On the existence of a positive realization

The positive realization problem for linear systems is to find conditions, for a given transfer function with nonnegative impulse response, to have a realization such that the resulting system is a positive system. Recently, it has been shown that, under a mild assumption on the long-term behaviour of the impulse response, this problem is related to the maximum modulus poles only. In this paper necessary and sufficient conditions for positive realizability of discrete-time systems are given. They show that also nondominant poles play a role in the most general case. Positive realizability conditions for the continuous-time case are also given.     

Predicting social cues during online discussions: Effects of evaluations and knowledge content

This study examined whether evaluations (agreements, disagreements), knowledge content (new ideas, justifications), or social cues (SCs) in recent messages affected a current message’s positive or negative SC during asynchronous, online discussions. Using statistical discourse analysis, we modeled 894 messages by 183 participants on 60 high school mathematics topics (typically eight people posted per topic) on a mathematics problem solving website not connected to any class or school. Results showed that recent agreements increased the likelihood of positive SC, whereas justifications reduced it. Disagreements increased the likelihood of negative SC, whereas new ideas reduced it. Meanwhile, recent positive or negative SCs did not affect the likelihood of a subsequent SC. Together, these results suggest that judicious use of positive SCs rather than negative SCs during disagreements can help students both construct knowledge and maintain social relationships.     

独立摄动参数不确定线性系统的正实控制

考虑了一类范数有界参数不确定线性系统的鲁棒正实性分析和设计问题，其中参数不确定性是独立摄动的．通过构造增广系统将不确定系统的鲁棒正实分析和控制问题转化为确定系统的情形，给出了鲁棒正实分析问题的线性矩阵不等式解法，导出了输出反馈控制器的存在条件．所得结论将范数有界参数不确定系统的鲁棒正实分析和控制的现有结果推进了一步．     

Averaging, maximum penalized likelihood and Bayesian estimation forimproving Gaussian mixture probability density estimates

We apply the idea of averaging ensembles of estimators to probability density estimation. In particular, we use Gaussian mixture models which are important components in many neural-network applications. We investigate the performance of averaging using three data sets. For comparison, we employ two traditional regularization approaches, i.e., a maximum penalized likelihood approach and a Bayesian approach. In the maximum penalized likelihood approach we use penalty functions derived from conjugate Bayesian priors such that an expectation maximization (EM) algorithm can be used for training. In all experiments, the maximum penalized likelihood approach and averaging improved performance considerably if compared to a maximum likelihood approach. In two of the experiments, the maximum penalized likelihood approach outperformed averaging. In one experiment averaging was clearly superior. Our conclusion is that maximum penalized likelihood gives good results if the penalty term in the cost function is appropriate for the particular problem. If this is not the case, averaging is superior since it shows greater robustness by not relying on any particular prior assumption. The Bayesian approach worked very well on a low-dimensional toy problem but failed to give good performance in higher dimensional problems.     

Numerical method of estimating the maximal likelihood of a smooth parametric manifold

Consideration was given to the numerical estimation of the maximum likelihood for the parameter vector describing a smooth manifold. Estimation is based on the results of observing motion of a dynamic plant whose trajectory belongs to this manifold and is measured with random errors having normal distribution with certain parameters. Application of the maximum likelihood method to such problems gives rise to the problem of nonlinear highdimensionality programming. Some constructive analytical results obtained enable significant reduction in the problem dimensionality. The problem of identifying the plane of motion of a dynamic plant was examined.     

Two algorithms for estimating test complexity levels

We study the problem of estimating the complexity levels of test problems and levels of preparation of the students that arises in learning management systems. To solve the problem, we propose two algorithms for processing test results. The first algorithm is based on the assumption that random answers of the test takers are described by a logistic distribution. To compute test problem complexities and levels of preparation of the students, we use the maximum likelihood method and the quasi-Newton Broyden–Fletcher–Goldfarb–Shanno optimization method, where the likelihood function is constructed in a special way based on Rasch’s model. The second algorithm is heuristic and is based on recurrent recomputation of initial estimates obtained by adding up the positive answers of students separately by columns and rows of the matrix of answers, where columns correspond to answers of all students for a specific test, and rows correspond to answers of a specific student for all tests. We consider an example where we compare the results of applying the proposed algorithms.     

一种半监督机器学习的EM算法改进方法

EM(Expectation Maximization)算法是含有隐变量(latent variable)的概率参数模型最大似然估计、极大后验概率估计最有效的算法,但很容易进入局部最优现象,对此提出基于半监督机器学习机制的EM算法.本文方法是在最大似然函数中加入惩罚最小二乘因子,同时引入非负约束作为先验信息,结合半监督机器学习方法,将EM算法改进转化为最小化求解问题,再采用最大似然方法求解EM模型,有效估计了混合矩阵和高斯混合模型参数,实现EM算法的改进.仿真结果表明,该方法能够很好地解决了EM算法容易局部最优化问题.     

