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modelling the spatial distribution of heavy vehicle loads on long-span bridges based on undirected graphical model

STRUCTURE AND INFRASTRUCTURE ENGINEERING 2019年第11期15卷 1485-1499页

作者： Chen, Zhicheng Bao, Yuequan Chen, Jiahui Li, Hui Harbin Inst Technol Minist Ind & Informat Technol Key Lab Intelligent Disaster Mitigat Harbin Heilongjiang Peoples R China Harbin Inst Technol Minist Educ Key Lab Struct Dynam Behav & Control Harbin Heilongjiang Peoples R China Harbin Inst Technol Sch Civil Engn Harbin Heilongjiang Peoples R China

Vehicle load modelling is highly important for bridge design and safety evaluation. Conventional modelling approaches for vehicle loads have limitations in characterizing the spatial distribution of vehicles. This article presents a probabilistic method for modelling the spatial distribution of heavy vehicle loads on long-span bridges by using the undirected graphical model (UGM). The bridge deck is divided into grid cells, a UGM with each node corresponding to each cell is employed to model the location distribution of heavy vehicles, by which probabilities of heavy-vehicle distribution patterns can be efficiently calculated through applying the junction tree algorithm. A Bayesian inference method is also developed for updating the location model in consideration of the non-stationarity of traffic process. Gross weights of heavy vehicles are modelled by incorporating additional random variables to the vehicle-location UGM, corresponding probability distributions are constructed conditioned on ignoring correlation and considering correlation, respectively. Case studies using simulated data as well as field monitoring data have been conducted to examine the method. Compared with previous studies involving vehicle load modelling, the presented method can implement probabilistic analysis for all spatial distribution patterns of heavy vehicles on the entire bridge deck.

关键词： Bridge loads bridges long-span heavy vehicles probabilistic methods probability distribution undirected graphical model

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Exploration of Dependencies among Sections in a Supermarket Using a Tree-Structured undirected graphical model

Exploration of Dependencies among Sections in a Supermarket ...

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12th IEEE International Conference on Data Mining (ICDM)

作者： Takai, Keiji Kansai Univ Data Min Lab Osaka Japan

ISBN: (纸本)9780769549255;9781467351645

In research of purchase behavior in a supermarket, it is important to understand dependencies among sections of the supermarket, with each section corresponding to a category of items. An undirected graphical model is a powerful tool for this purpose. A problem with the application of an undirected graphical model is that there are many variables and, thus, a lot of computation is needed. In this article, we first apply a tree-structured undirected graphical model to reduce the computational amount, and second, propose a method to impose a restriction, based on our needs, on the tree-structured undirected graphical model. The variables we use are the length of time spent in each section and the number of items bought from each section. We found that some of the sections have influence on the adjacent sections and that some of the other sections have no influence on the adjacent sections, but do have influence on the nonadjacent sections. We also found that the number of items and the length of stationary time in the sections that influence a large number of sections are negatively related to those same variables in the other sections. Based on this result, managerial implications are described. Finally, we summarize this article and discuss some problems in the application of graphical models.

关键词： Dependency Purchase Behavior undirected graphical model Tree Structure Restriction

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Regional category parsing in undirected graphical models

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PATTERN RECOGNITION LETTERS 2009年第14期30卷 1264-1272页

作者： Xie, Zhao Gao, Jun Wu, Xindong Hefei Univ Technol Sch Comp Sci & Informat Engn Hefei 230009 Peoples R China Univ Vermont Dept Comp Sci Burlington VT 05405 USA

This article presents an approach for regional categorization in complex natural scenes with undirected graphs. A novel MRF-like model is proposed with spatial constraints in the feature space based on existing directed graphs, and an approximation of pseudo-likelihood is introduced for probability inference and parameter estimation. With this approximation, we can deal with the intractability of potential functions and get spatial relations between patches of different classes for more information in their co-occurrence matrix. The Receiver-Operating-Characteristic curves in our experiments demonstrate a better performance from our proposed method in comparison with directed probabilistic models such as LDA and constellation. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Regional categorization undirected graphical model Pseudo-likelihood Probability inference Parameter estimation ROC curve

