协方差重置的两阶段递推贝叶斯参数辨识算法

为了在有色噪声干扰情况下获得无偏估计,基于辅助模型思想和分解技术,提出了一种带协方差重置的两阶段递推贝叶斯辨识算法。该算法首先把待辨识模型分解成两个虚拟子模型,然后分别辨识;同时,把估计到的噪声方差引入算法,并加入了一种新的协方差重置方法。计算量分析表明,与带协方差重置的最小二乘算法相比,所提算法可以减少计算量。仿真结果显示,所提算法的估计误差比传统最小二乘算法要小。实例建模证明了算法的有效性。     

Wiener系统的变聚点样条逼近递推贝叶斯算法

为了辨识过程噪声干扰的Wiener非线性系统,提出了一种基于三样条函数逼近的递推贝叶斯算法.众所周知,传统的多项式逼近具有不能外推、高阶易震荡等缺点.为了克服这些缺点,首先利用三样条函数对Wiener系统的非线性反函数进行逼近,在此基础上将待辨识系统参数化为伪线性回归系统.然后把估计到的噪声方差融入算法,接着使用递推贝叶斯算法对参数进行了估计.为了提高三样条函数对非线性反函数的逼近能力,一种基于均值的变聚点选择方法被应用于算法.文中还对算法的收敛性进行了分析,并用数值仿真和案例建模验证了算法的有效性.     

Bayesian estimation of Dirichlet mixture model with variational inference

In statistical modeling, parameter estimation is an essential and challengeable task. Estimation of the parameters in the Dirichlet mixture model (DMM) is analytically intractable, due to the integral expressions of the gamma function and its corresponding derivatives. We introduce a Bayesian estimation strategy to estimate the posterior distribution of the parameters in DMM. By assuming the gamma distribution as the prior to each parameter, we approximate both the prior and the posterior distribution of the parameters with a product of several mutually independent gamma distributions. The extended factorized approximation method is applied to introduce a single lower-bound to the variational objective function and an analytically tractable estimation solution is derived. Moreover, there is only one function that is maximized during iterations and, therefore, the convergence of the proposed algorithm is theoretically guaranteed. With synthesized data, the proposed method shows the advantages over the EM-based method and the previously proposed Bayesian estimation method. With two important multimedia signal processing applications, the good performance of the proposed Bayesian estimation method is demonstrated.     

空间连接系统分布式递推状态估计

针对空间连接系统, 提出一种分布式递推状态估计算法, 并给出算法收敛的充分必要条件. 该分布式估计器由一系列子估计器组成, 每个子估计器只利用本地子系统和相邻子系统的输出测量值估计本地子系统的状态. 与集总式Kalman 滤波相比, 在牺牲少量估计精度的情况下, 所提出算法大幅降低了计算复杂度和数据传输压力.     

推广的确定性均匀递归树演化模型的拓扑性质

在URT (uniform recursive tree)模型的基础上,提出一种推广的确定性均匀递归树演化模型GDURT (generalized deterministic uniform recursive tree).通过精确推导,求得该模型的累计度分布、平均路径长度、度相关性等拓扑性质,表明了该类网络模型与URT和DURT网络模型类似,为小世界网络,且具有指数度分布和协调的度相关特性,并对产生这些特性的原因作出了分析.     

AREION: Software effort estimation based on multiple regressions with adaptive recursive data partitioning

ContextAlong with expert judgment, analogy-based estimation, and algorithmic methods (such as Function point analysis and COCOMO), Least Squares Regression (LSR) has been one of the most commonly studied software effort estimation methods. However, an effort estimation model using LSR, a single LSR model, is highly affected by the data distribution. Specifically, if the data set is scattered and the data do not sit closely on the single LSR model line (do not closely map to a linear structure) then the model usually shows poor performance. In order to overcome this drawback of the LSR model, a data partitioning-based approach can be considered as one of the solutions to alleviate the effect of data distribution. Even though clustering-based approaches have been introduced, they still have potential problems to provide accurate and stable effort estimates.ObjectiveIn this paper, we propose a new data partitioning-based approach to achieve more accurate and stable effort estimates via LSR. This approach also provides an effort prediction interval that is useful to describe the uncertainty of the estimates.MethodEmpirical experiments are performed to evaluate the performance of the proposed approach by comparing with the basic LSR approach and clustering-based approaches, based on industrial data sets (two subsets of the ISBSG (Release 9) data set and one industrial data set collected from a banking institution).ResultsThe experimental results show that the proposed approach not only improves the accuracy of effort estimation more significantly than that of other approaches, but it also achieves robust and stable results according to the degree of data partitioning.ConclusionCompared with the other considered approaches, the proposed approach shows a superior performance by alleviating the effect of data distribution that is a major practical issue in software effort estimation.     

