Change point determination for a multivariate process using a two-stage hybrid scheme

Effective identification of the change point of a multivariate process is an important research issue since it is associated with the determination of assignable causes which may seriously affect the underlying process. Most existing studies either use the maximum likelihood estimator (MLE) method or the machine learning (ML) method to estimate or identify the change point of a process. Typically, the MLE method may be criticized for its assumption that the process distribution is known, and the ML method may have the deficiency of using a large number of input variables in the modeling procedure. Diverging from existing approaches, this study proposes an integrated hybrid scheme to mitigate the difficulties of the MLE and ML methods. The proposed scheme includes four components: the logistic regression (LR) model, the multivariate adaptive regression splines (MARS) model, the support vector machine (SVM) classifier and the change point identification strategy. It performs three tasks in order to effectively identify the change point in a multivariate process. The initial task is to use the LR and MARS models to reduce and refine the whole set of input or explanatory variables. The remaining variables are then served as input variables to the SVM in the second task. The last task is to integrate use of the SVM outputs with our proposed identification strategy to determine the change point in a multivariate process. Experimental simulation results reveal that the proposed hybrid scheme is able to effectively identify the change point and outperform the typical statistical process control (SPC) chart alone and the single stage SVM methods.     

Accurate estimation with one order statistic

Estimating parameters from certain survival distributions is shown to suffer little loss of accuracy in the presence of left censoring. The variance of maximum likelihood estimates (MLE) in the presence of type II right-censoring is almost un-degraded if there also is heavy left-censoring when estimating certain parameters. In fact, if only a single data point, the rth recorded failure time, is available, the MLE estimates using the one data point are similar in variance to the estimates using all r failure points for all but the most extreme values of r. Analytic results are presented for the case of the exponential and Rayleigh distributions, to include the exact distributions of the estimators for the parameters. Simulated results are also presented for the gamma distribution. Implications in life test design and cost savings are explained as a result. Also computational considerations for finding analytic results as well as simulated results in a computer algebra system are discussed.     

Piecewise Linear Models with Guaranteed Closeness to the Data

This paper addresses the problem of piecewise linear approximation of point sets without any constraints on the order of data points or the number of model components (line segments). We point out two problems with the maximum likelihood estimate (MLE) that present serious drawbacks in practical applications. One is that the parametric models obtained using a classical MLE framework are not guaranteed to be close to data points. It is typically impossible, in this classical framework, to detect whether a parametric model fits the data well or not. The second problem is related to accurately choosing the optimal number of model components. We first fit a nonparametric density to the data points and use it to define a neighborhood of the data. Observations inside this neighborhood are deemed informative; those outside the neighborhood are deemed uninformative for our purpose. This provides us with a means to recognize when models fail to properly fit the data. We then obtain maximum likelihood estimates by optimizing the Kullback-Leibler Divergence (KLD) between the nonparametric data density restricted to this neighborhood and a mixture of parametric models. We prove that, under the assumption of a reasonably large sample size, the inferred model components are close to their ground-truth model component counterparts. This holds independently of the initial number of assumed model components or their associated parameters. Moreover, in the proposed approach, we are able to estimate the number of significant model components without any additional computation.     

Existence Test for Asynchronous Interval Iteration

In the search for regions that contain fixed points of a real function of several variables, tests based on interval calculations can be used to establish existence or non-existence of fixed points in regions that are examined in the course of the search. The search can e.g. be performed as a synchronous (sequential) interval iteration: In each iteration step all components of the iterate are calculated based on the previous iterate. In this case it is straight forward to base simple interval existence and non-existence tests on the calculations done in each step of the iteration. The search can also be performed as an asynchronous (parallel) iteration: Only a few components are changed in each step and this calculation is in general based on components from different previous iterates. For the asynchronous iteration it turns out that simple tests of existence and non-existence can be based on the component wise calculations done in the course of the iteration. These component wise tests are useful for parallel implementation of the search, since the tests can then be performed local to each processor and only when a test is successful does a processor communicate this result to other processors.     

一种优化的消失点估计方法及误差分析

空间一组平行直线在图像平面上所成的像的交点称为消失点. 消失点可以提供大量的场景三维结构信息. 本文提出一种新的优化的消失点估计方法. 该方法基于随机采样一致算法(Random sample consensus, RANSAC)对图像空间中的线段进行聚类, 通过最小化Sampson误差获得消失点的极大似然估计(Maximum likelihood estimation, MLE). 该方法不需要预知摄像机参数及直线的三维位置信息. 为了对该算法进行定量评估, 构造了基于反向传播的消失点误差传递模型. 实验结果验证了本文提出算法的有效性.     

