基于概率图模型的点集匹配方法研究

在概率图模型框架下提出了一种将回归分析和聚类分析相结合的贝叶斯点集匹配方法,其中,回归分析用来估计两个点集之间的映射函数,而聚类分析用来建立两个点集中点与点之间的对应关系.本文将点集匹配问题表示为一种多层的概率有向图,并提出了一种由粗到精的变分逼近算法来估计点集匹配的不确定性;此外,还利用高斯混合模型估计映射函数回归中的异方差噪声和场景点密度估计中离群点的分布;同时,引入转移变量建立起模型点集与场景点集之间的关系,并与离群点混合模型共同对场景点的分布进行估计.实验结果表明,该方法与其他点集匹配算法相比,在鲁棒性和匹配精度方面均达到了较好的效果.     

文本聚类中的贝叶斯后验模型选择方法

对聚类分析中的模型选择特别是混合模型方法进行了较全面地介绍与总结，对其中的关键技术逐一进行了讨论。在此基础上，提出了贝叶斯后验模型选择方法，并把它与文档产生特征序列的物理模型相结合，给出了一个用于聚类分析的概率模型。对真实文本数据的测试中该模型取得了非常好的效果。同时对不同贝叶斯估计方法取得的效果进行了对比。     

HDP采样消息传递算法

分层狄利克雷过程是一种贝叶斯无参模型,用以分析海量数据的概率主题模型解决潜在狄利克雷分布无法解决的动态聚类的问题。本文从因子图的角度出发将消息传递算法与吉布斯采样算法结合用以解决贝叶斯无参模型后验概率推断问题,最终将该算法与LDA算法以及HDP算法在混淆度方面进行对比。实验结果表明该算法相比HDP采样算法收敛较快,最终也能收敛到LDA模型最优主题数目下的混淆度。     

一种基于层次聚类的k均值算法研究

依据信息论的思想,对基于层次的K-均值聚类算法(HKMA)过程进行了分析,该算法首先采用层次方法对文档进行初始聚类,得到的聚类总数作为k均值算法中的k值,在此基础上,通过k均值聚类对聚类结果进行修正。实验结果表明,HKMA执行时间整体上优于k-means算法,而且随着数据量的增大执行时间的增长幅度也较小。     

Variational Bayesian inference based robust multiple measurement sparse signal recovery

This work concentrates on not only probing into a novel Bayesian probabilistic model to formulate a general type of robust multiple measurement vectors sparse signal recovery problem with impulsive noise, but also developing an improved variational Bayesian method to recover the original joint row sparse signals. In the design of the model, two three-level hierarchical Bayesian estimation procedures are designed to characterize impulsive noise and joint row sparse source signals by means of Gaussian scale mixtures and multivariate generalized t distribution. Those hidden variables, included in signal and measurement models are estimated based on a variational Bayesian framework, in which multiple kinds of probability distributions are adopted to express their features. In the design of the algorithm, the proposed algorithm is a full Bayesian inference approach related to variational Bayesian estimation. It is robust to impulsive noise, since the posterior distribution estimation can be effectively approached through estimating unknown parameters. Extensive simulation results show that the proposed algorithm significantly outperforms the compared robust sparse signal recovery approaches under different kinds of impulsive noises.     

An empirical study of the simulation of various models used forimages

Markov random fields are typically used as priors in Bayesian image restoration methods to represent spatial information in the image. Commonly used Markov random fields are not in fact capable of representing the moderate-to-large scale clustering present in naturally occurring images and can also be time consuming to simulate, requiring iterative algorithms which can take hundreds of thousands of sweeps of the image to converge. Markov mesh models, a causal subclass of Markov random fields, are, however, readily simulated. We describe an empirical study of simulated realizations from various models used in the literature, and we introduce some new mesh-type models. We conclude, however, that while large-scale clustering may be represented by such models, strong directional effects are also present for all but very limited parameterizations. It is emphasized that the results do not detract from the use of Markov random fields as representers of local spatial properties, which is their main purpose in the implementation of Bayesian statistical approaches to image analysis. Brief allusion is made to the issue of parameter estimation     

分层Dirichlet过程及其应用综述

Dirichlet过程是一种应用于非参数贝叶斯模型中的随机过程, 特别是作为先验分布应用在概率图模型中. 与传统的参数模型相比, Dirichlet过程的应用更加广泛且模型更加灵活, 特别是应用于聚类问题时, 该过程能够自动确定聚类数目和生成聚类中心的分布参数. 因此, 近年来, 在理论和应用上均得到了迅速的发展, 引起越来越多的关注. 本文首先介绍Dirichlet过程, 而后描述了以Dirichlet过程为先验分布的Dirichlet过程混合模型及其应用, 接着概述分层Dirichlet过程及其在相关算法构造中的应用, 最后对分层Dirichlet过程的理论和应用进行了总结, 并对未来的发展方向作了探讨.     