Design of adaptive PID regulators based on recursive estimation of the process parameters

This paper introduces a new approach based on a stochastic-deterministic recursive adaptive scheme, estimating the process parameters and the time delay at the same time and using design formulae for automatic tuning of PID regulator parameters.     

Variational Bayesian noise estimation of point sets

Scanning devices acquire geometric information from the surface of an object in the form of a 3D point set. Such point sets, as any data obtained by means of physical measurement, contain some noise. To create an accurate model of the scanned object, this noise should be resolved before or during the process of surface reconstruction. In this paper, we develop a statistical technique to estimate the noise in a scanned point set. The noise is represented as normal distributions with zero mean and their variances determine the amount of the noise. These distributions are estimated with a variational Bayesian method, which is known to provide more robust estimations than point estimate methods, such as maximum likelihood and maximum a posteriori. Validation experiments and further tests with real scan data show that the proposed technique can accurately estimate the noise in a 3D point set.     

New results using an integrated model and recursive algorithm for image motion estimation

A linear equation in the affine parameters used to model image motion may be derived by Taylor series expansion and truncation, and windowed spatial integration. Two methods for reducing errors in the Taylor approximation are discussed and results are presented.     

A new algorithm for recursive estimation of parameters in controlled ARMA processes

A recursive algorithm for estimating the constant but unknown parameters of a controlled ARMA process is presented. The algorithm is a recursive version of an off-line algorithm using three stages of standard least-squares. In the first stage the parameters of a controlled AR model of degree p are estimated. The residuals used in this stage are employed in the second stage to estimate the parameters of a controlled ARMA process. The first two stages constitute a recursive version of Durbin's algorithm. The model obtained in the second stage is used to filter the input, output and residuals and these filtered variables are used in the final stage to obtain improved estimates of the controlled ARMA process. It is shown that the estimate is (globally) p-consistent, i.e. that the estimate converges a.s. as the number of data tends to infinity, to a vector which, in turn, converges to the true parameter vector as the degree p of the AR model tends to infinity.     

基于Bayes与多层Bayes估计的WSN链路选择算法

无线传感器网络（WSN）节点能量有限,采用传统的链路选择的方法（经验法）进行链路选择,需要发送大量的数据包作为测试样本,这在WSN中是不合适的。设计了两种基于Bayes估计与一种基于多层Bayes估计的WSN链路选择算法,分别记为BLSP-B1、BLSP-B2、BLSP-HE。仿真实验发现,在小样本的条件下,BLSP-B1、BLSP-B2、BLSP-HE选择高质量的链路的概率比经验法要高出10%～20%,其中BLSP-HE算法最稳健,性能较好。     

WFEN的贝叶斯估计及在高维预测模型中的应用

针对传统收缩估计中难以进行统计推断以及无法同时确定惩罚因子问题,在权融合弹性网回归（WFEN）的基础上,给出其Gibbs层次抽样模型并构造相应的贝叶斯估计量（Bayesian WFEN,BWFEN）。该算法根据Expectation-Maximization方法同时确定估计中的两个惩罚因子,并基于回归系数的经验后验分布计算估计量标准误和进行变量选择。 模拟实验表明,BWFEN的迭代过程具有良好的收敛性,在面对稀疏预测模型或者模型中的预测变量存在群组效应时具有较低的相对预测误差和较高的变量选择精度。在博客回复数预测模型的实际应用中,BWFEN也显著优于其他收缩估计方法。     

Remote sensing image fusion based on Bayesian linear estimation

A new remote sensing image fusion method based on statistical parameter estimation is proposed in this paper. More specially, Bayesian linear estimation (BLE) is applied to observation models between remote sensing images with different spa- tial and spectral resolutions. The proposed method only estimates the mean vector and covariance matrix of the high-resolution multispectral (MS) images, instead of assuming the joint distribution between the panchromatic (PAN) image and low-resolution multispectral image. Furthermore, the proposed method can enhance the spatial resolution of several principal components of MS images, while the traditional Principal Component Analysis (PCA) method is limited to enhance only the first principal component. Experimental results with real MS images and PAN image of Landsat ETM demonstrate that the proposed method performs better than traditional methods based on statistical parameter estimation, PCA-based method and wavelet-based method.     

