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Asymptotics of maximum likelihood estimation for stable law with continuous parameterization

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2021年第15期50卷 3695-3712页

作者： Matsui, Muneya Nanzan Univ Dept Business Adm Nagoya Aichi Japan

Asymptotics of maximum likelihood estimation for alpha-stable law are analytically investigated with a continuous parameterization. The consistency and asymptotic normality are shown on the interior of the whole parameter space. Although these asymptotics have been provided with Zolotarev's (B) parameterization, there are several gaps between. Especially in the latter, the density is discontinuous at alpha = 1 for and usual asymptotics are impossible. This is a considerable inconvenience for applications. By showing that these quantities are smooth in the continuous form, we fill the gaps between and provide a convenient theory. We numerically approximate the Fisher information matrix around the Cauchy law The results exhibit continuity at and this secures the accuracy of our calculations.

关键词： Characteristic function stable distributions Fisher information matrix maximum likelihood estimator score functions

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Efficient adaptive CUSUM control charts based on generalized likelihood ratio test to monitor process dispersion shift

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2021年第8期37卷 3192-3220页

作者： Zaman, Babar Univ Hafr Al Batin Dept Math Coll Sci Hafar al Batin Saudi Arabia

In practice, a shift in the process parameters (location and/or dispersion) is unknown in prior and cannot be diagnosed precisely with the classical cumulative sum (CUSUM) control chart. To overcome this issue, this study proposed two adaptive CUSUM (ACUSUM) control charts. The proposed control charts utilized linear weighted function that is inspired by generalized likelihood ration test (GLRT) to monitor small and certain range of shift in the process dispersion. In more details, the proposed control charts methodologies are based on GLRT, exponentially weight moving average statistic, and score functions. To obtain the run length of the proposed control charts for performance assessment, algorithms are designed in MATLAB based on Monte Carlo simulation technique. Further, average run length (ARL) is used as a performance measure tool to compare the control charts performance for a single shift. For certain range of shift, extra quadratic loss function, relative ARL, and performance comparison index performance measures based on ARL are calculated. Some existing control charts are used for comparison purpose. The proposed control charts show outstanding capability to detect out-of-control signal against these control charts. Moreover, real-life data of inside diameter of cylinder bore in an engine block are used to reveal the practicality and worth of the proposed control charts relative to other control charts.

关键词： adaptive generalized likelihood ration test Monte Carlo simulation performance measures score functions

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Gradient Estimation and Variance Reduction in Stochastic and Deterministic Models

Gradient Estimation and Variance Reduction in Stochastic and...

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作者： Keane, Ronan Cornell University

学位级别：Ph.D., Doctor of Philosophy

It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence, which have become great areas of interest not just for computer science but also for many other fields of study. More generally, there have been trends moving towards the use of bigger, more complex and higher capacity models. It also seems that stochastic models, and stochastic variants of existing deterministic models, have become important research directions in various fields. For all of these types of models, gradient-based optimization remains as the dominant paradigm for model fitting, control, and more. This dissertation considers unconstrained, nonlinear optimization problems, with a focus on the gradient itself, that key quantity which enables the solution of such problems. In chapter 1, we introduce the notion of reverse differentiation, a term which describes the body of techniques which enables the efficient computation of gradients. We cover relevant techniques both in the deterministic and stochastic cases. We present a new framework for calculating the gradient of problems which involve both deterministic and stochastic elements. The resulting gradient estimator can be applied in virtually any situation (including many where automatic differentiation alone fails due to the fact that it does not give gradient terms due to score functions). In chapter 2, we analyze the properties of the gradient estimator, with a focus on those properties which are typically assumed in convergence proofs of optimization algorithms. That chapter attempts to bridge some of the gap between what is assumed in a mathematical optimization proof, and what we need to prove to get a convergence result for a specific model/problem formulation. Chapter 3 gives various examples of applying our new gradient estimator. We further explore the idea of w

关键词： Automatic differentiation Baselines Gradient estimation Gradient-based optimization score functions Stochastic gradient

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A new local search algorithm with greedy crossover restart for the dominating tree problem

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EXPERT SYSTEMS WITH APPLICATIONS 2023年第PartA期229卷

作者： Niu, Dangdang Liu, Bin Yin, Minghao Zhou, Yupeng Northwest A&F Univ Coll Informat Engn Yangling 712100 Shaanxi Peoples R China Northeast Normal Univ Sch Comp Sci & Informat Technol Changchun 130117 Peoples R China Northwest A&F Univ Shaanxi Key Lab Agr Informat Percept & Intelligent Yangling 712100 Peoples R China Northwest A&F Univ Key Lab Agr Internet Things Minist Agr & Rural Affairs Yangling 712100 Shaanxi Peoples R China

