on a variational formulation and on the most probable path approximation yields a deterministic fractional boundary value problem to be solved numerically for obtaining the oscillator joint response PDF. Further, appropriate multi-dimensional bases are constructed for approximating, in a computationally efficient manner, the non-stationary joint response PDF. In this regard, two distinct approaches are pursued. The first employs expansions based on Kronecker products of bases (e.g., wavelets), while the second utilizes representations based on positive definite functions. Next, the localization capabilities of the WPI technique are exploited for determining PDF points in the joint space-time domain to be used for evaluating the expansion coefficients at a relatively low computational cost. Subsequently, compressive sampling procedures are employed in conjunction with group sparsity concepts and appropriate optimization algorithms for decreasing even further the associated computational cost. It is shown that the herein developed enhancement renders the technique capable of treating readily relatively high-dimensional stochastic systems. More importantly, it is shown that this enhancement in computational efficiency becomes more prevalent as the number of stochastic dimensions increases; thus, rendering the herein proposed sparse representation approach indispensable, especially for high-dimensional systems. Next, a quadratic approximation of the WPI is developed for enhancing the accuracy degree of the technique. Concisely, following a functional series expansion, higher-order terms are accounted for, which is equivalent to considering not only the most probable path but also fluctuations around it. These fluctuations are incorporated into a state-dependent factor by which the exponential part of each PDF value is multiplied. This localization of the state-dependent factor yields superior accuracy as compared to the standard most probable path WPI approximation where the factor is constant and state-invariant. An additional advantage relates to efficient structural reliability assessment, and in particular, to direct estimation of low probability events (e.g., failure probabilities), without possessing the complete transition PDF. Overall, the developments in this thesis render the WPI technique a potent tool for determining, in a reliable manner and with a minimal computational cost, the stochastic response of nonlinear oscillators subject to an extended range of excitation processes. Several numerical examples, pertaining to both nonlinear dynamical systems subject to external excitations and to a special class of engineering mechanics problems with stochastic media properties, are considered for demonstrating the reliability of the developed techniques. In all cases, the degree of accuracy and the computational efficiency exhibited are assessed by comparisons with pertinent MCS data.

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Книги з теми "Stochastic approximation techniques"

Workshop on Randomization and Approximation Techniques in Computer Science (1997 Bologna, Italy). Randomization and approximation techniques in computer science: International Workshop RANDOM '97, Bologna, Italy, July 11-12,1997 : proceedings. New York: Springer, 1997.

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Workshop on Randomization and Approximation Techniques in Computer Science (1997 Bologna, Italy). Randomization and approximation techniques in computer science: International workshop RANDOM'97, Bologna, Italy, July 11-12, 1997 : proceedings. Berlin: Springer, 1997.

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Andriopoulos, Apostolos Psaros. Sparse representations and quadratic approximations in path integral techniques for stochastic response analysis of diverse systems/structures. [New York, N.Y.?]: [publisher not identified], 2019.

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Частини книг з теми "Stochastic approximation techniques"

Kall, P., A. Ruszczyński, and K. Frauendorfer. "Approximation Techniques in Stochastic Programming." In Springer Series in Computational Mathematics, 33–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-61370-8_2.

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Chawla, Shuchi, and Tim Roughgarden. "Single-Source Stochastic Routing." In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 82–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11830924_10.

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Barbierato, Enrico, Marco Gribaudo, and Daniele Manini. "Fluid Approximation of Pool Depletion Systems." In Analytical and Stochastic Modelling Techniques and Applications, 60–75. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-43904-4_5.

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Marti, K. "Stochastic Programming: Numerical Solution Techniques by Semi-Stochastic Approximation Methods." In Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty, 23–43. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-2111-5_3.

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Nikolova, Evdokia. "Approximation Algorithms for Reliable Stochastic Combinatorial Optimization." In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 338–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15369-3_26.

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Alaei, Saeed, MohammadTaghi Hajiaghayi, and Vahid Liaghat. "The Online Stochastic Generalized Assignment Problem." In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 11–25. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-40328-6_2.

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Neupane, Thakur, Zhen Zhang, Curtis Madsen, Hao Zheng, and Chris J. Myers. "Approximation Techniques for Stochastic Analysis of Biological Systems." In Computational Biology, 327–48. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17297-8_12.

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Gupta, Anupam, MohammadTaghi Hajiaghayi, and Amit Kumar. "Stochastic Steiner Tree with Non-uniform Inflation." In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 134–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-74208-1_10.

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So, Anthony Man–Cho, Jiawei Zhang, and Yinyu Ye. "Stochastic Combinatorial Optimization with Controllable Risk Aversion Level." In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 224–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11830924_22.

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Bortolussi, Luca. "Limit Behavior of the Hybrid Approximation of Stochastic Process Algebras." In Analytical and Stochastic Modeling Techniques and Applications, 367–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13568-2_26.

