损失分布拟合的仿真方法

风险损失现象是现代经济主体面临的普遍存在的现象。其损失的概率分布存在计算困难问题,该文给出了一种随机仿真的方法近似计算其损失概率分布,该方法在一种保险业务数据分析系统中得以应用。     

Solving system-level synthesis problem by a multi-objective estimation of distribution algorithm

In this paper, the system-level synthesis problem (SLSP) is modeled as a multi-objective mode-identity resource-constrained project scheduling problem with makespan and resource investment criteria (MOMIRCPSP-MS-RI). Then, a hybrid Pareto-archived estimation of distribution algorithm (HPAEDA) is presented to solve the MOMIRCPSP-MS-RI. To be specific, the individual of the population is encoded as the activity-mode-priority-resource list (AMPRL), and a hybrid probability model is used to predict the most promising search area, and a Pareto archive is used to preserve the non-dominated solutions that have been explored, and another archive is used to preserve the solutions for updating the probability model. Moreover, specific sampling mechanism and updating mechanism for the probability model are both provided to track the most promising search area via the EDA-based evolutionary search. Finally, the modeling methodology and the HPAEDA are tested by an example of a video codec based on the H.261 image compression standard. Simulation results and comparisons demonstrate the effectiveness of the modeling methodology and the proposed algorithm.     

On the probability distribution of faults in complex software systems

ContextThere are several empirical principles related to the distribution of faults in a software system (e.g. the Pareto principle) widely applied in practice and thoroughly studied in the software engineering research providing evidence in their favor. However, the knowledge of the underlying probability distribution of faults, that would enable a systematic approach and refinement of these principles, is still quite limited.ObjectiveIn this paper we study the probability distribution of faults detected during verification in four consecutive releases of a large-scale complex software system for the telecommunication exchanges. This is the first such study analyzing closed software system, replicating two previous studies for open source software.MethodWe take into consideration the Weibull, lognormal, double Pareto, Pareto, and Yule–Simon probability distributions, and investigate how well these distributions fit our empirical fault data using the non-linear regression.ResultsThe results indicate that the double Pareto distribution is the most likely choice for the underlying probability distribution. This is not consistent with the previous studies on open source software.ConclusionThe study shows that understanding the probability distribution of faults in complex software systems is more complicated than previously thought. Comparison with previous studies shows that the fault distribution strongly depends on the environment, and only further replications would make it possible to build up a general theory for a given context.     

基于概率统计的软件测试方法研究

为了缩短软件测试周期,本文把马尔可夫链模型运用于软件可靠性测试中,提出了这一技术进行软件可靠性测试的方法。在测试过程中使用了新的评判准则分析测试结果,通过实例证明了该评判准则的实用性和有效性。     

Level estimation, classification and probability distribution architectures for trading the EUR/USD exchange rate

Dunis and Williams (Derivatives: use, trading and regulation 8(3):211–239, 2002; Applied quantitative methods for trading and investment. Wiley, Chichester, 2003) have shown the superiority of a Multi-layer perceptron network (MLP), outperforming its benchmark models such as a moving average convergence divergence technical model (MACD), an autoregressive moving average model (ARMA) and a logistic regression model (LOGIT) on a Euro/Dollar (EUR/USD) time series. The motivation for this paper is to investigate the use of different neural network architectures. This is done by benchmarking three different neural network designs representing a level estimator, a classification model and a probability distribution predictor. More specifically, we present the Mulit-layer perceptron network, the Softmax cross entropy model and the Gaussian mixture model and benchmark their respective performance on the Euro/Dollar (EUR/USD) time series as reported by Dunis and Williams. As it turns out, the Multi-layer perceptron does best when used without confirmation filters and leverage, while the Softmax cross entropy model and the Gaussian mixture model outperforms the Multi-layer perceptron when using more sophisticated trading strategies and leverage. This might be due to the ability of both models using probability distributions to identify successfully trades with a high Sharpe ratio.

