David Chiang, Darcey Riley · arXiv (Cornell University) · 2020
We propose the use of hyperedge replacement graph grammars for factor graphs, or factor graph grammars (FGGs) for short. FGGs generate sets of factor graphs and can describe a more general class of models than plate notation, dynamic graphical models, case-factor diagrams, and sum-product networks can. Moreover, inference can be done on FGGs without enumerating all the generated factor graphs. For finite variable domains (but possibly infinite sets of graphs), a generalization of variable elimination to FGGs allows exact and tractable inference in many situations. For finite sets of graphs (but possibly infinite variable domains), a FGG can be converted to a single factor graph amenable to standard inference techniques.
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Asif Gulraiz (20298253), Syed Sajjad Haider Zaidi (18707012), Bilal Mohammad Khan (21464190) · Figshare · 2025
<div> The paper discusses the recent developments and challenges in the energy sector, particularly focusing on the integration of renewable energy sources into microgrids and conventional power systems. It highlights the importance of predicting future energy generation for effective grid integration and discusses the use of Artificial Neural Network (ANN) and Auto-Regressive Moving Average (ARMA) models for this purpose. Additionally, it explores the role of distributed generation in providing ancillary services traditionally offered by conventional power systems and analyzes the impact of renewable energy sources on core parameters like frequency and voltage stability. It also discusses the rapid growth of solar photovoltaic (PV) systems and the need to assess their impacts on distribution networks. Furthermore, it addresses the ongoing energy crisis, particularly in South Asia, and proposes solutions such as power factor correction through technologies like Static VAR Compensators (SVCs) to enhance system stability and efficiency, especially in medium and long transmission lines. </div>
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Fabrizio Altarelli (770492), Alfredo Braunstein (52117), Luca Dall’Asta (770493) · Figshare · 2015
<p>Left: For the deterministic case the set of constraints is </p><p></p><p><mo>C</mo></p><p><mo>(</mo><mi>y</mi><mo>)</mo></p><mo>=</mo><p><mo>∏</mo></p><p><mi>u</mi><mo>∈</mo><mi>U</mi></p><p></p><p><mi>ψ</mi><mi>u</mi></p><p><mo>(</mo></p><p><mi>y</mi><mi>u</mi></p><mo>)</mo><p></p><p><mo>∏</mo></p><p><mi>a</mi><mo>∈</mo><mi>S</mi></p><p></p><p><mi>ϕ</mi><mi>a</mi></p><p><mo>(</mo></p><p><mi>y</mi><mi>a</mi></p><mo>)</mo><p></p><p></p><p></p>. Right: For the stochastic case, the factor graph includes mirror nodes (black lozanges) and the corresponing messages <i>Q</i><sub><i>u</i></sub>(<i>t</i><sub><i>u</i></sub>). The set of constraints is <p></p><p><mo>C</mo></p><p><mo>(</mo><mi>y</mi><mo>,</mo><mi>t</mi><mo>)</mo></p><mo>=</mo><p><mo>∏</mo></p><p><mi>u</mi><mo>∈</mo><mi>U</mi></p><p></p><p><mi>ψ</mi><mi>u</mi></p><p><mo>(</mo></p><p><mi>y</mi><mi>u</mi></p><mo>,</mo><p><mi>t</mi><mi>u</mi></p><mo>)</mo><p></p><p><mo>∏</mo></p><p><mi>a</mi><mo>∈</mo><mi>S</mi></p><p></p><p><mi>ϕ</mi><mi>a</mi></p><p><mo>(</mo></p><p><mi>y</mi><mi>a</mi></p><mo>)</mo><p></p><p></p><p></p>.<p></p>
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Zongchen Li (12476737), Guoxiong Zhou (12245608), Yaowen Hu (9187133) et al. · Figshare · 2022
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Philip R. Coryell (20036581), Paul B. Hardy (20036584), Susan Chubinskaya (18981) et al. · Figshare · 2024
<p>Average Z’ calculated every hour for 12hrs after the MMP-13 probe and APMA were added to each compound plate. Normal distribution was determined via Shapiro-Wilk test.</p> <p>(TIF)</p>
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Zhen Zhang, Fan Wu, Wee Sun Lee · arXiv (Cornell University) · 2019
Most of the successful deep neural network architectures are structured, often consisting of elements like convolutional neural networks and gated recurrent neural networks. Recently, graph neural networks have been successfully applied to graph structured data such as point cloud and molecular data. These networks often only consider pairwise dependencies, as they operate on a graph structure. We generalize the graph neural network into a factor graph neural network (FGNN) in order to capture higher order dependencies. We show that FGNN is able to represent Max-Product Belief Propagation, an approximate inference algorithm on probabilistic graphical models; hence it is able to do well when Max-Product does well. Promising results on both synthetic and real datasets demonstrate the effectiveness of the proposed model.