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Тези доповідей конференцій з теми "Stochastic approximation techniques"

Nakamura, Tomoki, Kazutaka Tomida, Shouta Kouno, Hidetsugu Irie, and Shuichi Sakai. "Stochastic Iterative Approximation: Software/hardware techniques for adjusting aggressiveness of approximation." In 2021 IEEE 39th International Conference on Computer Design (ICCD). IEEE, 2021. http://dx.doi.org/10.1109/iccd53106.2021.00023.

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Rai, Prashant, Mathilde Chevreuil, Anthony Nouy, and Jayant Sen Gupta. "A Regression Based Non-Intrusive Method Using Separated Representation for Uncertainty Quantification." In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82301.

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This paper aims at handling high dimensional uncertainty propagation problems by proposing a tensor product approximation method based on regression techniques. The underlying assumption is that the model output functional can be well represented in a separated form, as a sum of elementary tensors in the stochastic tensor product space. The proposed method consists in constructing a tensor basis with a greedy algorithm and then in computing an approximation in the generated approximation space using regression with sparse regularization. Using appropriate regularization techniques, the regression problems are well posed for only few sample evaluations and they provide accurate approximations of model outputs.

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JabŁonka, Anna, and Radosław Iwankiewicz. "Moment Equations and Modified Closure Approximation Techniques for Nonlinear Dynamic Systems under Renewal Impulse Process Excitations." In Proceedings of the 8th International Conference on Computational Stochastic Mechanics (CSM 8). Singapore: Research Publishing Services, 2018. http://dx.doi.org/10.3850/978-981-11-2723-6_30-cd.

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Luo, Liang, Zhi-Qin Zhao, and Xiao-Pin Li. "A Novel Surveillance Video Processing Using Stochastic Low-Rank And Generalized Low-Rank Approximation Techniques." In 2018 International Conference on Machine Learning and Cybernetics (ICMLC). IEEE, 2018. http://dx.doi.org/10.1109/icmlc.2018.8527059.

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Kretzschmar, Florian, Matthias Beggiato, and Alois Pichler. "Detection of Discomfort in Autonomous Driving via Stochastic Approximation." In 13th International Conference on Applied Human Factors and Ergonomics (AHFE 2022). AHFE International, 2022. http://dx.doi.org/10.54941/ahfe1002437.

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One of the most important goals in the field of autonomous driving development is to make the experience for the passenger as pleasant and comfortable as possible. In addition to traditional influence factors on passenger comfort, new aspects arise due to the transfer of control from the human to the vehicle. Some of these are apparent safety, motion sickness, user preferences regarding driving style and information needs. Ideally, the vehicle and the passenger should form a team, whereby the vehicle should be able to detect and predict situations of discomfort in real time and take measures accordingly. This requires not only the continuous monitoring of the passengers state but also the implementation of adequate mathematical models. To investigate how this teaming of human and automated agents can be shaped in the most effective way is a key topic of the Collaborative Research Center “Hybrid Societies (https://hybrid-societies.org/). In this framework, driving simulator data from the previous project “KomfoPilot” (https://bit.ly/komfopilot) is re-analyzed using new mathematical models. The participants in the study completed several automated drives and reported continuously situations of discomfort using a handset control. Sensor data was collected simultaneously using eye tracking glasses, a smart band, seat pressure sensors and video cameras for motion and face tracking. While pupil diameter, heart rate, interblink intervals, skin conductance and head movement have already been identified as potential single indicators of discomfort, it is now necessary to integrate these and other findings of the project into a functional multivariate model. In this paper, we investigate how such a model can be shaped to offer high prediction accuracy and viable practical implementation. The first important question – which arises from the heterogeneity of the participants – is whether to work with training data on an individual or aggregated level. We compare both possibilities by applying techniques from the field of stochastic approximation for clustering of the chosen training set and subsequent classification of the test data. In the case of an individual model for each participant, we furthermore divide the participants into subgroups and analyze whether there is a connection between the physiological reactions of a passenger and his/her demographic characteristics and driving experience. Finally, we discuss the potential of our method as a reliable prediction model as well as implications for future driving simulator studies and related research.

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He, Li, Qi Meng, Wei Chen, Zhi-Ming Ma, and Tie-Yan Liu. "Differential Equations for Modeling Asynchronous Algorithms." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/307.

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Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the discrete view has its intrinsic limitations: there is no characterizationof the optimization path and the proof techniques are induction-based and thus usually complicated. Inspired by the recent successful adoptions of stochastic differential equations (SDE) to the theoretical analysis of SGD, in this paper, we study the continuous approximation of ASGD by using stochastic differential delay equations (SDDE). We introduce the approximation method and study the approximation error. Then we conduct theoretical analysis on the convergence rate of ASGD algorithm based on the continuous approximation.There are two methods: moment estimation and energy function minimization can be used to analyzethe convergence rates. Moment estimation depends on the specific form of the loss function, while energy function minimization only leverages the convex property of the loss function, and does not depend on its specific form. In addition to the convergence analysis, the continuous view also helps us derive better convergence rates. All of this clearly shows the advantage of taking the continuous view in gradient descent algorithms.