不可达系统的鲁棒贝叶斯估计方法

本文针对模型扰动下的不可达系统,提出了一种新的针对退化分布下的极大极小博弈问题的求解和证明方法.首先,文章将有相对熵约束的极大极小博弈问题转换成了一个无约束的拉格朗日函数,并找到其在均值和奇异的方差矩阵方向上都为严格凹函数的条件;其次,本文通过求解其均值和方差的极大值,得到所对应的鲁棒贝叶斯估计器和奇异的扰动状态误差协方差矩阵;最后,文章证明存在一个唯一的拉格朗日乘子满足其约束条件.微机电系统加速度计漂移估计仿真结果表明对所提算法的有效性.     

递推局部线性回归估计及其应用

在非参数统计中,局部多项式回归是重要的工具,然而以往研究的算法基本都是非递推的.本文研究递推的局部线性回归估计及其应用.首先推导出递推算法,给出了回归函数及其导函数的非参数估计.在一定的条件下,证明了算法的强一致性.并且通过仿真例子研究了它在非线性条件异方差模型的回归函数估计和非线性ARX(nonlinear autoregressive system with exogenous inputs,NARX)系统辨识中的应用.     

Study on joint Bayesian model selection and parameter estimation method of GTD model

The Bayesian method is applied to the joint model selection and parameter estimation problem of the GTD model. An algorithm based on RJ-MCMC is designed. This algorithm not only improves the model order selection and parameter estimation accuracy by exploiting the priori information of the GTD model, but also solves the mixed parameter estimation problem of the GTD model properly. Its performance is tested using numerical simulations and data generated by electromagnetic code. It is shown that it gives good model order selection and parameter estimation results, especially for low SNR, closely-spaced components and short data situations.     

基于有监督Bayesian网络的垃圾邮件过滤

对影响邮件特性的邮件报文格式作了仔细的分析并对垃圾邮件的特征进行了分类归纳,在此基础上构建了一个有监督的Bayesian邮件分类网络。通过对该网络作Bayesian参数估计,实现了判定邮件类别的不确定推理。对不同邮件测试集的在线学习试验结果表明,有监督Bayesian邮件分类网络能够有效地实现垃圾邮件的相对完备特征学习,改善邮件过滤的准确率。     

基于贝叶斯通用背景模型的图像标注

在高斯图特征提取过程中,通用背景模型(Universal background model, UBM) 方法常用于根据总体分布估计每一幅图像中特征点分布的高斯混合模型(Gaussian mixture model, GMM)参数. 然而UBM估计的GMM权重参数中有很多接近零的数值,它们所对应的高斯分量对分布估计贡献小却又都参与了计算, 因此UBM的时间复杂度较高. 为解决这个问题,本文提出Bayes UBM方法. 通过引入受限的对称Dirichlet分布来描述GMM权重参数的先验分布,利用Bayes最大后验概率对GMM参数集进行估计. 实验表明Bayes UBM方法不仅有效地降低了时间复杂度,而且提高了Corel数据集上的图像标注精度.     

贝叶斯框架下的非参数估计Graph Cuts分割算法

假设图像中各像素灰度值是具有一定概率分布的随机变量,由贝叶斯定理,正确分割观测图像等价于求出具有最大后验概率的实际图像估计。在此框架下,提出了一种改进型Graph Cuts图像分割算法。与传统Graph Cuts分割算法相比,该算法在模型建立上有两个方面的改进：1)将模糊C均值聚类引入数据约束能量函数来得到各像素在某个标记下的概率,改善了收敛性能;2)使用非参数方法估计图像的统计分布,然后用此统计量构成图像分割的先验概率,并保证分割结果的局部平滑。由于非参数估计是由样本直接估计得到的结果,特别适用于小样本和分布函数不恒定的情况,因此拓展了算法的适用范围。实验结果表明,改进算法在遥感图像分割和医学图像分割中均提高了分割精度,证明了该算法的有效性。