Dwelling time probability density distribution of instances in a workflow model

This paper presents a method to judge whether a business process is successful or not. A business process is deemed successful if a large enough proportion of instances dwell in a workflow (wait and be executed) for less than given period. By analyzing instances’ dwelling time distribution in a workflow, the proportion of instances which dwell in the workflow for less than any given period will be achieved. The performance analysis of workflow model plays an important role in the research of workflow techniques and efficient implementation of workflow management. It includes the analysis of instances’ dwelling time distribution in a workflow process. Multidimensional workflow net (MWF-net) includes multiple timing workflow nets (TWF-nets) and the organization and resource information. The processes of transaction instances form a queuing model in which the transaction instances act as customers and the resources act as servers. The key contribution of this paper is twofold. First, this paper presents a theoretical method to calculate the instances’ dwelling time probability density in a workflow where the activities are structured and predictable. Second, by this method the analysis of instances’ dwelling time distribution and satisfactory degree based on dwelling time can be achieved. The service time of an instance is specified by the firing delay of the corresponding transition (executing time of the corresponding activity). It is assumed that the service request (processing of a transaction instance) arrives with exponentially distributed inter-arrival times and the firing delay of a transition (executing time of the corresponding activity) follows exponential distribution. Then, the instances’ dwelling time probability density analysis in each activity and each control structure of a workflow model is performed. According to the above results a method is proposed for computing the instances’ dwelling time probability density in a workflow model. Finally an example is used to show that the proposed method can be effectively utilized in practice.     

基于概率分布估计的混合采样算法

在类别不均衡的数据中, 类间和类内不均衡性问题都是导致分类性能下降的重要因素. 为了提高不均衡数据集下分类算法的性能, 提出一种基于概率分布估计的混合采样算法. 该算法依据数据概率分别对每个子类进行采样以保证类内的均衡性; 并扩大少数类的潜在决策域和减少多数类的冗余信息, 从而同时从全局和局部两个角度改善数据的平衡性. 实验结果表明, 该算法提高了传统分类算法在不均衡数据下的分类性能.

     

An effective estimation of distribution algorithm for the multi-mode resource-constrained project scheduling problem

In this paper, an estimation of distribution algorithm (EDA) is proposed to solve the multi-mode resource-constrained project scheduling problem (MRCPSP). In the EDA, the individuals are encoded based on the activity-mode list (AML) and decoded by the multi-mode serial schedule generation scheme (MSSGS), and a novel probability model and an updating mechanism are proposed for well sampling the promising searching region. To further improve the searching quality, a multi-mode forward backward iteration (MFBI) and a multi-mode permutation based local search method (MPBLS) are proposed and incorporated into the EDA based search framework to enhance the exploitation ability. Based on the design-of-experiment (DOE) test, suitable parameter combinations are determined and some guidelines are provided to set the parameters. Simulation results based on a set of benchmarks and comparisons with some existing algorithms demonstrate the effectiveness of the proposed EDA.     

几何学概率的无线传感器网络能耗估计模型

针对无线传感器网络能耗这一问题,提出了一种基于几何学概率的能耗估计模型.以节点的状态转换为基础,建立了基于半Markov链的节点能耗模型,并引入概率分布函数的概念.从传感器节点随机分布出发,假定节点之间可以相互通信,分别对在单个正六边形和相邻两个正六边形内的节点随机分布进行研究,推导得出能耗估计模型.仿真结果表明:该模型可以实现网络能耗的准确估计.     

Optimization by estimation of distribution with DEUM framework based on Markov random fields

This paper presents a Markov random field (MRF) approach to estimating and sampling the probability distribution in populations of solutions.The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields (DEUM).DEUM is a subclass of estimation of distribution algorithms (EDAs) where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph.The focus of this paper will be on describing the three main characteristics of DEUM framework,which distinguishes it from the traditional EDA.They are:1) use of MRF models,2) fitness modeling approach to estimating the parameter of the model and 3) Monte Carlo approach to sampling from the model.     