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To, C. W. S. "Large Nonlinear Random Responses of Spatially Non-Homogeneous Stochastic Shell Structures." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99261.

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This paper is concerned with large nonlinear random response analysis of spatially non-homogeneous stochastic shell structures under transient excitations. The latter are treated as nonstationary random excitation processes. The emphases are on (i) spatially non-homogeneous and homogeneous stochastic shell structures with large spatial variations, (ii) large nonlinear responses with finite strains and finite rotations, and (iii) intensive nonstationary random disturbances. The shell structures are approximated by the lower order mixed or hybrid strain based triangular shell finite elements developed earlier by the author and his associate. The nonstationary random nonlinear responses are evaluated by a procedure that consists of the stochastic central difference method, time co-ordinate transformation, and modified adaptive time scheme. Computationally, the procedure is very efficient compared with those entirely and partially based on Monte Carlo simulation, and is free from the limitations associated with those employing perturbation approximation techniques, such as the so-called stochastic finite element or probabilistic finite element method.

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Marti, K. "Approximation and Derivatives of Probability Functions in Probabilistic Structural Analysis and Design." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0048.

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Abstract Yield stresses, allowable stresses, moment capacities (plastic moments), external loadings, manufacturing errors are not given fixed quantities in practice, but have to be modelled as random variables with a certain joint probability distribution. Hence, problems from limit (collapse) load analysis or plastic analysis and from plastic and elastic design of structures are treated in the framework of stochastic optimization. Using especially reliability-oriented optimization methods, the behavioral constraints are quantified by means of the corresponding probability ps of survival. Lower bounds for ps are obtained by selecting certain redundants in the vector of internal forces; moreover, upper bounds for ps are constructed by considering a pair of dual linear pro-prams for the optimizational representation of the yield or safety conditions. Whereas ps can be computed e.g. by sampling methods or by asymptotic expansion techniques based on Laplace integral representations of certain multiple integrals, efficient techniques for the computation of the sensitivities (of various orders) of ps with respect to input or design variables have yet to be developed. Hence several new techniques are suggested for the numerical computation of derivatives of ps.

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Chen, Weizhe, Zihan Zhou, Yi Wu, and Fei Fang. "Temporal Induced Self-Play for Stochastic Bayesian Games." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/14.

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One practical requirement in solving dynamic games is to ensure that the players play well from any decision point onward. To satisfy this requirement, existing efforts focus on equilibrium refinement, but the scalability and applicability of existing techniques are limited. In this paper, we propose Temporal-Induced Self-Play (TISP), a novel reinforcement learning-based framework to find strategies with decent performances from any decision point onward. TISP uses belief-space representation, backward induction, policy learning, and non-parametric approximation. Building upon TISP, we design a policy-gradient-based algorithm TISP-PG. We prove that TISP-based algorithms can find approximate Perfect Bayesian Equilibrium in zero-sum one-sided stochastic Bayesian games with finite horizon. We test TISP-based algorithms in various games, including finitely repeated security games and a grid-world game. The results show that TISP-PG is more scalable than existing mathematical programming-based methods and significantly outperforms other learning-based methods.

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Hou, Bo-Jian, Lijun Zhang, and Zhi-Hua Zhou. "Storage Fit Learning with Unlabeled Data." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/256.

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By using abundant unlabeled data, semi-supervised learning approaches have been found very useful in various tasks. Existing approaches, however, neglect the fact that the storage available for the learning process is different under different situations, and thus, the learning approaches should be flexible subject to the storage budget limit. In this paper, we focus on graph-based semi-supervised learning and propose two storage fit learning approaches which can adjust their behaviors to different storage budgets. Specifically, we utilize techniques of low-rank matrix approximation to find a low-rank approximator of the similarity matrix so as to reduce the space complexity. The first approach is based on stochastic optimization, which is an iterative approach that converges to the optimal low-rank approximator globally. The second approach is based on Nystrom method, which can find a good low-rank approximator efficiently and is suitable for real-time applications. Experiments on classification tasks show that the proposed methods can fit dynamically different storage budgets and obtain good performances in different scenarios.

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Звіти організацій з теми "Stochastic approximation techniques"

Potamianos, Gerasimos, and John Goutsias. Stochastic Simulation Techniques for Partition Function Approximation of Gibbs Random Field Images. Fort Belvoir, VA: Defense Technical Information Center, June 1991. http://dx.doi.org/10.21236/ada238611.

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