基于贝叶斯和谐度的层次聚类

层次聚类是一种重要的数据分析技术。传统的层次聚类方法大都采用欧式距离度量类之间相似度,不能有效处理类之间重合和类密度变化大的情况。文中提出一种基于贝叶斯和谐度的层次聚类方法,采用和谐度增幅代替传统层次聚类方法采用的欧式距离。贝叶斯和谐度取自于贝叶斯阴阳和谐学习理论,能衡量整个数据的分布情况和指导选择合适的类别数。文中方法根据和谐度的变化来度量类之间的相似度,能克服传统层次聚类的缺点;同时更易选择阈值终止层次聚类的合并,从而产生合适的类别数。最后通过两个实验验证文中方法的有效性。     

Calculating the required cash in bank branches: a Bayesian-data mining approach

The issue of sufficiency of cash in bank branches is considered as an important issue especially for branch managers; because, not only the insufficiency of daily cash results in lack of response to needs of customers, but also may its excess result in increase in costs for banks. Hence, banks are always attempting to determine their required cash based on their daily operation. For this purpose, in this paper, 18 branches of a certain bank in a period of five months, due to diversity of the branches, have been classified by two methods of hierarchical clustering and Bayesian hierarchical clustering in similar clusters, and then by considering the results obtained from clustering, amounts of entered and consumed branch cash have been estimated by neural network (via classic and Bayesian approach), so that the cash required by branches can be calculated. The error criteria of the estimates show that calculations by applying Bayesian neural network method with considering Bayesian clustering have the least error compared to other methods.

     

双边定数截尾下广义指数分布的贝叶斯估计

在双边定数截尾样本下,给出了两参数广义指数分布参数的贝叶斯估计。基于共轭先验分布,分别在刻度平方误差损失函数和Linex损失函数下,给出参数的贝叶斯估计和多层贝叶斯估计,运用随机模拟方法对各种估计结果的优良性进行了分析比较。     

Flexible modelling of random effects in linear mixed models—A Bayesian approach

Flexible modelling of random effects in linear mixed models has attracted some attention recently. In this paper, we propose the use of finite Gaussian mixtures as in Verbeke and Lesaffre [A linear mixed model with heterogeneity in the random-effects population, J. Amu. Statist. Assoc. 91, 217-221]. We adopt a fully Bayesian hierarchical framework that allows simultaneous estimation of the number of mixture components together with other model parameters. The technique employed is the Reversible Jump MCMC algorithm (Richardson and Green [On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion). J. Roy. Statist. Soc. Ser. B 59, 731-792]). This approach has the advantage of producing a direct comparison of different mixture models through posterior probabilities from a single run of the MCMC algorithm. Moreover, the Bayesian setting allows us to integrate over different mixture models to obtain a more robust density estimate of the random effects. We focus on linear mixed models with a random intercept and a random slope. Numerical results on simulated data sets and a real data set are provided to demonstrate the usefulness of the proposed method.     

Bayesian mixture of AR models for time series clustering

In this paper, we propose a Bayesian framework for estimation of parameters of a mixture of autoregressive models for time series clustering. The proposed approach is based on variational principles and provides a tractable approximation to the true posterior density that minimizes Kullback–Liebler (KL) divergence with respect to prior distribution. This method simultaneously addresses the model complexity and parameter estimation problems. The proposed approach is applied both on simulated and real-world time series datasets. It is found to be useful in exploring and finding the true number of underlying clusters, starting from an arbitrarily large number of clusters.     

On the hierarchical Bayesian approach to image restoration:applications to astronomical images

In an image restoration problem one usually has two different kinds of information. In the first stage, one has knowledge about the structural form of the noise and local characteristics of the restoration. These noise and image models normally depend on unknown hyperparameters. The hierarchical Bayesian approach adds a second stage by putting a hyperprior on the hyperparameters, where information about those hyperparameters is included. In this work the author applies the hierarchical Bayesian approach to image restoration problems and compares it with other approaches in handling the estimation of the hyperparameters     

An Improved Hierarchical Dirichlet Process-Hidden Markov Model and Its Application to Trajectory Modeling and Retrieval

In this paper, we propose a hierarchical Bayesian model, an improved hierarchical Dirichlet process-hidden Markov model (iHDP-HMM), for visual document analysis. The iHDP-HMM is capable of clustering visual documents and capturing the temporal correlations between the visual words within a visual document while identifying the number of document clusters and the number of visual topics adaptively. A Bayesian inference mechanism for the iHDP-HMM is developed to carry out likelihood evaluation, topic estimation, and cluster membership prediction. We apply the iHDP-HMM to simultaneously cluster motion trajectories and discover latent topics for trajectory words, based on the proposed method for constructing the trajectory word codebook. Then, an iHDP-HMM-based probabilistic trajectory retrieval framework is developed. The experimental results verify the clustering accuracy of the iHDP-HMM and trajectory retrieval accuracy of the proposed framework.     

