Bayesian Graph Research Articles

A Comparison of Algorithms for Learning Hidden Variables in Bayesian Factor Graphs in Reduced Normal Form.

Bayesian-directed acyclic discrete-variable graphs are reduced to a simplified normal form made up of only replicator units (or equal constraint units), source, and single-input/single-output blocks. In this framework, the same adaptation algorithm can be applied to all the parametric blocks. We obtain and compare adaptation rules derived from a constrained maximum likelihood formulation and a minimum Kullback-Leibler divergence criterion using Karush-Kuhn-Tucker conditions. The learning algorithms are compared with two other updating equations based on localized decisions and on a variational approximation, respectively. The performance of the various algorithms is verified on synthetic data sets for various architectures. Factor graphs in reduced normal form provide an appealing framework for rapid deployment of Bayesian-directed graphs in the applications.

FBM: A Flexible Random Walk Based Generative Model for Social Network

This paper studies the static and dynamic characteristics of the real social networks as well as their proposed generative models, among which the Butterfly Model (1) is useful while not flexible enough to generate the social networks with the expected power-law exponent. And a novel Flexible Butterfly Model (FBM) is proposed based on the Butterfly Model and combined with the Monte Carlo method, and a Bayesian Graph Model for the training of the FBM Model is built in order to learn parameters from real social networks. Experiments have shown that the FBM model can adjust the law power exponent of the generated social network effectively by the introduced parameters. Meanwhile, the FBM model also maintains the vast majority of important characteristics that the Butterfly model has.

Spatial–Spectral Classification of Hyperspectral Images Using Discriminative Dictionary Designed by Learning Vector Quantization

In this paper, a novel discriminative dictionary learning method is proposed for sparse-representation-based classification (SRC) to label highly dimensional hyperspectral imagery (HSI). In SRC, a dictionary is conventionally constructed using all of the training pixels, which is not only inefficient due to the large size of typical HSI images but also ineffective in capturing class-discriminative information crucial for classification. We address the dictionary design problem with the inspiration from the learning vector quantization technique and propose a hinge loss function that is directly related to the classification task as the objective function for dictionary learning. The resulting online learning procedure systematically “pulls” and “pushes” dictionary atoms so that they become better adapted to distinguish between different classes. In addition, the spatial context for a test pixel within its local neighborhood is modeled using a Bayesian graph model and is incorporated with the sparse representation of a single test pixel in a unified probabilistic framework, which enables further refinement of our dictionary to capture the spatial class dependence that complements the spectral information. Experiments on different HSI images demonstrate that the dictionaries optimized using our method can achieve higher classification accuracy with substantially reduced dictionary size than using the whole training set. The proposed method also outperforms existing dictionary learning methods and attains the state-of-the-art results in both the spectral-only and spatial-spectral settings.

Non-parametric Bayesian graph models reveal community structure in resting state fMRI

Modeling of resting state functional magnetic resonance imaging (rs-fMRI) data using network models is of increasing interest. It is often desirable to group nodes into clusters to interpret the communication patterns between nodes. In this study we consider three different nonparametric Bayesian models for node clustering in complex networks. In particular, we test their ability to predict unseen data and their ability to reproduce clustering across datasets. The three generative models considered are the Infinite Relational Model (IRM), Bayesian Community Detection (BCD), and the Infinite Diagonal Model (IDM). The models define probabilities of generating links within and between clusters and the difference between the models lies in the restrictions they impose upon the between-cluster link probabilities. IRM is the most flexible model with no restrictions on the probabilities of links between clusters. BCD restricts the between-cluster link probabilities to be strictly lower than within-cluster link probabilities to conform to the community structure typically seen in social networks. IDM only models a single between-cluster link probability, which can be interpreted as a background noise probability. These probabilistic models are compared against three other approaches for node clustering, namely Infomap, Louvain modularity, and hierarchical clustering. Using 3 different datasets comprising healthy volunteers' rs-fMRI we found that the BCD model was in general the most predictive and reproducible model. This suggests that rs-fMRI data exhibits community structure and furthermore points to the significance of modeling heterogeneous between-cluster link probabilities.