Cited by 12Open access
Kyusoon Kim, Heeseok Oh · IEEE Transactions on Pattern Analysis and Machine Intelligence · 2025
We propose a novel factor model in the graph frequency domain for multivariate data residing on the vertices of a graph, referred to as a multivariate graph signal. By utilizing graph filters, our model extends the frequency-domain approach of the dynamic factor model from time series to graphs, enabling a graph-aware and multiscale interpretation of factors across graph frequencies. This latent modeling approach reduces the dimensionality of graph signals, thereby improving the understanding of their structure. It also allows the use of the extracted factors for subsequent analyses, such as clustering. We describe the estimation of factors and their loadings and investigate the consistency of the factor estimator. In addition, we propose two consistent estimators for determining the number of factors. The finite sample performance of the proposed method is demonstrated through simulation studies across various graph structures. We also compare it with classical factor analysis and examine how the choice of graph structure affects the results. The findings show that our model achieves lower reconstruction errors and successfully incorporates the graph structure. Furthermore, we illustrate the effectiveness of the proposed method by applying it to G20 economic data, water quality data from the Geum River, and passenger data from the Seoul Metropolitan subway.
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Indar Sugiarto, Paul Maier, Jörg Conradt · 2013
When working with probabilistic graphical models we usually have two options to build the model: either using a Bayesian network (BN) or a Markov random field (MRF). However, there exist one more graphical representation which is able to unify the properties of BN and MRF that is called Factor Graph. This paper describes conceptual methods in working with factor graph especially with discrete random variables, how to learn its parameter and how to perform inference for making a reasoning task with it. Here we use population coding principles to discretize continues values of messages transmitted within the factor graph to update the network's internal belief. We provide several illustrative examples to highlight important aspects when developing a model for factor graphs.
Cited by 3
Wei-Fang Niu, Henry Horng‐Shing Lu · WORLD SCIENTIFIC eBooks · 2024
Graph data have become an important channel in exploring relations among a large number of subjects in the big data era. In past decades, community structures have been found in many complex real-world networks and play a key role in the modeling of graph data, for example, the stochastic block model (SBM) and its extensions. However, recent studies have unveiled more sophisticated modules, and typical examples include star and bipartite structures. In most graph models, these link-pattern modules are piled up in terms of multiple communities. This paper proposes a graph factor model in which each node is endowed with several (latent) features. Factors are channels for edge connections and can be characterized by link functions that map features of pairs of nodes to the edge probabilities. This model may naturally incorporate different kinds of link-pattern modules including communities, stars, and bipartite structures. The inference for the model can be carried out through an Markov Chain Monte Carlo (MCMC) procedure. Both synthetic data and real-world networks are used for numerical illustrations.
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Sivakumaran, Arun · University of Pretoria · 2020
The mathematical model underpinning the research into the secure sensing algorithm. Belief propagation is applied on this model to generate messages to marginalise the joint distribution represented by this graph.
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Wilson Y. Chen, M. P. Wand · Journal of the Korean Statistical Society · 2020
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Б. Н. Четверушкин, Vladimir Anatolievich Sudakov, Yu. P. Titov · Доклады Российской академии наук Математика информатика процессы управления · 2024
The paper proposes an original method for processing large factor models based on graph condensation using machine learning models and artificial neural networks. The proposed mathematical apparatus can be used in problems of planning and managing complex organizational and technical systems, in optimizing large socio-economic objects on the scale of state sectors, to solve problems of preserving the health of the nation (searching for compatibility when taking medications, optimizing resource provision for healthcare).