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The multimedia recommendation algorithm based on probability graphical model

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MULTIMEDIA TOOLS AND APPLICATIONS 2022年第14期81卷 19035-19050页

作者： Li, Chen Li, Yu Wang, Chunhua Dong, Shifeng Gao, Haofei Zhao, Qian Wu, Wei Commun Univ China Beijing Peoples R China Beijing Aerosp Changfeng Sci & Ind Grp Beijing Peoples R China

In the multimedia big data, the demand for personalized multimedia recommendation algorithm is increasing to ease the multimedia information overload. The multimedia recommendation system has been applied in various industries and has been playing a significant role. With the development of multimedia big data, developing multimedia recommendation algorithms can effectively be used in multimedia data. However, a large number of prevailing recommendation systems cannot meet the multimedia recommendation requirements, since they ignore the user-item interactions with multimedia content. This essay realizes the multimedia recommendation based on probability graphical model, to deal with the cold start and data sparsity involved in collaborative filtering recommendation, proposing that add the user tag to user-item model. The essay optimizes the multimedia recommendation algorithm based on undirected graphical model and tests it with singular value decomposition, clustering and Naive Bayes separately. The essay also builds the checklist recommendation model and experiments extensively for comparison with the conditional multimedia recommendation algorithm, by using PersonalRank algorithm based on random-walk to work out the weight coefficient of the user tag. At the same time, the essay enhances the probability-graph multimedia recommendation algorithm by dimensionality reduction and clustering, with the result of noticeably improved precision and recall.

关键词： Multimedia recommendation Probability graphical model undirected graphical model Collaborative filtering Bayesians Network

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Negative binomial graphical model with excess zeros

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STATISTICAL ANALYSIS AND DATA MINING 2021年第5期14卷 449-465页

作者： Park, Beomjin Choi, Hosik Park, Changyi Univ Seoul Dept Stat Seoul South Korea Univ Seoul Grad Sch Dept Urban Big Data Convergence Seoul South Korea

Markov random field or undirected graphical models (GM) are a popular class of GM useful in various fields because they provide an intuitive and interpretable graph expressing the complex relationship between random variables. The zero-inflated local Poisson graphical model has been proposed as a graphical model for count data with excess zeros. However, as count data are often characterized by over-dispersion, the local Poisson graphical model may suffer from a poor fit to data. In this paper, we propose a zero-inflated local negative binomial (NB) graphical model. Due to the dependencies of parameters in our models, a direct optimization of the objective function is difficult. Instead, we devise expectation-minimization algorithms based on two different parametrizations for the NB distribution. Through a simulation study, we illustrate the effectiveness of our method for learning network structure from over-dispersed count data with excess zeros. We further apply our method to real data to estimate its network structure.

关键词： count data Markov random field over-dispersion undirected graphical model zero inflation

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On generating random Gaussian graphical models

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2020年 125卷 240-250页

作者： Cordoba, Irene Varando, Gherardo Bielza, Concha Larranaga, Pedro Univ Politecn Madrid Madrid Spain Univ Copenhagen Copenhagen Denmark

Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In order to ensure positive definiteness in (ii), a dominant diagonal is usually imposed. In this work we investigate different methods to generate random symmetric positive definite matrices with undirected graphical constraints. We show that if the graph is chordal it is possible to sample uniformly from the set of correlation matrices compatible with the graph, while for general undirected graphs we rely on a partial orthogonalization method. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Concentration graph Covariance graph Positive definite matrix simulation undirected graphical model Algorithm validation

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Estimating finite mixture of continuous trees using penalized mutual information

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2020年第20期49卷 4974-4987页

作者： Khalili, Atefeh Eskandari, Farzad Allameh Tabatabai Univ Dept Stat Tehran Iran

In this paper we introduce continuous tree mixture model that is the mixture of undirected graphical models with tree structured graphs and is considered as multivariate analysis with a non parametric approach. We estimate its parameters, the component edge sets and mixture proportions through regularized maximum likalihood procedure. Our new algorithm, which uses expectation maximization algorithm and the modified version of Kruskal algorithm, simultaneosly estimates and prunes the mixture component trees. Simulation studies indicate this method performs better than the alternative Gaussian graphical mixture model. The proposed method is also applied to water-level data set and is compared with the results of Gaussian mixture model.

