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IEEE TRANSACTIONS ON NANOBIOSCIENCE 2015年第5期14卷 545-552页

作者： Devaurs, Didier Molloy, Kevin Vaisset, Marc Shehu, Amarda Simeon, Thierry Cortes, Juan CNRS LAAS F-31400 Toulouse France Univ Toulouse LAAS F-31400 Toulouse France Rice Univ Dept Comp Sci Houston TX 77005 USA George Mason Univ Dept Comp Sci Fairfax VA 22030 USA

Obtaining accurate representations of energy landscapes of biomolecules such as proteins and peptides is central to the study of their physicochemical properties and biological functions. Peptides are particularly interesting, as they exploit structural flexibility to modulate their biological function. Despite their small size, peptide modeling remains challenging due to the complexity of the energy landscape of such highly-flexible dynamic systems. Currently, only stochastic sampling-based methods can efficiently explore the conformational space of a peptide. In this paper, we suggest to combine two such methods to obtain a full characterization of energy landscapes of small yet flexible peptides. First, we propose a simplified version of the classical Basin Hopping algorithm to reveal low-energy regions in the landscape, and thus to identify the corresponding meta-stable structural states of a peptide. Then, we present several variants of a robotics-inspired algorithm, the Transition-based Rapidly-exploring Random Tree, to quickly determine transition path ensembles, as well as transition probabilities between meta-stable states. We demonstrate this combined approach on met-enkephalin.

关键词： Energy landscape peptides stochastic algorithms

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A strong approximation theorem for stochastic recursive algorithms

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1999年第3期100卷 499-513页

作者： Borkar, VS Mitter, SK Indian Inst Sci Dept Comp Sci & Automat Bangalore 560012 Karnataka India MIT Informat & Decis Syst Lab Cambridge MA 02139 USA

The constant stepsize analog of Gelfand-Mitter type discrete-time stochastic recursive algorithms is shown to track an associated stochastic differential equation in the strong sense, i.e., with respect to an appropri... 详细信息

关键词： stochastic algorithms approximation of stochastic differential equations constant stepsize algorithms asymptotic behavior

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Non-Asymptotic Analysis of stochastic Approximation algorithms for Streaming Data

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ESAIM-PROBABILITY AND STATISTICS 2023年 27卷 482-514页

作者： Godichon-Baggioni, Antoine Werge, Nicklas Wintenberger, Olivier Sorbonne Univ Lab Probabil Stat & Modelisat LPSM F-75005 Paris France Univ Wien Wolfgang Pauli Inst Fak Math A-1090 Vienna Austria

We introduce a streaming framework for analyzing stochastic approximation/optimization problems. This streaming framework is analogous to solving optimization problems using time-varying mini-batches that arrive sequentially. We provide non-asymptotic convergence rates of various gradientbased algorithms;this includes the famous stochastic Gradient (SG) descent (a.k.a. Robbins-Monro algorithm), mini-batch SG and time-varying mini-batch SG algorithms, as well as their iterated averages (a.k.a. Polyak-Ruppert averaging). We show (i) how to accelerate convergence by choosing the learning rate according to the time-varying mini-batches, (ii) that Polyak-Ruppert averaging achieves optimal convergence in terms of attaining the Cramer-Rao lower bound, and (iii) how time-varying mini-batches together with Polyak-Ruppert averaging can provide variance reduction and accelerate convergence simultaneously, which is advantageous for many learning problems, such as online, sequential, and large-scale learning. We further demonstrate these favorable effects for various time-varying minibatches.

关键词： stochastic algorithms stochastic optimization machine learning online learning mini-batch streaming

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On stochastic evolving algorithms 22

On stochastic evolving algorithms

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Fister, Iztok, Jr. Fister, Iztok Univ Maribor Maribor Slovenia

ISBN: (纸本)9781450392686

This pioneering study tries to break the wall of the question, how to develop algorithms capable of self-improving. The foundation of this work is the extended model of the human mind, while the information flow between components is inspired by molecular genetics. As a result, the proposed evolving algorithms consist of complex rules and stochastic processing, while the preliminary results also revealed enormous potential for the future.