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Guorui Xiao, Zhengyang Xiao, Peiyuan Zhou et al. · Measurement Science and Technology · 2024
Abstract Kalman or Kalman-related filtering methods are routinely applied in precise point positioning (PPP). However, in robot simultaneous localization and mapping (SLAM) systems, factor graph optimization (FGO) has proven advantages over filtering methods in recent years, e.g. reducing the linearization error and support of plug-and-play features for multiple sensor fusion. Therefore, it would be interesting to apply the FGO to PPP. In addition, it will also facilitate the tight integration of PPP with Visual/LiDAR SLAM. In this work, PPP is solved under the FGO framework. A factor graph for PPP has been constructed. Results from 268 IGS-MGEX stations show that the FGO method can achieve a similar performance to that of Kalman filtering. First, the positioning accuracy in the convergence period can be improved for PPP based on FGO because it optimizes the entire state variables based on all the available observations. For applications that do not require real-time processing, the observation after the current state, e.g. future observations, can also be used to enhance the current state estimation. Second, the accuracy of static PPP is almost the same for the two methods with millimeter-accuracy for horizontal directions and centimeter-accuracy for vertical directions. Third, the kinematic PPP for both methods can achieve centimeter-level accuracy in horizontal directions and decimeter-level accuracy in vertical directions. Although the performance is comparable, it is noted that the computational efficiency of the FGO method is still a problem. For each epoch, the average elapsed time for Kalman filtering is 132 microseconds, while that of FGO method is 9664 microseconds. The elapsed time of the FGO method can be further improved if the fix-window optimization technique is applied, which will be investigated in the future.
Cited by 48Open access
Thành Tâm Nguyên · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · 2015
Factor graph is a representative graphical model to handle uncertainty of random variables. Factor graph has been used in various application domains such as named entity recognition, social network analysis, and credibility evaluation. In this paper, we study the problem of reducing uncertainty in factor graph towards reaching a common truth or deterministic information. We propose a pay-as-you-go approach that leverages user feedback for uncertainty reduction. As the availability of human input is often limited, we develop techiniques to identify the most uncertain spots in factor graph for maximizing the benefits of a given user feedback. We demonstrate the efficiency of our techniques on real-world applications.
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Yuexia Zhang, Pengfei Jia · Wireless Communications and Mobile Computing · 2022
To tackle the difficulty and high cost of UAV positioning in a 5G disaster environment, this study proposes a multi‐UAV coordinated positioning algorithm based on a factor graph (MUAV‐FGC). A factor graph model is designed for coordinated positioning of the master‐slave UAVs. In the positioning process, the influence of the speed and heading errors of the UAV on the positioning accuracy was analyzed, and the expected and variance values of the variables were used as the information transmitted between the factors. The error of the cooperative positioning algorithm was derived based on the factor graph. The coordinated positioning of multiple drones and the positioning accuracy improved. The simulation results show that, compared with the traditional extended Kalman filter (EKF) algorithm, the proposed MUAV‐FGC positioning algorithm reduces the mean positioning and root mean square error by approximately 18.86% and 17.54%, respectively, thus proving its effectiveness.