Chatter detection based on probability distribution of wavelet modulus maxima

This paper presents a statistical chatter detection method. The methodology is based on the study of discrete wavelet transform (DWT) scheme and statistical analysis of wavelet transform modulus maxima (WTMM). Wavelet transform modulus maxima is used to describe any point where wavelet transform of a signal is locally maximal at corresponding time location. Meanwhile, due to the noisy machining environment, a wavelet-based de-noising method including a hybrid thresholding function and a level-dependent universal threshold rule is proposed. A non-dimensional chatter index varying between 0 and 1 is designed based on the statistical analysis of the WTMM. The main advantages of the proposed chatter index include that: (a) its variation range is independent of process parameters and machining systems, and (b) its threshold value is much less susceptible to cutting condition changes since its value is in relative term. As a result, the chatter index could be used for different machining processes without the time-consuming recalibration process.     

A hybrid estimation of distribution algorithm for solving the resource-constrained project scheduling problem

In this paper, a hybrid estimation of distribution algorithm (HEDA) is proposed to solve the resource-constrained project scheduling problem (RCPSP). In the HEDA, the individuals are encoded based on the extended active list (EAL) and decoded by serial schedule generation scheme (SGS), and a novel probability model updating mechanism is proposed for well sampling the promising searching region. To further improve the searching quality, a Forward-Backward iteration (FBI) and a permutation based local search method (PBLS) are incorporated into the EDA based search to enhance the exploitation ability. Simulation results based on benchmarks and comparisons with some existing algorithms demonstrate the effectiveness of the proposed HEDA.     

Markov双曲迭代函数系参数与吸引子关系的研究

1 引言迭代函数系IFS(Iterated Function Systems),是混沌分形理论研究的一个重要部分,其理论与方法是分形自然景观模拟及分形图像压缩的理论基础。1985年,Williams和Hutchinson开创了分形几何中IFS的研究,建立了IFS的一般基础理论;M.F.Barnsley和S.Demko的进一步工作使得这一方法成为构造任意维数分形集方便、有效的方法,并将之应用到图像的压缩与处理,使得该方法引起人们的关注。由于普通     

Graphical model based continuous estimation of distribution algorithm

In this paper, a new estimation of distribution algorithm is introduced. The goal is to propose a method that avoids complex approximations of learning a probabilistic graphical model and considers multivariate dependencies between continuous random variables. A parallel model of some subgraphs with a smaller number of variables is learned as the probabilistic graphical model. In each generation, the joint probability distribution of the selected solutions is estimated using a Gaussian Mixture model. Then, learning the graphical model of dependencies among random variables and sampling are done separately for each Gaussian component. In the learning step, using the selected solutions of each Gaussian mixture component, the structure of a Markov network is learned. This network is decomposed to maximal cliques and a clique graph. Then, complete Bayesian network structures are learned for these subgraphs using an optimization algorithm. The proposed optimization problem is a 0–1 constrained quadratic programming which finds the best permutation of variables. Then, sampling is done from each Bayesian network of each Gaussian component. The introduced method is compared with the other network-based estimation of distribution algorithms for optimization of continuous numerical functions.     

Research on the unbiased probability estimation of error-correcting output coding

Supervised classification based on error-correcting output codes (ECOC) is an efficient method to solve the problem of multi-class classification, and how to get the accurate probability estimation via ECOC is also an attractive research direction. This paper proposed three kinds of ECOC to get unbiased probability estimates, and investigated the corresponding classification performance in depth at the same time. Two evaluating criterions for ECOC that has better classification performance were concluded, which are Bayes consistence and unbiasedness of probability estimation. Experimental results on artificial data sets and UCI data sets validate the correctness of our conclusion.     

A bi-population based estimation of distribution algorithm for the flexible job-shop scheduling problem

In this paper, an effective bi-population based estimation of distribution algorithm (BEDA) is proposed to solve the flexible job-shop scheduling problem (FJSP) with the criterion to minimize the maximum completion time (makespan). The BEDA stresses the balance between global exploration and local exploitation. In the framework of estimation of distribution algorithm, two sub-populations are used to adjust the machine assignment and operation sequence respectively with a splitting criterion and a combination criterion. At the initialization stage, multiple strategies are utilized in a combination way to generate the initial solutions. At the global exploration phase, a probability model is built with the superior population to generate the new individuals and a mechanism is proposed to update the probability model. At the local exploitation phase, different operators are well designed for the two sub-populations to generate neighbor individuals and a local search strategy based on critical path is proposed to enhance the exploitation ability. In addition, the influence of parameters is investigated based on Taguchi method of design of experiment, and a suitable parameter setting is determined. Finally, numerical simulation based on some widely used benchmark instances is carried out. The comparisons between BEDA and some existing algorithms as well as the single-population based EDA demonstrate the effectiveness of the proposed BEDA in solving the FJSP.     