Realization of continuous-time positive linear systems

Positive linear systems are used in biomathematics, economics, and other research areas. For discrete-time positive linear systems, part of the realization problem has been solved. In this paper the solution of the corresponding problem for continuous-time positive linear systems will be presented, which can be deduced from that of the discrete-time case by a transformation. Sufficient and necessary conditions for the existence of a positive realization are presented. To solve the problem of minimality, the solution of the factorization of positive matrices is needed.     

Solvability of static output-feedback stabilization for LTI positive systems

This paper addresses the stabilization problem of positive linear systems which have nonnegative states whenever the initial conditions are nonnegative. The synthesis of static output-feedback controllers that ensure the positivity and asymptotic stability of the closed-loop system is investigated. It is shown that this important problem is completely solved for single-input and single-output positive systems. The proposed approach can be applied to multi-input positive systems with controllers having one rank gains. All the provided conditions are necessary and sufficient and can be solved in terms of Linear Programming.     

Positive vectors clustering using inverted Dirichlet finite mixture models

In this work we present an unsupervised algorithm for learning finite mixture models from multivariate positive data. Indeed, this kind of data appears naturally in many applications, yet it has not been adequately addressed in the past. This mixture model is based on the inverted Dirichlet distribution, which offers a good representation and modeling of positive non-Gaussian data. The proposed approach for estimating the parameters of an inverted Dirichlet mixture is based on the maximum likelihood (ML) using Newton Raphson method. We also develop an approach, based on the minimum message length (MML) criterion, to select the optimal number of clusters to represent the data using such a mixture. Experimental results are presented using artificial histograms and real data sets. The challenging problem of software modules classification is investigated within the proposed statistical framework, also.     

丢失数据下的条件极大似然辨识

针对仿射结构形式在丢失数据下的条件极大似然辨识问题, 首先引入交换矩阵将原随机矢量分解成观测和丢失部分; 然后确定出观测数据在丢失数据下的条件均值和条件方差, 以此建立条件似然函数; 进而从理论上给出了条件极大似然函数关于未知参数矢量、未知白噪声方差值和丢失数据的求导公式, 并从工程上给出一种可分离的优化算法; 最后通过仿真算例验证了该辨识方法的有效性.     

Effective Maximum Likelihood Grid Map With Conflict Evaluation Filter Using Sonar Sensors

In this paper, we address the problem of building a grid map using cheap sonar sensors, i.e., the problem of using erroneous sensors when seeking to model an environment as accurately as possible. We rely on the inconsistency of information among sonar measurements and the sound pressure of the waves from the sonar sensors to develop a new method of detecting incorrect sonar readings, which is called the conflict evaluation with sound pressure (CEsp). To fuse the correct measurements into a map, we start with the maximum likelihood (ML) approach due to its ability to manage the angular uncertainty of sonar sensors. However, since this approach suffers from heavy computational complexity, we convert it to a light logic problem called the maximum approximated likelihood (MAL) approach. Integrating the MAL approach with the CEsp method results in the conflict evaluated maximum approximated likelihood (CEMAL) approach. The CEMAL approach generates a very accurate map that is close to the map that would be built by accurate laser sensors and does not require adjustment of parameters for various environments.      

基于最大似然估计的加权质心定位算法

为解决无线传感器网络中节点自身定位问题,针对接收信号强度指示（received signal strength indication,RSSI）测距误差大和质心定位算法精度低的问题,提出一种基于最大似然估计的加权质心定位算法．首先通过计算将估计距离与实际距离之间的最大似然估计值作为权值,然后在权值模型中,引进一个参数k优化未知节点周围锚节点分布,最后计算出未知节点的位置并加以修正．仿真结果表明,基于最大似然估计的加权质心算法具有定位精度高和成本低的特点,优于基于距离倒数的质心加权和基于RSSI倒数的质心加权算法,适用于大面积的室内定位．     

基于类别相关近邻子空间的最大似然稀疏表示鲁棒图像识别算法

为了构建一个快速鲁棒的图像识别算法, 提出基于类别相关近邻子空间的最大似然稀疏表示图像识别算法. 考虑到每个测试样本的不同分布特性及训练样本选择的类别代表性原则, 不再将所有训练样本作为稀疏表示的字典, 而是基于距离相近准则选择合适子空间, 从每个类别中选取自适应数量的局部近邻构成新的字典, 在减少训练样本的同时保留了稀疏表示原有的子空间结构. 然后基于最大似然稀疏表示识别方法, 将稀疏表示的保真度表示为余项的最大似然函数, 并将识别问题转化为加权的稀疏优化问题. 在公用人脸与数字识别数据库上的实验证明该算法的合理性, 提高识别速度的同时保证了识别精度和算法的鲁棒性, 特别是对于遮挡与干扰图像具有较好的适应性.     

