Single Graphical Model Research Articles

Copula Graphical Models for Heterogeneous Mixed Data

This article proposes a graphical model that handles mixed-type, multi-group data. The motivation for such a model originates from real-world observational data, which often contain groups of samples obtained under heterogeneous conditions in space and time, potentially resulting in differences in network structure among groups. Therefore, the iid assumption is unrealistic, and fitting a single graphical model on all data results in a network that does not accurately represent the between group differences. In addition, real-world observational data is typically of mixed discrete-and-continuous type, violating the Gaussian assumption that is typical of graphical models, which leads to the model being unable to adequately recover the underlying graph structure. Both these problems are solved by fitting a different graph for each group, applying the fused group penalty to fuse similar graphs together and by treating the observed data as transformed latent Gaussian data, respectively. The proposed model outperforms related models on learning partial correlations in a simulation study. Finally, the proposed model is applied on real on-farm maize yield data, showcasing the added value of the proposed method in generating new production-ecological hypotheses. An R package containing the proposed methodology can be found on https://CRAN.R-project.org/package=heteromixgm. Supplementary materials for this article are available online.

Robust depth estimation on real-world light field images using Gaussian belief propagation

Depth estimation on light field images has been well researched on synthetic datasets. However, existing methods often fail on real-world light field images because of the real-world noises. Due to the lack of real-world light field image datasets for depth estimation, the learning-based methods, e.g., convolutional neural networks, are not capable of performing well on real-world light field images with only synthetic datasets available. In this paper, we adopt the optical flow estimation method to estimate depth from light field images since (i) the existing optical flow methods have shown robustness with significant real-world noises; (ii) the adopted optical flow estimation method does not require any training data, thus not limited to the synthetic datasets. The depth can be solved via the approach of optical flow estimation because (i) a sub-aperture image array can be converted from a light field image; (ii) the optical flow between every two adjacent sub-aperture images of the image array is exactly the disparity between the two images. Furthermore, since a sub-aperture array contains numerous adjacent image pairs, numerous optical flow maps can be generated from the sub-aperture array. We show the depth can be well refined from these numerous optical flow maps through modeling these maps in a single graphical model (a pairwise Gaussian MRF to be precise) and inferencing this graphical model by Gaussian belief propagation (GaBP). Experiments show that i) the proposed method achieves better depth estimation than the state-of-the-art methods on real-world light field images; ii) the proposed method can estimate the depth of objects at a far distance (3.5–9.5 m) much more accurately than the state-of-the-art convolutional neural networks.

DEVELOPMENT OF THE STEREOMETRIC METHOD TO THE ANALYSIS OF ECONOMIC CATEGORIES AND PROCESSES AND ITS APPLICATION IN SECURITY AND TAXATION

The article is aimed at the enhancement of the stereometric approach to analysing economic categories and processes and investigating directions of its application in the science of security and taxation. Methodology. The methodological basis of the study consists of general scientific methods of analysis and synthesis, a comparative study of existing models of economic categories, which are based on the stereometric approach. The empirical method is used to describe the problem of using a stereometric approach to determining the economic security of an enterprise. The results of the study. The article demonstrates that modern realities increasingly require spatial thinking from economists, thus conditioning the appearance of 3D models of some economic categories in economic research papers. A number of stereometric elements have been applied by both foreign and Ukrainian scholars in the economic sphere for several decades. The article points out that no current model could claim the complete realization of the stereometric approach as an independent unidirectional array of the content of principles and methods of analysing economic categories and processes. There are also determined regularities not considered by other scientists, as well as current problems and omissions. Practical implications. There are substantiated differences between the stereometric and graphical methods of economic analysis. The stereometric approach is suggested to be meant as one of the economic analysis approaches based on visualization of economic categories and processes on the basis of geometric solids allowing qualitative and quantitative assessment of the level and dynamics of the selected array of indicators put into a single graphical model. There is revealed essence and principles of the stereometric approach use in the economy and in the science of security in particular. Economic security is treated as one of the ternary nature being resources, processes and a condition simultaneously. The article suggests a pyramid to determine economic security and proves that changes of quality, speed, and quantity of business processes expressed by changes of corresponding angles of the pyramid impact both the condition and the general level of economic security. Relevance/originality. The presented proposals on enhancing the stereometric approach create a theoretical foundation for applied research in various industries. The enhanced stereometric approach enables building a general-theoretical concept of economic security considering its connections with such notions as competitiveness and development.