考虑门店持有库存的同城整车配送优化模型

研究连锁零售企业配送中心和连锁门店构成的二级库存系统,考虑门店持有库存对配送中心库存的影响,以门店客户服务水平对系统总成本进行约束优化,建立了连锁零售配送中心同城整车配送库存优化模型,并给出了一个具体的的算例。     

Improving the estimation of Kendall's tau when censoring affects only one of the variables

This paper considers the estimation of Kendall's tau for bivariate data (X,Y) when only Y is subject to right-censoring. Although τ is estimable under weak regularity conditions, the estimators proposed by Brown et al. [1974. Nonparametric tests of independence for censored data, with applications to heart transplant studies. Reliability and Biometry, 327-354], Weier and Basu [1980. An investigation of Kendall's τ modified for censored data with applications. J. Statist. Plann. Inference 4, 381-390] and Oakes [1982. A concordance test for independence in the presence of censoring. Biometrics 38, 451-455], which are standard in this context, fail to be consistent when τ≠0 because they only use information from the marginal distributions. An exception is the renormalized estimator of Oakes [2006. On consistency of Kendall's tau under censoring. Technical Report, Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY], whose consistency has been established for all possible values of τ, but only in the context of the gamma frailty model. Wang and Wells [2000. Estimation of Kendall's tau under censoring. Statist. Sinica 10, 1199-1215] were the first to propose an estimator which accounts for joint information. Four more are developed here: the first three extend the methods of Brown et al. [1974. Nonparametric tests of independence for censored data, with applications to heart transplant studies. Reliability and Biometry, 327-354], Weier and Basu [1980, An investigation of Kendall's τ modified for censored data with applications. J. Statist. Plann. Inference 4, 381-390] and Oakes [1982, A concordance test for independence in the presence of censoring. Biometrics 38, 451-455] to account for information provided by X, while the fourth estimator inverts an estimation of Pr(Y_i?y|X_i=x_i,Y_i>c_i) to get an imputation of the value of Y_i censored at C_i=c_i. Following Lim [2006. Permutation procedures with censored data. Comput. Statist. Data Anal. 50, 332-345], a nonparametric estimator is also considered which averages the obtained from a large number of possible configurations of the observed data (X₁,Z₁),…,(X_n,Z_n), where Z_i=min(Y_i,C_i). Simulations are presented which compare these various estimators of Kendall's tau. An illustration involving the well-known Stanford heart transplant data is also presented.     

Exact recording of Metropolis–Hastings-class Monte Carlo simulations using one bit per sample

The Metropolis–Hastings (MH) algorithm is the prototype for a class of Markov chain Monte Carlo methods that propose transitions between states and then accept or reject the proposal. These methods generate a correlated sequence of random samples that convey information about the desired probability distribution. Deciding how this information gets recorded is an important step in the practical design of MH-class algorithm implementations. Many implementations discard most of this information in order to reduce demands on storage capacity and disk writing throughput. Here, we describe how recording a bit string containing 1?s for acceptance and 0?s for rejection allows the full sample sequence to be recorded with no information loss, facilitating decoupling of simulation design from the constraints of data analysis. The recording uses only one bit per sample, which is an upper bound on the rate at which information about the desired distribution is acquired. We also demonstrate the method and quantify its benefits on a nontrivial colloidal system of charged particles in the canonical ensemble. The method imposes no restrictions on the system or simulation design and is compatible with descendants of the MH algorithm.     

分布估计算法研究进展

作为一种新颖的基于概率模型的进化算法,近年来分布估计算法（EDA）得到了广泛的研究和发展.在介绍分布估计算法原理和特点的基础上,重点综述了近些年分布估计算法的研究进展,包括改进概率模型、保持种群多样性以及设计混合算法,进而总结了分布估计算法在理论及应用方面的研究现状,最后提出了有待进一步研究的若干方向和内容.