The dominating tree problem (DTP), a variant of the classical minimum dominating set problem, aims to find a dominating tree of minimum costs on a given connected, undirected and edge-weighted graph. In this paper, we design an efficient local search algorithm named LSGCR_DTP to solve DTP. To this end, we propose four new strategies to make it efficient. Firstly, we design a new connecting method for non-connected dominating sets, which no longer depends on the shortest paths between each pair of vertices used in the existing DTP solvers. Secondly, we propose a new method for improving the current feasible connected dominating sets by adding some special vertices to them. Thirdly, a vertex selection strategy for balancing the connecting property and dominating property of solution is introduced. Fourthly, a new restart strategy based on greedy mechanism and crossover operation is integrated to our local search algorithm. Experimental results show that the LSGCR_DTP algorithm can find the best solutions on about 81.5% conventional benchmarks, which outperforms state-of-the-art DTP solvers, including O_ABCDT, EA/G, ABC_DTP and GAITLS. Specially, the solution records of 7 instances are broken by LSGCR_DTP, and LSGCR_DTP can be used to solve many massive graphs with tens or even hundreds of thousand vertices which cannot be solved by the contrastive algorithm.

关键词： Combinatorial optimization Dominating tree problem Iterated local search Restart score functions

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Shortest path algorithm of a network via picture fuzzy digraphs and its application

Shortest path algorithm of a network via picture fuzzy digra...

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International Conference on Advances in Materials Research (ICAMR)

作者： Mani, Parimala Vasudevan, Biju Sivaraman, Murali Bannari Amman Inst Technol Dept Math Sathyamangalam 638401 India Jubail Univ Coll Dept Gen Studies Jubail Industrial City Saudi Arabia Jansons Inst Technol Dept Math Coimbatore 641659 Tamil Nadu India

Many extension and generalization of fuzzy sets have been introduced and studied in the literature. Picture fuzzy set acquired more concentration in the domain of decision making, as many real time circumstances might have choices of more than one and researchers are looking for optimum choice/decision. Picture fuzzy digraph is a generalization of intuitionistic fuzzy set and fuzzy graph. In this paper, we redefine some preliminary operations of picture fuzzy graph and it is referred as picture fuzzy digraph (in short PFDG). We discuss some arithmetic operations and relations among PFDG. We further proposed a method to solve a shortest path problem using score function. (c) 2021 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the International Conference on Advances in Materials Research-2019.

关键词： Digraphs Picture fuzzy set Picture fuzzy graphs Picture fuzzy digraphs score functions

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Robust design optimization by spline dimensional decomposition

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PROBABILISTIC ENGINEERING MECHANICS 2022年 68卷 1页

作者： Lee, Dongjin Jahanbin, Ramin Rahman, Sharif Univ Iowa Dept Mech Engn Iowa City IA 52242 USA

This article highlights new spline-empowered computational methods for solving robust design optimization (RDO) problems in complex mechanical systems. The methods are predicated on a spline dimensional decomposition (SDD) of a high-dimensional, discontinuous, or nonsmooth stochastic response for statistical moment analysis, a novel fusion of SDD and score functions for calculating the second-moment sensitivities with respect to the design variables, and standard gradient-based optimization algorithms. New closed-form formulae are derived for the design sensitivities that are concurrently determined along with the moments. The methods depend on how the statistical moment and sensitivity analyses are engaged with an optimization algorithm, engendering direct and multi-point single-step design processes. Numerical results reveal that the proposed methods deliver accurate and computationally efficient optimal solutions to RDO problems, including an industrial-scale shape design of a robotic gripper jaw.

关键词： RDO Second-moment analysis SDD Orthonormalized B-splines ANOVA dimensional decomposition score functions Stochastic optimization

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Reliability-based design optimization under dependent random variables by a generalized polynomial chaos expansion

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2022年第1期65卷 21-21页

作者： Lee, Dongjin Rahman, Sharif Univ Iowa Dept Mech Engn Iowa City IA 52242 USA

This article brings forward a new computational method for reliability-based design optimization (RBDO) of complex mechanical systems subject to input random variables following arbitrary, dependent probability distributions. It involves a generalized polynomial chaos expansion (GPCE) for reliability analysis subject to dependent input random variables, a novel fusion of the GPCE approximation and score functions for estimating the sensitivities of the failure probability with respect to design variables, and standard gradient-based optimization algorithms, resulting in a multi-point single-step design process. The method, designated as the multi-point single-step GPCE method or simply the MPSS-GPCE method, yields analytical formulae for computing the failure probability and its design sensitivities concurrently from a single stochastic simulation or analysis. For this reason, the MPSS-GPCE method affords the ability to solve industrial-scale problems with large design spaces. Numerical results stemming from mathematical functions or elementary engineering problems indicate that the new method provides more accurate or computationally efficient design solutions than existing methods or reference solutions. Furthermore, the shape design optimization of a jet engine compressor blade root was successfully conducted, demonstrating the power of the new method in confronting practical RBDO problems.

