Bayesian hybrid generative discriminative learning based on finite Liouville mixture models

Recently hybrid generative discriminative approaches have emerged as an efficient knowledge representation and data classification engine. However, little attention has been devoted to the modeling and classification of non-Gaussian and especially proportional vectors. Our main goal, in this paper, is to discover the true structure of this kind of data by building probabilistic kernels from generative mixture models based on Liouville family, from which we develop the Beta-Liouville distribution, and which includes the well-known Dirichlet as a special case. The Beta-Liouville has a more general covariance structure than the Dirichlet which makes it more practical and useful. Our learning technique is based on a principled purely Bayesian approach which resulted models are used to generate support vector machine (SVM) probabilistic kernels based on information divergence. In particular, we show the existence of closed-form expressions of the Kullback-Leibler and Rényi divergences between two Beta-Liouville distributions and then between two Dirichlet distributions as a special case. Through extensive simulations and a number of experiments involving synthetic data, visual scenes and texture images classification, we demonstrate the effectiveness of the proposed approaches.     

Bayesian analysis of finite mixtures of multinomial and negative-multinomial distributions

The Bayesian implementation of finite mixtures of distributions has been an area of considerable interest within the literature. Computational advances on approximation techniques such as Markov chain Monte Carlo (MCMC) methods have been a keystone to Bayesian analysis of mixture models. This paper deals with the Bayesian analysis of finite mixtures of two particular types of multidimensional distributions: the multinomial and the negative-multinomial ones. A unified framework addressing the main topics in a Bayesian analysis is developed for the case with a known number of component distributions. In particular, theoretical results and algorithms to solve the label-switching problem are provided. An illustrative example is presented to show that the proposed techniques are easily applied in practice.     

Bayesian change detection based on spatial sampling and Gaussian mixture model

A Gaussian mixture model (GMM) and Bayesian inferencing based unsupervised change detection algorithm is proposed to achieve change detection on the difference image computed from satellite images of the same scene acquired at different time instances. Each pixel of the difference image is represented by a feature vector constructed from the difference image values of the neighbouring pixels to consider the contextual information. The feature vectors of the difference image are modelled as a GMM. The conditional posterior probabilities of changed and unchanged pixel classes are automatically estimated by partitioning GMM into two distributions by minimizing an objective function. Bayesian inferencing is then employed to segment the difference image into changed and unchanged classes by using the conditional posterior probability of each class. Change detection results are shown on real datasets.     

Infinite Liouville mixture models with application to text and texture categorization

This paper addresses the problem of proportional data modeling and clustering using mixture models, a problem of great interest and of importance for many practical pattern recognition, image processing, data mining and computer vision applications. Finite mixture models are broadly applicable to clustering problems. But, they involve the challenging problem of the selection of the number of clusters which requires a certain trade-off. The number of clusters must be sufficient to provide the discriminating capability between clusters required for a given application. Indeed, if too many clusters are employed overfitting problems may occur and if few are used we have a problem of underfitting. Here we approach the problem of modeling and clustering proportional data using infinite mixtures which have been shown to be an efficient alternative to finite mixtures by overcoming the concern regarding the selection of the optimal number of mixture components. In particular, we propose and discuss the consideration of infinite Liouville mixture model whose parameter values are fitted to the data through a principled Bayesian algorithm that we have developed and which allows uncertainty in the number of mixture components. Our experimental evaluation involves two challenging applications namely text classification and texture discrimination, and suggests that the proposed approach can be an excellent choice for proportional data modeling.     

On Bayesian analysis of a finite generalized Dirichlet mixture via a Metropolis-within-Gibbs sampling

In this paper, we present a fully Bayesian approach for generalized Dirichlet mixtures estimation and selection. The estimation of the parameters is based on the Monte Carlo simulation technique of Gibbs sampling mixed with a Metropolis-Hastings step. Also, we obtain a posterior distribution which is conjugate to a generalized Dirichlet likelihood. For the selection of the number of clusters, we used the integrated likelihood. The performance of our Bayesian algorithm is tested and compared with the maximum likelihood approach by the classification of several synthetic and real data sets. The generalized Dirichlet mixture is also applied to the problems of IR eye modeling and introduced as a probabilistic kernel for Support Vector Machines.

A Bayesian approach to model dispersal for decision support

In agricultural and environmental sciences dispersal models are often used for risk assessment to predict the risk associated with a given configuration and also to test scenarios that are likely to minimise those risks. Like any biological process, dispersal is subject to biological, climatic and environmental variability and its prediction relies on models and parameter values which can only approximate the real processes. In this paper, we present a Bayesian method to model dispersal using spatial configuration and climatic data (distances between emitters and receptors; main wind direction) while accounting for uncertainty, with an application to the prediction of adventitious presence rate of genetically modified maize (GM) in a non-GM field. This method includes the design of candidate models, their calibration, selection and evaluation on an independent dataset. A group of models was identified that is sufficiently robust to be used for prediction purpose. The group of models allows to include local information and it reflects reliably enough the observed variability in the data so that probabilistic model predictions can be performed and used to quantify risk under different scenarios or derive optimal sampling schemes.     