关键词： evolving algorithms cognitive model stochastic algorithms

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Deep Statistical Comparison for Multi-Objective stochastic Optimization algorithms

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SWARM AND EVOLUTIONARY COMPUTATION 2021年 61卷

作者： Eftimov, Tome Korosec, Peter Jozef Stefan Inst Comp Syst Dept Jamova Cesta 39 Ljubljana 1000 Slovenia

Making a statistical comparison of meta-heuristic multi-objective optimization algorithms is crucial for identifying the strengths and weaknesses of a newly proposed algorithm. Currently, state-of-the-art comparison approaches involve user-preference-based selection of a single quality indicator or an ensemble of quality indicators as a comparison metric. Using these quality indicators, high-dimensional data is transformed into one-dimensional data. By doing this, information contained in the high-dimensional space can be lost, which will affect the results of the comparison. To avoid losing this information, we propose a novel ranking scheme that compares the distributions of high-dimensional data. Experimental results show that the proposed approach reduces potential information loss when statistical significance is not observed in high-dimensional data. Consequently, the selection of a quality indicator is required only in cases when statistical significance is observed in high-dimensional data. With this the cases that are affected by the user preference selection are reduced.

关键词： statistical comparison multi-objective problems stochastic algorithms benchmarking high-dimensional data

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ARTIFICIAL INTELLIGENCE AND stochastic OPTIMIZATION algorithms FOR THE CHAOTIC DATASETS

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FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2023年第6期31卷 2240175-2240175页

作者： Wang, Fuzhang Sohail, Ayesha Wong, Wing-Keung Azim, Qurat Ul Ain Farwa, Shabieh Sajad, Maria Nanchang Inst Technol Nanchang 330044 Peoples R China Xuzhou Univ Technol Sch Math & Stat Xuzhou 2221018 Jiangsu Peoples R China COMSATS Univ Islamabad Dept Math Lahore Campus Islamabad 54000 Pakistan Asia Univ FinTech & Blockchain Res Ctr Dept Finance Taichung Taiwan Asia Univ Big Data Res Ctr Taichung Taiwan China Med Univ Hosp Dept Med Res Yude Rd Taichung 404327 Taiwan Hang Seng Univ Hong Kong Dept Econ & Finance Hong Kong Peoples R China COMSATS Univ Islamabad Dept Math WahCant CampusMall RdQuaid Ave Rawalpindi Punjab Pakistan

Almost every natural process is stochastic due to the basic consequences of nature's existence and the dynamical behavior of each process that is not stationary but evolves with the passage of time. These stochastic processes not only exist and appear in the fields of biological sciences but are also evident in industrial, agricultural and economical research datasets. stochastic processes are challenging to model and to solve as well. The stochastic patterns when repeated result into random fractals and are very common in natural processes. These processes are usually simulated with the aid of smart computational and optimization tools. With the progress in the field of artificial intelligence, smart tools are developed that can model the stochastic processes by generalization and genetic optimization. Based on the basic theoretical description of the stochastic optimization algorithms, the stochastic learning tools, stochastic modeling, stochastic approximation and stochastic fractals, a comparative analysis is presented with the aid of the stochastic fractal search, multi-objective stochastic fractal search and pattern search algorithms.

关键词： stochastic Machine Learning Tools stochastic algorithms Genetic algorithms stochastic Fractal Search Imaging Data Analysis

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Distributed stochastic Nash equilibrium seeking under heavy-tailed noises

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AUTOMATICA 2025年 173卷

作者： Sun, Chao Chen, Bo Wang, Jianzheng Wang, Zheming Yu, Li Zhejiang Univ Technol Dept Automat Hangzhou Peoples R China

