Evaluating Traffic Congestion Using the Traffic Occupancy and Speed Distribution Relationship: An Application of Bayesian Dirichlet Process Mixtures of Generalized Linear Model

Accurate classification and prediction of future traffic conditions are essential for developing effective strategies for congestion mitigation on the highway systems. Speed distribution is one of the traffic stream parameters, which has been used to quantify the traffic conditions. Previous studies have shown that multi-modal probability distribution of speeds gives excellent results when simultaneously evaluating congested and free-flow traffic conditions. However, most of these previous analytical studies do not incorporate the influencing factors in characterizing these conditions. This study evaluates the impact of traffic occupancy on the multi-state speed distribution using the Bayesian Dirichlet Process Mixtures of Generalized Linear Models (DPM-GLM). Further, the study estimates the speed cut-point values of traffic states, which separate them into homogeneous groups using Bayesian change-point detection (BCD) technique. The study used 2015 archived one-year traffic data collected on Florida’s Interstate 295 freeway corridor. Information criteria results revealed three traffic states, which were identified as free-flow, transitional flow condition (congestion onset/offset), and the congested condition. The findings of the DPM-GLM indicated that in all estimated states, the traffic speed decreases when traffic occupancy increases. Comparison of the influence of traffic occupancy between traffic states showed that traffic occupancy has more impact on the free-flow and the congested state than on the transitional flow condition. With respect to estimating the threshold speed value, the results of the BCD model revealed promising findings in characterizing levels of traffic congestion.

Spike-and-Slab Dirichlet Process Mixture Models

In this paper, Spike-and-Slab Dirichlet Process (SS-DP) priors are introduced and discussed for non-parametric Bayesian modeling and inference, especially in the mixture models context. Specifying a spike-and-slab base measure for DP priors combines the merits of Dirichlet process and spike-and-slab priors and serves as a flexible approach in Bayesian model selection and averaging. Computationally, Bayesian Expectation-Maximization (BEM) is utilized to obtain MAP estimates. Two simulated examples in mixture modeling and time series analysis contexts demonstrate the models and computational methodology.

Combined UAMP and MF Message Passing Algorithm for Multi-Target Wideband DOA Estimation with Dirichlet Process Prior

When estimating the direction of arrival (DOA) of wideband signals from multiple sources, the performance of sparse Bayesian methods is influenced by the frequency bands occupied by signals in different directions. This is particularly true when multiple signal frequency bands overlap. Message passing algorithms (MPA) with Dirichlet process (DP) prior can be employed in a sparse Bayesian learning (SBL) framework with high precision. However, existing methods suffer from either high complexity or low precision. To address this, we propose a low-complexity DOA estimation algorithm based on a factor graph. This approach introduces two strong constraints via a stretching transformation of the factor graph. The first constraint separates the observation from the DP prior, enabling the application of the unitary approximate message passing (UAMP) algorithm for simplified inference and mitigation of divergence issues. The second constraint compensates for the deviation in estimation angle caused by the grid mismatch problem. Compared to state-of-the-art algorithms, our proposed method offers higher estimation accuracy and lower complexity.

Dirichlet process and its developments: a survey

The core of the nonparametric/semiparametric Bayesian analysis is to relax the particular parametric assumptions on the distributions of interest to be unknown and random,and assign them a prior.Selecting a suitable prior therefore is especially critical in the nonparametric Bayesian fitting.As the distribution of distribution,Dirichlet process(DP)is the most appreciated nonparametric prior due to its nice theoretical proprieties,modeling flexibility and computational feasibility.In this paper,we review and summarize some developments of DP during the past decades.Our focus is mainly concentrated upon its theoretical properties,various extensions,statistical modeling and applications to the latent variable models.

Dirichlet Process Gaussian Mixture Models:Choice of the Base Distribution

In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of components. Nonparametric mixture models sidestep the problem of finding the ＂correct＂ number of mixture components by assuming infinitely many components. In this paper Dirichlet process mixture （DPM） models are cast as infinite mixture models and inference using Markov chain Monte Carlo is described. The specification of the priors on the model parameters is often guided by mathematical and practical convenience. The primary goal of this paper is to compare the choice of conjugate and non-conjugate base distributions on a particular class of DPM models which is widely used in applications, the Dirichlet process Gaussian mixture model （DPGMM）. We compare computational efficiency and modeling performance of DPGMM defined using a conjugate and a conditionally conjugate base distribution. We show that better density models can result from using a wider class of priors with no or only a modest increase in computational effort.

Topic model for graph mining based on hierarchical Dirichlet process

In this paper,a nonparametric Bayesian graph topic model(GTM)based on hierarchical Dirichlet process(HDP)is proposed.The HDP makes the number of topics selected flexibly,which breaks the limitation that the number of topics need to be given in advance.Moreover,theGTMreleases the assumption of‘bag of words’and considers the graph structure of the text.The combination of HDP and GTM takes advantage of both which is named as HDP–GTM.The variational inference algorithm is used for the posterior inference and the convergence of the algorithm is analysed.We apply the proposed model in text categorisation,comparing to three related topic models,latent Dirichlet allocation(LDA),GTM and HDP.