关键词： RBDO Reliability analysis GPCE Design sensitivity analysis score functions Stochastic optimization

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Arithmetic and Geometric Operators of Pentagonal Neutrosophic Number and its Application in Mobile Communication Service Based MCGDM Problem

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NEUTROSOPHIC SETS AND SYSTEMS 2020年 32卷 61-79页

作者： Chakraborty, Avishek Banik, Baisakhi Mondal, Sankar Prasad Alarm, Shariful Narula Inst Technol Dept Basic Sci Kolkata 700109 India Indian Inst Engn Sci & Technol Dept Math Sibpur 711103 Howrah India Techno Engn Coll Banipur Dept Basic Sci Habra 743233 W Bengal India MaulanaAbulKalam Azad Univ Technol Dept Appl Sci Nadia 721249 W Bengal India

In this paper, the theory of pentagonal neutrosophic number has been studied in a disjunctive frame of reference. Moreover, the dependency and independency of the membership functions for the pentagonal neutrosophic number are also classified here. Additionally, the development of a new score function and its computation have been formulated in distinct rational perspectives. Further, weighted arithmetic averaging operator and weighted geometric averaging operator in the pentagonal neutrosophic environment are introduced here using an influx of different logical & innovative thought. Also, a multi-criteria group decision-making problem (MCGDM) in a mobile communication system is formulated in this paper as an application in the pentagonal neutrosophic arena. Lastly, the sensitivity analysis portion reflects the variation of this noble work.

关键词： Pentagonal neutrosophic number Weighted arithmetic and geometric averaging operator score functions MCGDM

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Local search for weighted sum coloring problem

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APPLIED SOFT COMPUTING 2021年 106卷 107290-107290页

作者： Niu, Dangdang Liu, Bin Yin, Minghao Northwest A&F Univ Coll Informat Engn Yangling 712100 Shaanxi Peoples R China Guangxi Normal Univ Guangxi Key Lab Multisource Informat Min & Secur Guilin 541004 Peoples R China Northeast Normal Univ Sch Comp Sci & Informat Technol Changchun 130117 Peoples R China Northwest A&F Univ Shaanxi Key Lab Agr Informat Percept & Intelligen Yangling 712100 Shaanxi Peoples R China Northwest A&F Univ Minist Agr & Rural Affairs Key Lab Agr Internet Things Yangling 712100 Shaanxi Peoples R China

The weighted sum coloring problem (WSCP) is a weighted vertex coloring problem in which a weight is associated with each color. Its aim is to find a coloring of the vertices of a graph with the minimum sum of the costs of the used colors. The WSCP has important applications in the batch scheduling of distributed systems. In this paper, we obtain an integer linear programming (ILP) model for the WSCP, and design an efficient local search algorithm named LS-WSC to solve WSCP. To this end, we propose two ideas to make LS-WSC effective. Firstly, we design an adaptive strategy to change the number of color classes in current solution, which allows LS-WSC to search more feasible solution regions. Secondly, we design a greedy function and a tabu strategy, which make LS-WSC search in right direction. We also design a genetic algorithm GA-WSC to solve WSCP, which is used to experimentally evaluate the result of local search algorithms. The preliminary experimental results show that LSWSC outperforms the famous CPLEX on almost all instances, and is competitive with the approximate algorithm GREEDY on most benchmark instances with vertex number less than 200. However, the performance of LS-WSC is worse than GREEDY algorithm's on most benchmark instances with vertex number greater than 200. Overall, the performance of LS-WSC is only marginally better than GAWSC's. In order to improve the performance of LS-WSC, we use the configuration checking strategy to update the searching process of LS-WSC, and the new algorithm for solving WSCP is named as CCLS-WSC. The further experimental results show that CCLS-WSC algorithm outperforms the famous CPLEX, the approximate algorithm GREEDY, the genetic algorithm GA-WSC and LS-WSC on all benchmark instances. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Constrained optimization Weighted sum coloring Iterated local search score functions Configuration checking

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Integrating Differential Privacy in the Statistical Disclosure Control Tool-Kit for Synthetic Data Production

Integrating Differential Privacy in the Statistical Disclosu...

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International Conference on Privacy in Statistical Databases (PSD)

作者： Shlomo, Natalie Univ Manchester Sch Social Sci Social Stat Dept Humanities Bridgeford St G17A Manchester M13 9PL Lancs England

ISBN: (纸本)9783030575205;9783030575212

A standard approach in the statistical disclosure control tool-kit for producing synthetic data is the procedure based on multivariate sequential chained-equation regression models where each successive regression includes variables from the preceding regressions. The models depend on conditional Bayesian posterior distributions and can handle continuous, binary and categorical variables. Synthetic data are generated by drawing random values from the corresponding predictive distributions. Multiple copies of the synthetic data are generated and inference carried out on each of the data sets with results combined for point and variance estimates under well-established combination rules. In this paper, we investigate whether algorithms and mechanisms found in the differential privacy literature can be added to the synthetic data production process to raise the privacy standards used at National Statistical Institutes. In particular, we focus on a differentially private functional mechanism of adding random noise to the estimating equations of the regression models. We also incorporate regularization in the OLS linear models (ridge regression) to compensate for noisy estimating equations and bound the global sensitivity. We evaluate the standard and modified multivariate sequential chained-equation regression approach for producing synthetic data in a small-scale simulation study.

关键词： Sequential chained-equation regression models Functional mechanism score functions Ridge regression

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