This paper studies the distributed stochastic Nash equilibrium seeking problem under heavy-tailed noises. Unlike the traditional stochastic Nash equilibrium algorithms, where the gradient noises are usually assumed to have a bounded variance, we assume that the gradient noises can be heavytailed, which can have an unbounded variance. A distributed Nash equilibrium seeking law combining projected gradient descent and gradient clipping is proposed. Sufficient conditions on the step-sizes are given to guarantee almost sure and in mean square convergence to the Nash equilibrium of the game. A numerical example is given to show the effectiveness and efficiency of the algorithm. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Nash equilibrium seeking Distributed algorithms stochastic algorithms

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Asset and Factor Risk Budgeting: a balanced approach

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QUANTITATIVE FINANCE 2025年第2期25卷 181-195页

作者： Cetingoz, Adil Rengim Gueant, Olivier Univ Paris 1 Pantheon sorbonne Ctr Econ Sorbonne 106 Blvd Hop F-75642 Paris 13 France

Portfolio optimization methods have evolved significantly since Markowitz introduced the mean-variance framework in 1952. While the theoretical appeal of this approach is undeniable, its practical implementation poses important challenges, primarily revolving around the intricate task of estimating expected returns. As a result, practitioners and scholars have explored alternative methods that prioritize risk management and diversification. One such approach is Risk Budgeting, where portfolio risk is allocated among assets according to predefined risk budgets. The effectiveness of Risk Budgeting in achieving true diversification can, however, be questioned, given that asset returns are often influenced by a small number of risk factors. From this perspective, one question arises: is it possible to allocate risk at the factor level using the Risk Budgeting approach? First, we introduce a comprehensive framework to address this question by introducing risk measures directly associated with risk factor exposures and demonstrating the desirable mathematical properties of these risk measures, making them suitable for optimization. Then, we propose a novel framework to find portfolios that effectively balance the risk contributions from both assets and factors. Leveraging standard stochastic algorithms, our framework enables the use of a wide range of risk measures to construct diversified portfolios.

关键词： Diversification Factor models Factor investing Portfolio optimization Risk budgeting Risk measures stochastic algorithms

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stochastic Analysis of the LMS and NLMS algorithms for Cyclostationary White Gaussian and Non-Gaussian Inputs

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2018年第18期66卷 4753-4765页

作者： Eweda, Eweda Bershad, Neil J. Bermudez, Jose Carlos M. C4 Adv Solut Abu Dhabi 128627 U Arab Emirates Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92660 USA Univ Fed Santa Catarina Dept Elect Engn BR-88040900 Florianopolis SC Brazil

This paper studies the stochastic behavior of the LMS and NLMS algorithms in a system identification framework for a cyclostationary white input without assuming a Gaussian distribution for the input. The input cyclostationary signal is modeled by a white random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation behavior of the adaptive weights as a function of the input cyclostationarity. Analytical models are first derived for the LMS and NLMS algorithms for cyclostationary white inputs. These models show the dependence of the two algorithms upon the kurtosis of the input. Significant differences are found between the behaviors of the two algorithms when the analysis is applied to non-Gaussian cases. Monte Carlo simulations provide strong support for the theory.

关键词： Adaptive filters analysis LMS algorithm NLMS algorithm stochastic algorithms non-Gaussian processes

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stochastic Analysis of the Signed LMS algorithms for Cyclostationary White Gaussian Inputs

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第7期65卷 1673-1684页

作者： Eweda, Eweda Bershad, Neil J. C4 Adv Solut Abu Dhabi 43269 U Arab Emirates Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92660 USA

This paper studies the stochastic behavior of the signed variants of the LMS algorithm for a system identification framework when the input signal is a cyclostationary white Gaussian process. Three algorithms are studied: the signed regressor, the signed error, and the sign-sign algorithms. The input cyclostationary signal is modeled by a white Gaussian random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation behavior of the adaptive weights with the input cyclostationarity. These models are used to derive new results concerning the performance of the algorithms. Some of these results are surprising. Monte Carlo simulations of the three algorithms provide strong support for the theory.

关键词： Adaptive Filters Analysis Signed LMS algorithms stochastic algorithms

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