Robust fitting of mixtures using the trimmed likelihood estimator

The maximum likelihood estimator (MLE) has commonly been used to estimate the unknown parameters in a finite mixture of distributions. However, the MLE can be very sensitive to outliers in the data. In order to overcome this the trimmed likelihood estimator (TLE) is proposed to estimate mixtures in a robust way. The superiority of this approach in comparison with the MLE is illustrated by examples and simulation studies. Moreover, as a prominent measure of robustness, the breakdown point (BDP) of the TLE for the mixture component parameters is characterized. The relationship of the TLE with various other approaches that have incorporated robustness in fitting mixtures and clustering are also discussed in this context.     

混合Ⅱ型截尾样本下简单步加试验的统计分析

将Bootstrap方法引入到加速寿命试验中,在产品寿命服从Rayleigh分布的情形下,研究混合Ⅱ型截尾简单步加试验的可靠性统计分析问题,获得了参数的极大似然估计和区间估计,给出了正常应力水平下可靠度、失效率、平均寿命等可靠性指标的估计方法,最后利用Monte-Carlo方法验证了结论的正确性和可行性。     

Estimation, principal components and hamiltonian systems

In this paper we show how symplectic geometry can be used to analyse a fundamental problem in estimation theory — the fitting of lines and planes to a data set in n dimensions. Symplectic methods yield information not only on the critical point structure of the Maximum Likelihood Estimation (MLE) function (see Byrnes and Willems [7]), but also on the asymmetries in the distribution of the data points in n-space.     

自适应AP选择无线室内定位算法

针对接收信号强度的无线室内定位算法中无线接入点（AP）具有相关性和区域性问题,提出自适应AP选择无线室内定位算法。针对AP具有相关性,在线阶段提出基于互信息和信息熵的AP选择算法,联合衡量AP子集内所有AP间的相关性,搜索包含有效位置信息最多的AP子集。对于AP的区域性问题,离线阶段对参考点高斯邻域内原始RSS采样数据进行最小二乘高斯曲线拟合,并提出优先度函数衡量AP性能。最后,采用KL散度实现待定位节点位置估计。与WKNN、MLE算法相比,该算法有效地提高了无线室内定位精度。     

Inference for a simple step-stress model with competing risks for failure from the exponential distribution under time constraint

In reliability analysis, accelerated life-testing allows for gradual increment of stress levels on test units during an experiment. In a special class of accelerated life tests known as step-stress tests, the stress levels increase discretely at pre-fixed time points, and this allows the experimenter to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. Moreover, when a test unit fails, there are often more than one fatal cause for the failure, such as mechanical or electrical. In this article, we consider the simple step-stress model under time constraint when the lifetime distributions of the different risk factors are independently exponentially distributed. Under this setup, we derive the maximum likelihood estimators (MLEs) of the unknown mean parameters of the different causes under the assumption of a cumulative exposure model. Since it is found that the MLEs do not exist when there is no failure by any particular risk factor within the specified time frame, the exact sampling distributions of the MLEs are derived through the use of conditional moment generating functions. Using these exact distributions as well as the asymptotic distributions, the parametric bootstrap method, and the Bayesian posterior distribution, we discuss the construction of confidence intervals and credible intervals for the parameters. Their performance is assessed through Monte Carlo simulations and finally, we illustrate the methods of inference discussed here with an example.     

期望最大算法及其应用(1)

EM算法是实现极大似然估计的一种有效方法,主要用于非完全数据的参数估计。它通过假设隐变量的存在,极大地简化了似然方程;对于一些特殊的参数估计问题,利用EM算法也很容易实现。而极大似然估计是一种常用的参数估计方法,EM算法使其应用更加广泛。文章从应用者的角度出发,内容是自包含的。     

基于小波变换多维时间序列最新变化点检测

现代数据科学中存在大量的多维时间序列数据,检测多维时间序列中的最新变化点对于短期预测很重要。一种改进的方法被提出,以检测此类多维时间序列数据中最新变化点。通过使用小波变换,将多维时间序列中的变化点检测问题转化为相对较容易的多维面板数据中的变化点检测问题。该方法旨在跨时间序列合并信息,以便优先推断多个序列中同一时间点的最...     

On NURBS algorithms using tangent cones

This paper considers tangent cones for NURBS surfaces. The first part gives new bounds for the tangent field, which extends the results of [Wang, G.-J., Sederberg, T.W., Saito, T., 1997. Partial derivatives of rational Bézier surfaces. Computer Aided Geometric Design 14, 377–381] to NURBS surfaces. In particular, if the weights of the NURBS surface have a tensor product structure, the tangent cones are spanned by the differences of the control points in one direction. The second part revisits uniqueness criteria for intersections between curves and surfaces and non-existence criteria for self-intersections, which are based on tangent cones. Using a unified proof, we reprove known theorems and deduce new criteria, e.g. for the non-existence of self-intersections.     