Evolving Bayesian Graph for Three-Dimensional Vehicle Model Building From Video

Traffic videos often capture slowly changing views of moving vehicles. These different and incrementally related views provide visual cues for 3-D perception of the vehicles from 2-D videos. This paper focuses on 3-D model building of multiple vehicles with different shapes from a single generic 3-D vehicle model by incrementally accumulating evidences in streaming traffic videos collected from a single static uncalibrated camera. When we do not know a priori the class of the following vehicle to be seen (which is true in a real traffic scenario), a flexible and evolvable Bayesian graphical model (BGM) is required, where the number of nodes, the structure of links between them, and the associated conditional probability distributions can change on the fly. Current BGMs fail to provide such online flexibility. We propose a novel BGM, which is called structure-modifiable adaptive reason-building temporal Bayesian graph (SmartBG), that self-modifies in a data-driven way to model uncertainty propagation in 3-D vehicle model building from 2-D video features, where only a subset of the 2-D vehicle features is visible at any time point, e.g., out of field-of-view (entry/exit) and self-occlusion. Uncertainties are used as relative weights to fuse evidences and to compute the overall reliability of the generated models. Results for different vehicles from several traffic videos and two different viewpoints demonstrate the performance of the proposed method.

Term of Rib Cage in Application to the Algebraic Bayesian Network Join Graphs Analysis

A new terminological approach to join graph processing formalization based on a term of rib cage that is an edge set is suggested. A new system of the join graphs theory accurate terms such as weight, narrowing, sinew, backbone connectivity, minimal join graph is suggested. Also the term of join graph and Minimal Join Graph Set Theorem formulating are defined more preciously. A lemma of independent backbone path stating that there are two such edge sets from given collection of non-overlapping edge sets, that a backbone path between them is non-overlapping with any another edge set is formulated and proven.

Bayesian MRF Modeling and Graph Cuts for Phase Unwrapping with Discontinuity Phase Flaws：A Comparative Study

Phase unwrapping (PU) is a difficult task commonly found in applications involving interferometric synthetic aperture radar (InSAR), magnetic resonance imaging (MRI) and optical surface profile measurements; all of which involve mathematically ill-posed problems. Conventional algorithms exhibit strong shortcomings in PU when phase discontinuity flaws exist. To simulate these situations, we are custom-designed test data with a phase discontinuity flaw. This simulated data is a 3D Gaussian distribution with an arc-shaped notch as a phase flaw. PU is carried out by Bayesian inference and MRF (Markov Random Field) modeling. A graph cut algorithm is employed for optimization with respect to energy minimization. Three other conventional algorithms are also employed and their PU performance is compared. The results show the good performance and effectiveness of the Bayesian MRF modeling method. These experimental results are important references for phase unwrapping problems when phase discontinuities exist.

Learning Non-Linear Functions With Factor Graphs

We show how to use a discrete-variable factor graph for learning non-linear continuous functions from examples. The paper proposes a scheme for embedding soft quantization in a probabilistic Bayesian graph. The quantized input variables are grouped into a compound variable that is mapped through a stochastic matrix into the discrete output distribution. Specific output values are then obtained through a process of de-quantization. The information flow carried by message propagation is bi-directional and an algorithm for learning the factor graph parameters is explicitly derived. The model, that can easily merge discrete and continuous variables, is demonstrated with examples and simulations.

Reconstruction of Dominant Gene Regulatory Network from Microarray Data Using Rough Set and Bayesian Approach

Biological databases, containing genetic information of patients, are undergoing tremendous growth beyond our analysing capability. However such analysis can reveal new findings about the cause and subsequent treatment of any disease. Interactions between genes and the proteins they synthesize shape Genetic Regulatory Networks (GRN). In this context, it has been developed a model capable of representing small dominant GRN, combining characteristics from the Rough Set and Bayesian Network. The investigation has been carried out on the publicly available microarray dataset for Lung Adenocarcinoma, obtained from the National Center for Biotechnology Information (NCBI) website. The analysis revealed that Rough Set Theory (RST) is able to extract the various dominant genes in term of reducts which play an important role in causing the disease and also able to provide a unique simplified rule set for building expert systems in medical sciences with high accuracy and coverage factor. The next part of this work is based on reconstruction of GRN using Bayesian network, which is a mathematical tool for modelling conditional independences between stochastic variables like different gene expression. This proposed Bayesian approach using scaled mutual information for scoring is applied to the dataset corresponding to most dominant responsible genes for Adenocarcinoma to uncover, gene/protein interactions and key biological features of the cellular system. Finally different interacting regulatory path which are the gene signature for a particular disease, between dominating genes are inferred from the probability distribution table and Bayesian Graph. Such reconstructed regulatory network is attractive for their ability to describe complex stochastic processes like gene transcription, classification of biological sequencing and intuitive model of causal influence successfully. This may serve as a signature pattern of the disease Adenocarcinoma, which has been extracted from huge microarray dataset. Extraction of this signature pattern is very useful for diagnosis of this disease.