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Shuai Zhao (803827), Yunhai Tong (3366311), Zitian Wang (3366314) et al. · Figshare · 2016
<p>The edge from <i>Industry</i> to <i>Capitalization</i> makes the former a parent of the latter, and the latter a child of the former. The rule is also applied to all the other edges.</p>
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Yicong Li, Kuanjiu Zhou, Shuo Yu et al. · ArXiv.org · 2025
Comprehensible neural network explanations are foundations for a better understanding of decisions, especially when the input data are infused with malicious perturbations. Existing solutions generally mitigate the impact of perturbations through adversarial training, yet they fail to generate comprehensible explanations under unknown perturbations. To address this challenge, we propose AGAIN, a fActor GrAph-based Interpretable neural Network, which is capable of generating comprehensible explanations under unknown perturbations. Instead of retraining like previous solutions, the proposed AGAIN directly integrates logical rules by which logical errors in explanations are identified and rectified during inference. Specifically, we construct the factor graph to express logical rules between explanations and categories. By treating logical rules as exogenous knowledge, AGAIN can identify incomprehensible explanations that violate real-world logic. Furthermore, we propose an interactive intervention switch strategy rectifying explanations based on the logical guidance from the factor graph without learning perturbations, which overcomes the inherent limitation of adversarial training-based methods in defending only against known perturbations. Additionally, we theoretically demonstrate the effectiveness of employing factor graph by proving that the comprehensibility of explanations is strongly correlated with factor graph. Extensive experiments are conducted on three datasets and experimental results illustrate the superior performance of AGAIN compared to state-of-the-art baselines.
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Association for Artificial Intelligence 2022, Cheung, Ngai-Man, Cooray, Thilini · Underline Science Inc. · 2022
Unsupervised graph-level representation learning plays a crucial role in a variety of tasks such as molecular property prediction and community analysis, especially when data annotation is expensive. Currently, most of the best-performing graph embedding methods are based on Infomax principle. The performance of these methods highly depends on the selection of negative samples and hurt the performance, if the samples were not carefully selected. Inter-graph similarity-based methods also suffer if the selected set of graphs for similarity matching is low in quality. To address this, we focus only on utilizing the current input graph for embedding learning. We are motivated by an observation from real-world graph generation processes where the graphs are formed based on one or more global factors which are common to all elements of the graph (e.g., topic of a discussion thread, solubility level of a molecule). We hypothesize extracting these common factors could be highly beneficial. Hence, this work proposes a new principle for unsupervised graph representation learning: Graph-wise Common latent Factor EXtraction (GCFX). We further propose a deep model for GCFX, deepGCFX, based on the idea of reversing the above-mentioned graph generation process which could explicitly extract common latent factors from an input graph and achieve improved results on downstream tasks to the current state-of-the-art. Through extensive experiments and analysis, we demonstrate that, while extracting common latent factors is beneficial for graph-level tasks to alleviate distractions caused by local variations of individual nodes or local neighbourhoods, it also benefits node-level tasks by enabling long-range node dependencies, especially for disassortative graphs.
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ZHU Xinjuan, TONG Xiaokai, WANG Xihan et al. · SHILAP Revista de lepidopterología · 2022
In view of the problems of data sparsity and cold-start in traditional recommender model, the introduction of knowledge graph as side-information can address the above problems and be interpretable. However, knowledge graph is more biased towards propagation of knowledge than user preferences and difficult to capture high-order relations. To solve these problems, collaborative factor module was introduced into propagation-based method in this paper to capture high-order relations and discover latent patterns. In addition, a density gate composed of three co-occurrence matrix density parameters was designed, so that the collaborative factor module could dynamically control the output by the sparsity of the co-occurrence matrix. Contrast experiments were carried out on public film, book and music data sets. The experimental results demonstrate that the model performs well in the click-through-rate scenario, and the indicators are significantly improved on the data sets whose relations of knowledge graph are difficult to explain user preferences.
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Hwa-Lu Jhi, Jung-Chieh Chen, Chih‐Hung Lin et al. · IEEE Transactions on Wireless Communications · 2012
A high-accuracy and low-complexity TOA-based algorithm is proposed to estimate mobile station (MS) location. First, a factor-graph-based distributive approach is used, which can work in a multi-state system as well. By effectively exchanging the available soft-information or stochastic property of the variables, this distributive approach can perform almost as well as conventional algorithm while requiring much less computational workload. Second, data screening method was applied to reduce complexity and data discrimination to improve accuracy. Simulation results demonstrate that this approach can maintain good accuracy while achieving low complexity. Since this approach is accurate and easy to implement, it will better satisfy the demands of real applications.
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