基于概率算法自适应更新背景的运动车辆检测

交通流量检测是智能交通系统中的一个重要研究方向和热点问题,基于视频的车辆检测是交通流量采集分析的核心技术,它为交通流量参数的实时获取提供了可能。为实现在复杂交通视频场景中实时准确检测各类的运动车辆,在研究传统背景差分算法的缺点的工作基础上,提出一个自适应的贝叶斯概率背景检测算法,进而完成了较准确的运动车辆分类检测。实验结果表明该方法具有高效实时的特点,能够较准确地实现复杂交通路面的背景提取和运动车辆的检测,具有良好的鲁棒性。     

基于贝叶斯推理的多线索视觉注意模型

针对大多数视觉注意模型都采用简单加权线性融合的方式获取显著图,提出了一个更符合生物学机制的基于贝叶斯推理的多线索视觉注意模型,模拟视觉系统腹侧通路与背侧通路中的视觉注意过程,采用贝叶斯推理的方式集成自顶向下与自底向上的信息,同时还集成了多种视觉线索,包括形状、颜色和上下文等.利用该模型进行遥感影像中的目标检测与定位的结果表明,该模型能有效的检测出目标并给出目标所在的位置.     

Discrete data clustering using finite mixture models

Finite mixture models have been applied for different computer vision, image processing and pattern recognition tasks. The majority of the work done concerning finite mixture models has focused on mixtures for continuous data. However, many applications involve and generate discrete data for which discrete mixtures are better suited. In this paper, we investigate the problem of discrete data modeling using finite mixture models. We propose a novel, well motivated mixture that we call the multinomial generalized Dirichlet mixture. The novel model is compared with other discrete mixtures. We designed experiments involving spatial color image databases modeling and summarization, and text classification to show the robustness, flexibility and merits of our approach.     

Representing and processing lineages over uncertain data based on the Bayesian network

Processing lineages (also called provenances) over uncertain data consists in tracing the origin of uncertainty based on the process of data production and evolution. In this paper, we focus on the representation and processing of lineages over uncertain data, where we adopt Bayesian network (BN), one of the popular and important probabilistic graphical models (PGMs), as the framework of uncertainty representation and inferences. Starting from the lineage expressed as Boolean formulae for SPJ (Selection–Projection–Join) queries over uncertain data, we propose a method to transform the lineage expression into directed acyclic graphs (DAGs) equivalently. Specifically, we discuss the corresponding probabilistic semantics and properties to guarantee that the graphical model can support effective probabilistic inferences in lineage processing theoretically. Then, we propose the function-based method to compute the conditional probability table (CPT) for each node in the DAG. The BN for representing lineage expressions over uncertain data, called lineage BN and abbreviated as LBN, can be constructed while generally suitable for both safe and unsafe query plans. Therefore, we give the variable-elimination-based algorithm for LBN's exact inferences to obtain the probabilities of query results, called LBN-based query processing. Then, we focus on obtaining the probabilities of inputs or intermediate tuples conditioned on query results, called LBN-based inference query processing, and give the Gibbs-sampling-based algorithm for LBN's approximate inferences. Experimental results show the efficiency and effectiveness of our methods.     

基于贝叶斯分类算法的客户流失分析模型研究

客户关系管理以客户为中心,通过再造企业组织体系和优化业务流程,展开系统的客户研究,最大程度地改善、提高了整个客户关系生命周期的绩效,从而提高客户的满意度和忠诚度,提高运营效率和利润收益。该文研究和探讨了客户关系管理系统开发的技术环节及实现过程,并对基于贝叶斯分类算法的客户流失分析模型的建立进行了分析。     

A Sequential Monte Carlo Method for Bayesian Analysis of Massive Datasets

Markov chain Monte Carlo (MCMC) techniques revolutionized statistical practice in the 1990s by providing an essential toolkit for making the rigor and flexibility of Bayesian analysis computationally practical. At the same time the increasing prevalence of massive datasets and the expansion of the field of data mining has created the need for statistically sound methods that scale to these large problems. Except for the most trivial examples, current MCMC methods require a complete scan of the dataset for each iteration eliminating their candidacy as feasible data mining techniques.In this article we present a method for making Bayesian analysis of massive datasets computationally feasible. The algorithm simulates from a posterior distribution that conditions on a smaller, more manageable portion of the dataset. The remainder of the dataset may be incorporated by reweighting the initial draws using importance sampling. Computation of the importance weights requires a single scan of the remaining observations. While importance sampling increases efficiency in data access, it comes at the expense of estimation efficiency. A simple modification, based on the rejuvenation step used in particle filters for dynamic systems models, sidesteps the loss of efficiency with only a slight increase in the number of data accesses.To show proof-of-concept, we demonstrate the method on two examples. The first is a mixture of transition models that has been used to model web traffic and robotics. For this example we show that estimation efficiency is not affected while offering a 99% reduction in data accesses. The second example applies the method to Bayesian logistic regression and yields a 98% reduction in data accesses.     