关键词： Tree mixture model penalized maximum likelihood continuous multivariate analysis non parametric inference mixture model graphical mixture model undirected graphical model

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The networked partial correlation and its application to the analysis of genetic interactions

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS 2017年第3期66卷 647-665页

作者： Roverato, Alberto Castelo, Robert Univ Bologna Bologna Italy Univ Pompeu Fabra Barcelona Spain

Genetic interactions confer robustness on cells in response to genetic perturbations. This often occurs through molecular buffering mechanisms that can be predicted by using, among other features, the degree of coexpression between genes, which is commonly estimated through marginal measures of association such as Pearson or Spearman correlation coefficients. However, marginal correlations are sensitive to indirect effects and often partial correlations are used instead. Yet, partial correlations convey no information about the (linear) influence of the coexpressed genes on the entire multivariate system, which may be crucial to discriminate functional associations from genetic interactions. To address these two shortcomings, here we propose to use the edge weight derived from the covariance decomposition over the paths of the associated gene network. We call this new quantity the networked partial correlation and use it to analyse genetic interactions in yeast.

关键词： Concentration matrix Covariance decomposition Gene coexpression Partial correlation undirected graphical model

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Estimation of nonparanormal graphical models based on ranked set sampling (RSS)

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2023年第6期93卷 932-955页

作者： Aghabozorgi, Hamid Haji Eskandari, Farzad Allameh Tabatabai Univ Dept Stat Tehran Iran

Gaussian graphical model, which assumes that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, has been widely used to study the intrinsic dependence between the variables. However, we often encounter non-normal data, and we use variable transformation to achieve normality. Motivated by sparse additive models, the nonparanormal model extends the Gaussian graphical model to semiparametric Gaussian copula models, in which it is assumed that the variables follow a joint multivariate normal distribution after a set of unknown smooth monotone transformations. The basic methods of estimating undirected graphs in high-dimensional settings apply the simple random sampling (SRS) method to estimate the parameters of the model. We consider the ranked set sampling (RSS) approach for estimating the nonparanormal graphical model. Computationally, we show that using RSS leads to a better inference about the unknown features of the nonparanormal graphical model, and the proposed rank-based estimator performs as well as its counterparts estimators defined based on SRS. We study the numerical performance of the proposed method through a simulation study under both ideal and noisy settings and apply it to a genomic data set.

关键词： Gaussian copula nonparanormal model ranked set sampling undirected graphical model

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Sparse Nonparametric graphical models

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STATISTICAL SCIENCE 2012年第4期27卷 519-537页

作者： Lafferty, John Liu, Han Wasserman, Larry Univ Chicago Dept Stat Chicago IL 60637 USA Univ Chicago Dept Comp Sci Chicago IL 60637 USA Princeton Univ Dept Operat Res & Financial Engn Princeton NJ 08544 USA Carnegie Mellon Univ Dept Stat Pittsburgh PA 15213 USA Carnegie Mellon Univ Machine Learning Dept Pittsburgh PA 15213 USA

We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet,Markov random fields are already essentially nonparametric, since the cliques can take only a finite number of values. Continuous data are different. The Gaussian graphical model is the standard parametric model for continuous data, but it makes distributional assumptions that are often unrealistic. We discuss two approaches to building more flexible graphical models. One allows arbitrary graphs and a nonparametric extension of the Gaussian;the other uses kernel density estimation and restricts the graphs to trees and forests. Examples of both methods are presented. We also discuss possible future research directions for nonparametric graphical modeling.

关键词： Kernel density estimation Gaussian copula high-dimensional inference undirected graphical model oracle inequality consistency

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