Hierarchical topic modeling with nested hierarchical Dirichlet process

This paper deals with the statistical modeling of latent topic hierarchies in text corpora. The height of the topic tree is assumed as fixed, while the number of topics on each level as unknown a priori and to be inferred from data. Taking a nonpara-metric Bayesian approach to this problem, we propose a new probabilistic generative model based on the nested hierarchical Dirichlet process (nHDP) and present a Markov chain Monte Carlo sampling algorithm for the inference of the topic tree structure as well as the word distribution of each topic and topic distribution of each document. Our theoretical analysis and experiment results show that this model can produce a more compact hierarchical topic structure and captures more fine-grained topic rela-tionships compared to the hierarchical latent Dirichlet allocation model.

Distributionally Robust Learning Based on Dirichlet Process Prior in Edge Networks

In order to meet the real-time performance requirements,intelligent decisions in Internet of things applications must take place right here right now at the network edge.Pushing the artificial intelligence frontier to achieve edge intelligence is nontrivial due to the constrained computing resources and limited training data at the network edge.To tackle these challenges,we develop a distributionally robust optimization(DRO)-based edge learning algorithm,where the uncertainty model is constructed to foster the synergy of cloud knowledge and local training.Specifically,the cloud transferred knowledge is in the form of a Dirichlet process prior distribution for the edge model parameters,and the edge device further constructs an uncertainty set centered around the empirical distribution of its local samples.The edge learning DRO problem,subject to these two distributional uncertainty constraints,is recast as a single-layer optimization problem using a duality approach.We then use an Expectation-Maximization algorithm-inspired method to derive a convex relaxation,based on which we devise algorithms to learn the edge model.Furthermore,we illustrate that the meta-learning fast adaptation procedure is equivalent to our proposed Dirichlet process prior-based approach.Finally,extensive experiments are implemented to showcase the performance gain over standard approaches using edge data only.

结合MAML和Dirichlet过程的小样本点云分类

点云被广泛使用在各种三维应用场景中,但是实际应用中通常存在扫描、标注费时费力等局限性,因此基于小样本数据集的点云分类网络更加符合应用需求.为了有效地提高深度学习分类算法在小样本点云数据集上的分类效果,提出一种针对小样本数据集的点云分类方法.针对训练数据集不平衡问题,首先采用基于相似度依赖的Dirichlet中餐馆过程对数据集进行预处理,在无需人工指定聚类个数的前提下对样本进行重新聚类,以提升分类网络在小样本数据集上的性能;然后在重新聚类后的样本上使用模型无关(model agnostic meta learning,MAML)算法训练PointNet++,达到用少量点云样本就能快速适应新任务的能力.所提方法不但降低了模型对数据量的依赖,提高了模型泛化能力,而且成功地把MAML算法从二维图像分类拓展到三维点云分类中;在Modelnet40数据集上的实验结果表明,与PointNet++相比,该方法的训练时间减少了一半,分类准确率平均提高6.67%,验证了该方法在小样本数据集上的有效性.

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.

Dirichlet过程及其在自然语言处理中的应用

Dirichlet过程是一种典型的变参数贝叶斯模型,其优点是参数的个数和性质灵活可变,可通过模型和数据来自主地计算,近年来它已成为机器学习和自然语言处理研究领域中的一个研究热点。该文较为系统的介绍了Dirichlet过程的产生、发展,并重点介绍了其模型计算,同时结合自然语言处理中的具体应用问题进行了详细分析。最后讨论了Dirichlet过程未来的研究方向和发展趋势。

基于Dirichlet过程的无线视频码率变化识别算法

研究了通过对终端视频帧质量的聚类分析来识别无线视频传输中码率变化的方法,以便为无线视频传输过程中视频码率自适应调整提供参考依据。针对经典模糊C均值(FCM)算法和K均值(K-means)算法需要设定聚类数目的问题,提出一种基于荻利克雷过程(DP)的FCM算法——DP-FCM算法。该算法将Dirichlet过程和FCM算法相结合,由视频帧信息权重峰值信噪比(IWPSNR)值使用DP过程混合模型模拟估计出聚类数目,然后进行FCM模糊聚类,通过设定合理的阈值,合并聚类结果相似项,完成视频帧的聚类,从而实现视频传输码率变化的识别。以LIVE视频库为试验数据源,对该算法进行了性能测试。试验结果表明,DP-FCM算法能够在无需设定聚类数目的前提下实现视频传输码率变化的分类识别。

基于一般Dirichlet过程的非参数贝叶斯分析

基于Jayaram Sethuraman在1994提出的扩展Dirichlet过程先验,将其推广到更一般的情形,使Dirichlet过程和扩展Dirichlet过程都成为一般Dirichlet过程的特例,并对非参数的贝叶斯进行了研究和讨论,给出了一般Dirichlet分布的期望、二阶矩等,证明了一般Dirichlet过程的支撑是足够大的,说明一般Dirichlet过程的构造是合理而又恰当的.

