An online classification EM algorithm based on the mixture model

Mixture model-based clustering is widely used in many applications. In certain real-time applications the rapid increase of data size with time makes classical clustering algorithms too slow. An online clustering algorithm based on mixture models is presented in the context of a real-time flaw-diagnosis application for pressurized containers which uses data from acoustic emission signals. The proposed algorithm is a stochastic gradient algorithm derived from the classification version of the EM algorithm (CEM). It provides a model-based generalization of the well-known online k-means algorithm, able to handle non-spherical clusters. Using synthetic and real data sets, the proposed algorithm is compared with the batch CEM algorithm and the online EM algorithm. The three approaches generate comparable solutions in terms of the resulting partition when clusters are relatively well separated, but online algorithms become faster as the size of the available observations increases.     

On linear lon-odds and estimation of discriminant coefficients

Fisher's Linear Discriminant Function Can be used to classify an individual who has sampled from one of two multivariate normal Populations. In the following, this function is viewed as the other given his data vector it is assumed that the Population means and common covariance matrix are unknown. The vector of discriminant coeffients β(p×1) is the gradient of posterior log-odds and certain of its lineqar functions are directional derivatives which have a practical meaning. Accordingly, we treat the problems of estimating several linear functions of β The usual estimatoes of these functions are scaled versions of the unbiased estmators. In this Paper, these estimators are domainated by explicit alterenatives under a quadratic loss function. we reduce the problem of estimating β to that of estimating the inverse convariance matrix.     

Testing the rate ratio under inverse sampling based on gradient statistic

Inverse sampling is widely applied in studies with dichotomous outcomes, especially when the subjects arrive sequentially or the response of interest is difficult to obtain. In this paper, we investigate the rate ratio test problem under inverse sampling based on gradient statistic with the asymptotic method and parametric bootstrap technique. The gradient statistic has many advantages, for example, it is simple to calculate and competitive with Wald-type, score and likelihood ratio tests in terms of local power. Numerical studies are carried out to evaluate the performance of our gradient test and the existing tests, namely Wald-type, score and likelihood ratio tests. The simulation results suggest that the gradient test based on the parametric bootstrap method has excellent type I error control and large powers even in small sample design. Two real examples, from a heart disease study and a drug comparison study, are applied to illustrate our methods.     

地方高校本科生研究与创新能力培养的模式与路径——以汉语言文学专业为例

"研究与创新能力"是指高校本科生在研究性学习基础上形成的初步科研创新能力。从高校人才培养目标和能力养成的渐进性规律出发,提出研究与创新能力培养的梯度模式,研究性教学与课题式培养是这一模式的关键环节。梯度模式的有效实施有必要引入评价机制。以答辩形式科学评定本科生的学业创造能力,是这一能力评定的实施路径。     

长江中游经济圈的建设——基于梯度推移过程的思考分析

长江中游经济圈是我国实现中部崛起最重要的区域之一。通过对梯度推移过程的思考分析,对长江中游的梯度发展模式做了初步探讨。旨在通过对梯度推移过程的分析来探讨长江中游经济圈建设的点轴开发研究,从而探讨长江中游经济圈的建设问题。     

一般约束极大极小值的梯度投影算法

对一类带等式、不等式约束的极大极小值问题进行了研究,将其转化为带等式、不等式约束的非线性规划问题,并利用梯度投影算法进行求解。该算法在有限步达到最优点或产生一系列点,且其极限点是最优点。该算法减少了计算量,克服了数值实现上的困难,证明了算法的收敛性。     

Small-sample likelihood inference in extreme-value regression models

We deal with a general class of extreme-value regression models introduced by Barreto-Souza and Vasconcellos [Bias and skewness in a general extreme-value regression model, Comput. Statist. Data Anal. 55 (2011), pp. 1379–1393]. Our goal is to derive an adjusted likelihood ratio statistic that is approximately distributed as χ² with a high degree of accuracy. Although the adjusted statistic requires more computational effort than its unadjusted counterpart, it is shown that the adjustment term has a simple compact form that can be easily implemented in standard statistical software. Further, we compare the finite-sample performance of the three classical tests (likelihood ratio, Wald, and score), the gradient test that has been recently proposed by Terrell [The gradient statistic, Comput. Sci. Stat. 34 (2002), pp. 206–215], and the adjusted likelihood ratio test obtained in this article. Our simulations favour the latter. Applications of our results are presented.     

Simple and Globally Convergent Methods for Accelerating the Convergence of Any EM Algorithm

Abstract.  The expectation-maximization (EM) algorithm is a popular approach for obtaining maximum likelihood estimates in incomplete data problems because of its simplicity and stability (e.g. monotonic increase of likelihood). However, in many applications the stability of EM is attained at the expense of slow, linear convergence. We have developed a new class of iterative schemes, called squared iterative methods (SQUAREM), to accelerate EM, without compromising on simplicity and stability. SQUAREM generally achieves superlinear convergence in problems with a large fraction of missing information. Globally convergent schemes are easily obtained by viewing SQUAREM as a continuation of EM. SQUAREM is especially attractive in high-dimensional problems, and in problems where model-specific analytic insights are not available. SQUAREM can be readily implemented as an 'off-the-shelf' accelerator of any EM-type algorithm, as it only requires the EM parameter updating. We present four examples to demonstrate the effectiveness of SQUAREM. A general-purpose implementation (written in R) is available.     

民族间农民婚嫁行为变迁的比较研究——来自湖北432户农户家庭的调查

研究发现,湖北农户家庭人口年龄分布呈现一种典型的"M"型,这预示着在未来10-20年湖北农村会有一次人口出生的高峰期,但新的生育高峰对未来人口快速增长的冲击程度明显要较上一高峰小得多.随着时代的变迁,受教育程度的提高,农民的婚嫁行为也发生着显著变化,主要表现在:初婚嫁年龄明显反弹,婚姻倾度显著增大,通婚半径也相应加长.尽管这一结论在民族间、村落间有些差异,但总的趋势是一致的.导致农民婚嫁行为变化的根源主要来自农村教育的普及.     

On a differential equation approach to the weighted orthogonal Procrustes problem

The weighted orthogonal Procrustes problem, an important class of data matching problems in multivariate data analysis, is reconsidered in this paper. It is shown that a steepest descent flow on the manifold of orthogonal matrices can naturally be formulated. This formulation has two important implications: that the weighted orthogonal Procrustes problem can be solved as an initial value problem by any available numerical integrator and that the first order and the second order optimality conditions can also be derived. The proposed approach is illustrated by numerical examples.