基于极大似然准则和最大期望算法的自适应UKF 算法

针对噪声先验统计特性未知情况下的非线性系统状态估计问题,提出了基于极大似然准则和 最大期望算法的自适应无迹卡尔曼滤波(Unscented Kalman filter, UKF) 算法.利用极大似然准则构造含有噪声统计特性的对数似然函数,通 过最大期望算法将噪声估计问题转化为对数似然函数数学期望极大化问题,最终得到带次优递 推噪声统计估计器的自适应UKF算法.仿真分析表明,与传统UKF算法相比,提出的自适应UKF算法 有效克服了传统UKF算法在系统噪声统计特性未知情况下滤波精度下降的问题,并实现了系统噪 声统计特性的在线估计.     

Fuzzy clustering to estimate the parameters of block mixture models

Finite mixture models are being increasingly used to provide model-based cluster analysis. To tackle the problem of block clustering which aims to organize the data into homogeneous blocks, recently we have proposed a block mixture model; we have considered this model under the classification maximum likelihood approach and we have developed a new algorithm for simultaneous partitioning based on the classification EM algorithm. From the estimation point of view, classification maximum likelihood approach yields inconsistent estimates of the parameters and in this paper we consider the block clustering problem under the maximum likelihood approach; unfortunately, the application of the classical EM algorithm for the block mixture model is not direct: difficulties arise due to the dependence structure in the model and approximations are required. Considering the block clustering problem under a fuzzy approach, we propose a fuzzy block clustering algorithm to approximate the EM algorithm. To illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.     

Implementation, interpretation, and analysis of a suboptimal boundary finding algorithm

This paper presents a suboptimal boundary estimation algorithm for noisy images which is based upon an optimal maximum likelihood problem formulation. Both the maximum likelihood formulation and the resulting algorithm are described in detail, and computational results are given. In addition, the potential power of the likelihood formulation is demonstrated through the presentation of three simple but insightful analyses of algorithm performance. These analyses are based on a technique we have developed for comparing the accuracies of different boundary finding algorithms. This technique also helps in understanding the interplay of object shape and data models in the relative performances of boundary finders. Some of the algorithm design considerations resulting from the use of our analysis technique are new and, at first, surprising. Our technique appears to be the only one developed for comparing the accuracies of different boundary finding algorithms.     

The effects of positive affect and personal information search on outcomes in call centers: An empirical study

Despite the increasing availability of computer-based information sources within organizations, employees continue to rely on other people as important sources of information. However, relatively little is known about the relations among positive affect, personal information search, and related outcomes — especially in organizations. Using data from 276 service representatives in one organization we find that positive affect is positively related to the likelihood of searching for information through personal sources. Moreover, we find that the relations between the likelihood of searching for information via personal sources and work outcomes, such as productivity and job satisfaction, are moderated by positive affect. Specifically, we find that positive affect negatively moderates the relations between personal information search and productivity, but positively moderates the relations between personal information search and job satisfaction. As we will discuss, these findings not only contribute to the IT and organizational behavior literatures but also have significant implications for practitioners.     

A robust estimator for the tail index of Pareto-type distributions

In extreme value statistics, the extreme value index is a well-known parameter to measure the tail heaviness of a distribution. Pareto-type distributions, with strictly positive extreme value index (or tail index) are considered. The most prominent extreme value methods are constructed on efficient maximum likelihood estimators based on specific parametric models which are fitted to excesses over large thresholds. Maximum likelihood estimators however are often not very robust, which makes them sensitive to few particular observations. Even in extreme value statistics, where the most extreme data usually receive most attention, this can constitute a serious problem. The problem is illustrated on a real data set from geopedology, in which a few abnormal soil measurements highly influence the estimates of the tail index. In order to overcome this problem, a robust estimator of the tail index is proposed, by combining a refinement of the Pareto approximation for the conditional distribution of relative excesses over a large threshold with an integrated squared error approach on partial density component estimation. It is shown that the influence function of this newly proposed estimator is bounded and through several simulations it is illustrated that it performs reasonably well at contaminated as well as uncontaminated data.     

对数正态分布几何过程的统计推断

1.定义和概念 对来自具有趋势项点过程的一组数据进行建模时,一种直接的方法是用某种单调过程对这些数据进行模拟,作为这种特殊的单调过程,现介绍所谓的几何过程的定义