基于多层Bayes估计的战略协同网络供应链可靠性研究

对战略协同网络中供应链可靠性进行分析和判定.得到了可靠度计算公式,并以此为依据收集定时截尾数据.根据战略协同网络供应链可靠性统计特性,建立两种Bayes估计方法和一种多层Bayes估计方法,分别应用于样本供应链可靠性评估中.在估计供应链失效率的基础上,对供应链町靠度进行估计.仿真结果显示,应用多层Bayes估计方法效果较好.     

Using Support Vector Machines to Enhance the Performance of Bayesian Face Recognition

In this paper, we first develop a direct Bayesian-based support vector machine (SVM) by combining the Bayesian analysis with the SVM. Unlike traditional SVM-based face recognition methods that require one to train a large number of SVMs, the direct Bayesian SVM needs only one SVM trained to classify the face difference between intrapersonal variation and extrapersonal variation. However, the additional simplicity means that the method has to separate two complex subspaces by one hyperplane thus affecting the recognition accuracy. In order to improve the recognition performance, we develop three more Bayesian-based SVMs, including the one-versus-all method, the hierarchical agglomerative clustering-based method, and the adaptive clustering method. Finally, we combine the adaptive clustering method with multilevel subspace analysis to further improve the recognition performance. We show the improvement of the new algorithms over traditional subspace methods through experiments on two face databases - the FERET database and the XM2VTS database     

A variational Bayesian strategy for solving the DOA estimation problem in sparse array

This paper reformulates the problem of direction-of-arrival (DOA) estimation for sparse array from a variational Bayesian perspective. In this context, we propose a hierarchical prior for the signal coefficients that amounts marginally to a sparsity-inducing penalty in maximum a posterior (MAP) estimation. Further, the specific hierarchy gives rise to a variational inference technique which operates in latent variable space iteratively. Our hierarchical formulation of the prior allow users to model the sparsity of the unknown signal with a high degree, and the corresponding Bayesian algorithm leads to sparse estimators reflecting posterior information beyond the mode. We provide experimental results with synthetic signals and compare with state-of-the-art DOA estimation algorithm, in order to demonstrate the superior performance of the proposed approach.     

A probabilistic model for predicting software development effort

Recently, Bayesian probabilistic models have been used for predicting software development effort. One of the reasons for the interest in the use of Bayesian probabilistic models, when compared to traditional point forecast estimation models, is that Bayesian models provide tools for risk estimation and allow decision-makers to combine historical data with subjective expert estimates. In this paper, we use a Bayesian network model and illustrate how a belief updating procedure can be used to incorporate decision-making risks. We develop a causal model from the literature and, using a data set of 33 real-world software projects, we illustrate how decision-making risks can be incorporated in the Bayesian networks. We compare the predictive performance of the Bayesian model with popular nonparametric neural-network and regression tree forecasting models and show that the Bayesian model is a competitive model for forecasting software development effort.     

A Bayesian approach to model-based clustering for binary panel probit models

Considering latent heterogeneity is of special importance in nonlinear models in order to gauge correctly the effect of explanatory variables on the dependent variable. A stratified model-based clustering approach is adapted for modeling latent heterogeneity in binary panel probit models. Within a Bayesian framework an estimation algorithm dealing with the inherent label switching problem is provided. Determination of the number of clusters is based on the marginal likelihood and a cross-validation approach. A simulation study is conducted to assess the ability of both approaches to determine on the correct number of clusters indicating high accuracy for the marginal likelihood criterion, with the cross-validation approach performing similarly well in most circumstances. Different concepts of marginal effects incorporating latent heterogeneity at different degrees arise within the considered model setup and are directly at hand within Bayesian estimation via MCMC methodology. An empirical illustration of the methodology developed indicates that consideration of latent heterogeneity via latent clusters provides the preferred model specification over a pooled and a random coefficient specification.     

PROBABILISTIC HEURISTICS FOR HIERARCHICAL WEB DATA CLUSTERING

Clustering Web data is one important technique for extracting knowledge from the Web. In this paper, a novel method is presented to facilitate the clustering. The method determines the appropriate number of clusters and provides suitable representatives for each cluster by inference from a Bayesian network. Furthermore, by means of the Bayesian network, the contents of the Web pages are converted into vectors of lower dimensions. The method is also extended for hierarchical clustering, and a useful heuristic is developed to select a good hierarchy. The experimental results show that the clusters produced benefit from high quality.