二值图像中基于陡变度的拐角点集检测方法

文章认为目前流行的拐角点检测方法有三个缺点：一是在数字图像空间中曲率存在计算误区,因而用曲率定位拐角点不合适;二是导致图像边缘产生拐角的不仅有单点,还有点集,因此不求拐角点集是不妥的;三是大曲率点不等价于拐角点。鉴于此,文章提出一种基于陡变度的拐角点集检测方法,其思想是：在二值图像中,图像边缘可看成是一维流形,陡变点集将一维流形分割成大小不等的光滑流形段,如果光滑流形通过该陡变点集后方向发生急剧改变,则此陡变点集是拐角点集。通过实验对比,文章中提出的算法检测结果优于目前流行算法的检测结果。     

二值量测误差FIR系统参数迭代辨识

本文考虑了量测数据为二值输出且含量测误差的一类有限脉冲响应(FIR)系统的参数辨识问题, 其中, 量测误差使得二值型量测值有一定概率得到相反的取值. 首先, 对所考虑的 FIR 系统, 给出了参数的极大似然估计(MLE), 证明了在噪声满足一定正则条件下MLE的强收敛性和渐近正态性. 此外, 通过分析似然函数的性质, 给出了一种基于期望最大化(EM)方法的MLE迭代求解算法. 为适应更一般的量测误差情形, 给出了带投影的迭代求解算法, 并从理论上证明了迭代估计序列的有界性. 进一步, 在给定数量的观测下, 得到了似然函数具有唯一最大值点的必要和充分条件, 并在持续激励输入条件下, 证明了迭代估计误差以指数速度收敛到零. 最后, 利用数值模拟结果验证了所提出算法的有效性.     

一种反延时电路的可靠性评估

针对反延时难以实现的状况,提出了用延时电路并联实现反延时的方法,并用极大似然法和经验Bayes法讨论了系统可靠性评估问题,给出了系统失效率、可靠度和平均寿命等可靠性指标的估计。利用计算机Monte-Carlo随机模拟的方法对可靠性指标的Bayes估计和极大似然估计进行比较,结果表明,经验Bayes估计优于极大似然估计。     

回归模型中变点识别的一种稳健方法

变点识别是数据分析中一个非常重要的研究内容.文中针对目前变点识别研究中忽略了方法的稳健性,未能充分考虑异常值的影响的不足,提出利用一种高度稳健的回归类混合分解算法来识别变点.该方法从混合回归模型的角度,将含有变点的回归模型看作回归类的混合,通过逐步挖掘数据集中的回归类,并对排序后的回归类进行分析,进而确定变点的位置及个数.数值模拟表明,在识别变点的过程中无须预先指定变点的数目,并且具有高度的稳健性和有效性.     

Fundamental properties and performance of conventional bearings-only target motion analysis

This paper considers the problem of estimating the position and velocity of an object from noise corrupted bearing measurements obtained by a single moving observation platform. The process is inherently nonlinear and exhibits unusual observability properties that are geometry-dependent. A maximum likelihood estimate (MLE) of the target motion analysis solution is developed and its performance analyzed. A comparison is drawn between the MLE and two previously reported methods, a nonlinear modified-instrumental variable estimate (MIV) and the pseudo-linear estimate (PLE). Both the MIV and PLE are shown to derive from approximations to the nonlinear measurement equation and therefore share some common properties with the MLE. The limits on performance that can be expected from processing bearing data are detailed. Specifically, for long range-to-baseline geometries, approximate expressions for the Cramer-Rao bound are derived. Extension of the results to the practical filters approximately predicts numerically observed behavior. For less restrictive geometries, bounds are presented. Incorporation of a target speed constraint on the MLE results in a transition to a lower dimensional problem as noise level and range increases. Monte Carlo experimental results are presented and the improvements realized by the MLE techniques are evident.     

基于尺度不变特征点的抗几何攻击水印算法

利用基于尺度空间理论的特征点检测方法,检测出的特征点不但在大尺度缩放变换下重复率高,而且每个特征点的特征尺度随图像缩放尺度等比例变化。以特征尺度及特征点相对位置作为参考,生成一种几何变换自适应图形作为水印嵌入的区域。随着特征点相对位置的变化,自适应图形会产生相应变化,达到抗几何攻击的目的。实验表明,该算法能有效抵抗各种几何攻击,具有较好的性能。     

Point and interval estimation for extreme-value regression model under Type-II censoring

Inference for the extreme-value regression model under Type-II censoring is discussed. The likelihood function and the score functions of the unknown parameters are presented. The asymptotic variance-covariance matrix is derived through the inverse of the expected Fisher information matrix. Since the maximum likelihood estimators (MLE) cannot be solved analytically, an approximation to these MLE are proposed. The variance-covariance matrix of these approximate estimators is also derived. Next, confidence intervals are proposed based on the MLE and the approximate estimators. An extensive simulation study is carried out in order to study the bias and variance of all these estimators. We also examine the coverage probabilities as well as the expected widths of the confidence intervals. Finally, all the inferential procedures discussed here are illustrated with practical data.