分层Dirichlet过程原理及应用综述

Dirichlet过程是一种应用于非参数贝叶斯模型中的随机过程。通过其良好的聚类性质,基于此的模型可以通过简单的Gibbs采样决定参数的个数,从而为模型选择提供方便。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。分层Dirichlet过程是LDA模型的非参数模型推广,可以用来构建无穷个基本组元的混合模型。HDP被广泛地应用在概率话题模型的领域。首先说明Dirichlet过程的原理和采样方法,然后将其推广到分层Dirichlet过程中,并重点介绍基于Dirichlet过程的混合模型,最后对分层Dirichlet过程的应用进行了介绍。

Dirichlet过程混合模型在非线性过程监控中的应用

针对高斯混合模型在模型选择阶段易产生有噪声或过拟合的模型估计问题,提出基于Dirichlet过程混合模型的非参数贝叶斯故障诊断方法.通过重新定义高斯混合模型中的混合权重,利用stick-breaking法建立Dirichlet过程混合模型.通过具有截断作用的变分法近似推理出模型参数以及隐含变量,利用所得后验对故障模型进行估计,并提出基于后验概率的监测统计量以度量出故障状态在后验中的波动.在连续搅拌釜式反应器和Tennessee Eastman化工过程上的实验结果表明,该方法在故障检测方面优于传统的核主元分析法,并且具有较高的故障诊断率.

基于时间Dirichlet过程混合模型的在线目标跟踪

针对目标跟踪过程中,可变目标表观的特征数据会发生"分布漂移"的问题,提出一种基于非参贝叶斯多模表观模型的目标跟踪方法。首先,以时间Dirichlet过程为先验分布,把先前估计的目标样本划分为不同的聚集,使得每个聚集表示一类表观,同时,每个表观类被建模为判别式分类器;然后,基于贝叶斯后验推断,权衡先前表观模型的分类误差和拆分聚集的代价,从数据中自主学习表观模型;最后,基于Noisy-OR模型,以贪心(Greedy)策略协同各表观分类器判别出目标。仿真结果表明该方法能较好的跟踪可变目标表观,改善了目标跟踪性能。

基于Dirichlet过程混合模型的指节偏移测度特征学习

针对人机协调装配光强相对稳定的室内环境,为获取指节图像特征,丰富手部位姿信息,提出基于无穷Dirichlet过程混合模型的指节识别方法。在局部Markov假设的基础上,将条件随机测度的学习问题转化为随机聚类学习问题;运用无穷Dirichlet过程混合模型描述概率密度,将聚类数量表述为随机态;利用Gibbs采样方法,对分层概率形式的密度结构进行迭代学习;给出了基于Dirichlet过程混合模型的坍塌Gibbs采样算法,运用样本集进行了模型训练学习。最后,采用固定阈值对手部图像指节进行识别,验证了所提方法的有效性。

基于狄利克雷多项式过程模型与K-means结合的菌群分析

群体分型是一种有助于更好的理解人类身心健康等复杂生物学问题的有效方法,聚类是一种为了对样本分组来降低复杂性的定义肠型的方法,而传统K-means聚类算法的K值选取无法确定,本文在传统K-means聚类算法的基础上进行了改进,并公开数据集上进行了验证,实验表明改进算法能够解决K值选取无法确定的问题,且聚类结果的稳定性、准确性和聚类质量都得到显著提高。将改进后的模型运用于肠道菌群OTUs数据,发现不仅能够有效地区分2-型糖尿病患者样本间的相似性,而且能鉴定出影响菌群结构异质性最大的OTUs菌,为临床解决2-型糖尿病问题提供了一种新的思路。

基于Dirichlet过程混合的高斯过程模型混合采样推理

提出了基于Dirichlet过程混合的高斯过程模型揭示复杂动态系统结构数据的多态性的内在机制.针对均值结构与协方差结构稀疏性的差异性,设计了参数先验与非参数先验来构建基于Polya urn与过松弛层采样的混合采样框架体系.该混合采样方案不但能够在统一的Metropolis-Hasting(M-H)概率评价准则下实现,而且能够最大限度地克服高斯随机走步的缺陷,方便、快速地获得马尔科夫样本链的展开.仿真结果表明,混合采样算法比高斯过程回归模型及高斯过程函数回归混合模型具有更广泛的适应性及更好的预测效果.

Dirichlet过程混合模型SAR图像分割算法

传统的合成孔径雷达(SAR)图像参数化有限模型都有其特定的物理背景或者数学假设,很难准确估计SAR图像中各地物的密度分布,为了解决这一问题,提出一种基于非参数化无限混合模型的SAR图像分割方法,该方法利用Dirichlet过程对SAR图像进行建模,进一步采用非参数化Bayes模型分割包含复杂地物目标的SAR图像。Dirichlet分布作为一种基于分布的分布可以确定不同类别的先验概率,由样本估计出密度函数来描述图像,从而可以更精确地分割各类地物。该算法在模拟图像与真实SAR图像上进行了比对测试,实验结果验证了Dirichlet过程混合模型SAR图像分割算法的有效性和稳健性。