An unsupervised anomaly detection approach using energy-based spatiotemporal graphical modeling

This paper presents a new data-driven framework for unsupervised system-wide anomaly detection for modern distributed complex systems within which there exists a strong connectivity among sub-systems, operating in diverse modes and encountering a large variety of anomalies. The framework is based on a spatiotemporal feature extraction scheme built on the concept of symbolic dynamics for discovering and representing causal interactions among subsystems. The extracted features from the spatiotemporal pattern network (STPN) are then used to learn system-wide patterns via a Restricted Boltzmann Machine (RBM), to form an energy based anomaly detection approach. While STPN is treated as a weak learner of system modes (in terms of difficulty in discovering true graphical representations), RBM is treated as a boosting approach to form a strong learner of system characteristics. Case studies with simulated data and real data from an integrated building system are used to validate the proposed approach. The results show that: (i) the increase in RBM free energy in the off-nominal conditions compared to that in the nominal conditions can be used for anomaly detection; (ii) the proposed framework formulates a strong learning model (STPN+RBM) from weak frequentist model–STPN, via boosting with RBM; and (iii) the STPN+RBM framework can capture multiple nominal operating modes of distributed complex systems with a single graphical model.

Overlapping Decomposition for Gaussian Graphical Modeling

Correlation based graphical models are developed to detect the dependence relationships among random variables and provide intuitive explanations for these relationships in complex systems. Most of the existing works focus on learning a single correlation based graphical model for all the random variables. However, it is difficult to understand and interpret the massive dependencies of the variables learned from a single graphical model at a global level especially when the graph is large. In order to provide a clearer understanding for the dependence relationships among a large number of random variables, in this paper, we propose the problem of estimating an overlapping decomposition for the Gaussian graphical model of a large scale to generate overlapping sub-graphical models, where strong and meaningful correlations remain in each subgraph with a small scale. Specifically, we propose a greedy algorithm to achieve the overlapping decomposition for the Gaussian graphical model. A key technique of the algorithm is that the problem of solving a $(k+1)$ -node Gaussian graphical model can be approximately reduced to the problem of solving a one-step vector regularization problem based on a solved $k$ -node Gaussian graphical model with theoretical guarantee. Based on this technique, a greedy expansion algorithm is proposed to generate the overlapping subgraphs. Moreover, we extend the proposed method to deal with dynamic graphs where the dependence relationships among random variables vary with the time. We evaluate the proposed methods on synthetic dataset and a real-life traffic dataset, and the experimental results show the superiority of the proposed methods.

El Estudio Paramental en el Modelo de Información del Edificio Histórico o “Proyecto HBIM”

The Building Information Modeling (BIM) has now become a collaborative system that greatly benefits the industries involved in the AEC sector. The essence of BIM is to be a container core with graphic and alphanumeric information, where each discipline participatory dump their knowledge to suit the peculiarities of the building in coordination with the other agents involved. If this same scenario is moved to Heritage, we see that the needs are the same; archaeologist, architect, historian, restorer or engineer are at the same crossroads when it comes to passing on their assumptions and subject to debate before approval. The article will present an effective methodology to implement the stratigraphic study of surfaces. The intention is to dump the information gathered in Phase auscultation in a single graphical model, operating from different disciplines and allows inter operationalize avoiding unnecessary data duplication and contradictory. An intervention project supported by an information model of the Historic Building, which we can call HBIM Project (Historic Building Information Modelling Project) is established.

Concurrent filtering and smoothing: A parallel architecture for real-time navigation and full smoothing

We present a parallelized navigation architecture that is capable of running in real-time and incorporating long-term loop closure constraints while producing the optimal Bayesian solution. This architecture splits the inference problem into a low-latency update that incorporates new measurements using just the most recent states (filter), and a high-latency update that is capable of closing long loops and smooths using all past states (smoother). This architecture employs the probabilistic graphical models of factor graphs, which allows the low-latency inference and high-latency inference to be viewed as sub-operations of a single optimization performed within a single graphical model. A specific factorization of the full joint density is employed that allows the different inference operations to be performed asynchronously while still recovering the optimal solution produced by a full batch optimization. Due to the real-time, asynchronous nature of this algorithm, updates to the state estimates from the high-latency smoother will naturally be delayed until the smoother calculations have completed. This architecture has been tested within a simulated aerial environment and on real data collected from an autonomous ground vehicle. In all cases, the concurrent architecture is shown to recover the full batch solution, even while updated state estimates are produced in real-time.