Exploring Many-Core Design Templates for FPGAs and ASICs

We present a highly productive approach to hardware design based on a many-core microarchitectural template used to implement compute-bound applications expressed in a high-level data-parallel language such as OpenCL. The template is customized on a per-application basis via a range of high-level parameters such as the interconnect topology or processing element architecture. The key benefits of this approach are that it (i) allows programmers to express parallelism through an API defined in a high-level programming language, (ii) supports coarse-grained multithreading and fine-grained threading while permitting bit-level resource control, and (iii) reduces the effort required to repurpose the system for different algorithms or different applications. We compare template-driven design to both full-custom and programmable approaches by studying implementations of a compute-bound data-parallel Bayesian graph inference algorithm across several candidate platforms. Specifically, we examine a range of template-based implementations on both FPGA and ASIC platforms and compare each against full custom designs. Throughout this study, we use a general-purpose graphics processing unit (GPGPU) implementation as a performance and area baseline. We show that our approach, similar in productivity to programmable approaches such as GPGPU applications, yields implementations with performance approaching that of full-custom designs on both FPGA and ASIC platforms.

Dynamic Networks from Hierarchical Bayesian Graph Clustering

Biological networks change dynamically as protein components are synthesized and degraded. Understanding the time-dependence and, in a multicellular organism, tissue-dependence of a network leads to insight beyond a view that collapses time-varying interactions into a single static map. Conventional algorithms are limited to analyzing evolving networks by reducing them to a series of unrelated snapshots.Here we introduce an approach that groups proteins according to shared interaction patterns through a dynamical hierarchical stochastic block model. Protein membership in a block is permitted to evolve as interaction patterns shift over time and space, representing the spatial organization of cell types in a multicellular organism. The spatiotemporal evolution of the protein components are inferred from transcript profiles, using Arabidopsis root development (5 tissues, 3 temporal stages) as an example.The new model requires essentially no parameter tuning, out-performs existing snapshot-based methods, identifies protein modules recruited to specific cell types and developmental stages, and could have broad application to social networks and other similar dynamic systems.

ASSESSING DIFFERENCES BETWEEN REALIZED AND ANTICIPATED GAINS FROM ELECTRONIC HEALTH RECORD ADOPTION.

The article presents the results of research on the adoption of electronic health record (EHR) systems, focusing on a cost-benefit analysis from the standpoint of physician practice. It is noted thta return on investment for EHR features direct costs and inderect savings for physicians, which has led to slow adoption rates. An overview of the research protocol, which used Bayesian Belief Network graphs to model the responses from a survey of physicians in Texas. It was found that existing users tended to emphasize the improved workflows which EHR provided, whereas those who had not yet adopted EHR thought of it primarily in terms of cost savings.

Belief propagation with Gaussian priors for pilot-assisted communication over fading ISI channels

Application of the belief propagation (BP) algorithm is proposed for pilot-assisted reception of Gaussian distributed symbols over unknown inter-symbol interference channels whose parameters are also Gaussian distributed. The proposed Bayesian network graph for the demodulator includes the channel parameters as explicit nodes, allowing the combined estimation of the channel and information bearing symbols with the aid of pilot symbols. Since direct application of BP is not tractable for this model, the algorithm is obtained by introducing approximations of the message distributions appropriately. The proposed algorithm is parallel in nature, is suitable for sparse channels, and can be easily extended to coded systems for joint demodulation and decoding. The numerical results show near-optimal performance in the minimum mean squared error sense for a small example, and a performance better than that of iterative semi-blind equalization with batch matrix-based estimators for the general case.

Bayesian Networks and Decision Graphs, 2nd Edition by Finn V. Jensen, Thomas D. Nielsen

Bayesian Networks and Decision Graphs, 2nd Edition by Finn V. Jensen, Thomas D. Nielsen

Bayesian graph edit distance

This paper describes a novel framework for comparing and matching corrupted relational graphs. The paper develops the idea of edit-distance originally introduced for graph-matching by Sanfeliu and Fu (1983). We show how the Levenshtein distance (1966) can be used to model the probability distribution for structural errors in the graph-matching problem. This probability distribution is used to locate matches using MAP label updates. We compare the resulting graph-matching algorithm with that recently reported by Wilson and Hancock. The use of edit-distance offers an elegant alternative to the exhaustive compilation of label dictionaries. Moreover, the method is polynomial rather than exponential in its worst-case complexity. We support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem. This demonstrates experimentally that the gain in efficiency is not at the expense of quality of match.