Semantic modeling of natural scenes based on contextual Bayesian networks

This paper presents a novel approach based on contextual Bayesian networks (CBN) for natural scene modeling and classification. The structure of the CBN is derived based on domain knowledge, and parameters are learned from training images. For test images, the hybrid streams of semantic features of image content and spatial information are piped into the CBN-based inference engine, which is capable of incorporating domain knowledge as well as dealing with a number of input evidences, producing the category labels of the entire image. We demonstrate the promise of this approach for natural scene classification, comparing it with several state-of-art approaches.     

Bayesian learning of finite generalized inverted Dirichlet mixtures: Application to object classification and forgery detection

The advent of mixture models has opened the possibility of flexible models which are practical to work with. A common assumption is that practitioners typically expect that data are generated from a Gaussian mixture. The inverted Dirichlet mixture has been shown to be a better alternative to the Gaussian mixture and to be of significant value in a variety of applications involving positive data. The inverted Dirichlet is, however, usually undesirable, since it forces an assumption of positive correlation. Our focus here is to develop a Bayesian alternative to both the Gaussian and the inverted Dirichlet mixtures when dealing with positive data. The alternative that we propose is based on the generalized inverted Dirichlet distribution which offers high flexibility and ease of use, as we show in this paper. Moreover, it has a more general covariance structure than the inverted Dirichlet. The proposed mixture model is subjected to a fully Bayesian analysis based on Markov Chain Monte Carlo (MCMC) simulation methods namely Gibbs sampling and Metropolis–Hastings used to compute the posterior distribution of the parameters, and on Bayesian information criterion (BIC) used for model selection. The adoption of this purely Bayesian learning choice is motivated by the fact that Bayesian inference allows to deal with uncertainty in a unified and consistent manner. We evaluate our approach on the basis of two challenging applications concerning object classification and forgery detection.     

基于FPGA的混合高斯背景建模实现

为了解决PC机上高清视频运动目标检测的实时性瓶颈问题,设计了一种基于FPGA的运动目标检测系统.系统采用基于自适应混合高斯背景模型的背景差分法,对环境扰动具有很好的适应性.本设计应用于1 280×1 024高清视频的运动目标检测,针对硬件实现的特点,对OpenCV混合高斯背景模型算法进行改进和适当的参数定点化,设计了适...     

基于模糊贝叶斯网络的堆垛机系统可靠性分析

为解决因缺乏实际数据而无法准确估计堆垛机系统和部件的失效概率问题,提出了基于模糊集理论和主观贝叶斯方法的模糊贝叶斯网络诊断策略.该方法首先将故障树转换成相应的贝叶斯网络,然后运用模糊集理论,将专家给出的关于基本事件失效概率的主观语言评判值转换成模糊数,并通过去模糊化处理得到精确解.针对因事件的多态性所引起的条件概率不确定问题,该方法采用主观贝叶斯方法进行估计.通过堆垛机通信模块的可靠性分析实例,验证了该方法是有效的,表明其能够克服在系统建模时的参数不确定问题.     

Bayesian estimation based on trimmed samples from Pareto populations

Trimmed samples are widely employed in several areas of statistical practice, especially when some sample values at either or both extremes might have been contaminated. The problem of estimating the inequality and precision parameters of a Pareto distribution based on a trimmed sample and prior information is considered. From an inferential viewpoint, the problem of finding the highest posterior density (HPD) estimates of the Pareto parameters is discussed. The existence and uniqueness of the HPD estimates are established under mild conditions; explicit and accurate lower and upper bounds are also provided. Adopting a decision-theoretic perspective, several Bayesian estimators for standard loss functions are presented. In addition, two-sided and HPD credibility intervals for each Pareto parameter and joint HPD credibility regions for both parameters are derived, which have the corresponding frequentist confidence level in the noninformative case. Finally, an illustrative example concerning annual wage data is included.     

A framework for the analysis of dynamic processes based on Bayesian networks and case-based reasoning

Bayesian networks are knowledge representation schemes that can capture probabilistic relationships among variables and perform probabilistic inference. Arrival of new evidence propagates through the network until all variables are updated. At the end of propagation, the network becomes a static snapshot representing the state of the domain for that particular time. This weakness in capturing temporal semantics has limited the use of Bayesian networks to domains in which time dependency is not a critical factor. This paper describes a framework that combines Bayesian networks and case-based reasoning to create a knowledge representation scheme capable of dealing with time-varying processes. Static Bayesian network topologies are learned from previously available raw data and from sets of constraints describing significant events. These constraints are defined as sets of variables assuming significant values. As new data are gathered, dynamic changes to the topology of a Bayesian network are assimilated using techniques that combine single-value decomposition and minimum distance length. The new topologies are capable of forecasting the occurrences of significant events given specific conditions and monitoring changes over time. Since environment problems are good examples of temporal variations, the problem of forecasting ozone levels in Mexico City was used to test this framework.     

基于贝叶斯分类的网上书店潜在用户挖掘

以网上书店为例,利用贝叶斯分类预测技术,进行了发现潜在客户群体的研究,用随机选取的10组样本进行试验预测,预测准确率达96.5%,表明了该算法是有效的。