Relating Things and Stuff via ObjectProperty Interactions.

In the last few years, substantially different approaches have been adopted for segmenting and detecting "things" (object categories that have a well defined shape such as people and cars) and "stuff" (object categories which have an amorphous spatial extent such as grass and sky). While things have been typically detected by sliding window or Hough transform based methods, detection of stuff is generally formulated as a pixel or segment-wise classification problem. This paper proposes a framework for scene understanding that models both things and stuff using a common representation while preserving their distinct nature by using a property list. This representation allows us to enforce sophisticated geometric and semantic relationships between thing and stuff categories via property interactions in a single graphical model. We use the latest advances made in the field of discrete optimization to efficiently perform maximum a posteriori (MAP) inference in this model. We evaluate our method on the Stanford dataset by comparing it against state-of-the-art methods for object segmentation and detection. We also show that our method achieves competitive performances on the challenging PASCAL '09 segmentation dataset.

Markov Random Field-based Fitting of a Subdivision-based Geometric Atlas.

An accurate labeling of a multi-part, complex anatomical structure (e.g., brain) is required in order to compare data across images for spatial analysis. It can be achieved by fitting an object-specific geometric atlas that is constructed using a partitioned, high-resolution deformable mesh and tagging each of its polygons with a region label. Subdivision meshes have been used to construct such an atlas because they can provide a compact representation of a partitioned, multi-resolution, object-specific mesh structure using only a few control points. However, automated fitting of a subdivision mesh-based geometric atlas to an anatomical structure in an image is a difficult problem and has not been sufficiently addressed. In this paper, we propose a novel Markov Random Field-based method for fitting a planar, multi-part subdivision mesh to anatomical data. The optimal fitting of the atlas is obtained by determining the optimal locations of the control points. We also tackle the problem of landmark matching in tandem with atlas fitting by constructing a single graphical model to impose pose-invariant, landmark-based geometric constraints on atlas deformation. The atlas deformation is also governed by additional constraints imposed by the mesh's geometric properties and the object boundary. We demonstrate the potential of the proposed method on the difficult problem of segmenting a mouse brain and its interior regions in gene expression images which exhibit large intensity and shape variability. We obtain promising results when compared with manual annotations and prior methods.

Joint estimation of multiple graphical models

Gaussian graphical models explore dependence relationships between random variables, through the estimation of the corresponding inverse covariance matrices. In this paper we develop an estimator for such models appropriate for data from several graphical models that share the same variables and some of the dependence structure. In this setting, estimating a single graphical model would mask the underlying heterogeneity, while estimating separate models for each category does not take advantage of the common structure. We propose a method that jointly estimates the graphical models corresponding to the different categories present in the data, aiming to preserve the common structure, while allowing for differences between the categories. This is achieved through a hierarchical penalty that targets the removal of common zeros in the inverse covariance matrices across categories. We establish the asymptotic consistency and sparsity of the proposed estimator in the high-dimensional case, and illustrate its performance on a number of simulated networks. An application to learning semantic connections between terms from webpages collected from computer science departments is included.

A methodology for eliciting and modeling exceptions

Exceptions in safety–critical systems must be addressed during conceptual design and risk analysis. We developed a conceptual model of exceptions, a methodology for eliciting and modeling exceptions, and templates for modeling them in an extension of the Object-Process Methodology (OPM)—a system analysis and design methodology and language that uses a single graphical model for describing systems, including their timing exceptions, which has been shown to be an effective modeling methodology. Using an antibiotics treatment guideline as a case study, we demonstrate the value of our approach in eliciting and modeling exceptions that occur in clinical care systems.

A Constructive Graphical Model Approach for Knowledge‐Based Systems: A Vehicle Monitoring Case Study

Graphical models have been widely applied to uncertain reasoning in knowledge‐based systems. For many of the problems tackled, a single graphical model is constructed before individual cases are presented and the model is used to reason about each new case. In this work, we consider a class of problems whose solution requires inference over a very large number of models that are impractical to construct a priori. We conduct a case study in the domain of vehicle monitoring and then generalize the approach taken. We show that the previously held negative belief on the applicability of graphical models to such problems is unjustified. We propose a set of techniques based on domain decomposition, model separation, model approximation, model compilation, and re‐analysis to meet the computational challenges imposed by the combinatorial explosion. Experimental results on vehicle monitoring demonstrated good performance at near‐real‐time.