A Stochastic Block Prior for Clustering in Graphical Models

BackgroundGraphical models were identified as a promising new approach to modeling high-dimensional clinical data. They provided a probabilistic tool to display, analyze and visualize the net-like dependence structures by drawing a graph describing the conditional dependencies between the variables. Until now, the main focus of research was on building Gaussian graphical models for continuous multivariate data following a multivariate normal distribution. Satisfactory solutions for binary data were missing. We adapted the method of Meinshausen and Bühlmann to binary data and used the LASSO for logistic regression. Objective of this paper was to examine the performance of the Bolasso to the development of graphical models for high dimensional binary data. We hypothesized that the performance of Bolasso is superior to competing LASSO methods to identify graphical models.MethodsWe analyzed the Bolasso to derive graphical models in comparison with other LASSO based method. Model performance was assessed in a simulation study with random data generated via symmetric local logistic regression models and Gibbs sampling. Main outcome variables were the Structural Hamming Distance and the Youden Index.We applied the results of the simulation study to a real-life data with functioning data of patients having head and neck cancer.ResultsBootstrap aggregating as incorporated in the Bolasso algorithm greatly improved the performance in higher sample sizes. The number of bootstraps did have minimal impact on performance. Bolasso performed reasonable well with a cutpoint of 0.90 and a small penalty term. Optimal prediction for Bolasso leads to very conservative models in comparison with AIC, BIC or cross-validated optimal penalty terms.ConclusionsBootstrap aggregating may improve variable selection if the underlying selection process is not too unstable due to small sample size and if one is mainly interested in reducing the false discovery rate. We propose using the Bolasso for graphical modeling in large sample sizes.

The inference and modeling of network‐like structures in genomic data is of prime importance in systems biology. Complex stochastic associations and interdependencies can very generally be described as a graphical model. However, the paucity of available samples in current high‐throughput experiments renders learning graphical models from genome data, such as microarray expression profiles, a challenging and very hard problem. Here we review several recently developed approaches to small‐sample inference of graphical Gaussian modeling and discuss strategies to cope with the high dimensionality of functional genomics data. Particular emphasis is put on regularization methods and an empirical Bayes network inference procedure.

Occupational exposure assessment is important in preventing occupational coal worker’s diseases. Methods have been proposed to assess compliance with exposure limits which aim to protect workers from developing diseases. A Bayesian framework with informative prior distribution obtained from historical or expert judgements has been highly recommended for compliance testing. The compliance testing is assessed against the occupational exposure limits (OEL) and categorization of the exposure, ranging from very highly controlled to very poorly controlled exposure groups. This study used a Bayesian framework from historical and expert elicitation data to compare the posterior probabilities of the 95th percentile (P95) of the coal dust exposures to improve compliance assessment and decision-making. A total of 10 job titles were included in this study. Bayesian framework with Markov chain Monte Carlo (MCMC) simulation was used to draw a full posterior probability of finding a job title to an exposure category. A modified IDEA (“Investigate”, “Discuss”, “Estimate”, and “Aggregate”) technique was used to conduct expert elicitation. The experts were asked to give their subjective probabilities of finding coal dust exposure of a job title in each of the exposure categories. Sensitivity analysis was done for parameter space to check for misclassification of exposures. There were more than 98% probabilities of the P95 exposure being found in the poorly controlled exposure group when using expert judgments. Historical data and non-informative prior tend to show a lower probability of finding the P95 in higher exposure categories in some titles unlike expert judgments. Expert judgements tend to show some similarity in findings with historical data. We recommend the use of expert judgements in occupational risk assessment as prior information before a decision is made on current exposure when historical data are unavailable or scarce.

Graphical models are used to examine conditional independence among random variables. In this chapter we take graphical models for the multivariate complex normal distribution w.r.t. simple undirected graphs into consideration. This is the first published presentation of these models. Graphical models for the multivariate real normal distribution, also called covariance selection models, have already been studied in the literature. The initial work on covariance selection models is done by Dempster (1972) and Wermuth (1976) and a presentation of these models is given in Eriksen (1992). Graphical models for contingency tables are introduced in statistics by Darroch et al. (1980) and further these are well-described in Lauritzen (1989). Graphical association models are treated in general in Whittaker (1990) and Lauritzen (1993). The complex normal graphical models are quite similar to the covariance selection models. We have chosen to develop this chapter without use of exponential families. We study definition of the model, maximum likelihood estimation and hypothesis testing. To verify some of the results in the chapter we use results from mathematical analysis. These can be found in e.g. Rudin (1987). In graphical models one uses the concentration matrix instead of the variance matrix as it is more advantageous. Therefore we define this matrix and derive a relation which is basic for complex normal graphical models. Afterwards we formally define a complex normal graphical model w.r.t. a simple undirected graph. As these models are used to examine conditional independence of selected pairs of variables given the remaining ones we are mainly interested in inference on the concentration matrix. It is possible to base the maximum likelihood estimation of the concentration matrix on a complex random matrix with mean zero.

The connection of clinical care with clinical research is the main purpose of the Learning Health System (LHS) integrating scientific information, informatics, and patient care. The LHS generates new medical knowledge as a by-product of the care process. For this purpose, the aggregation of data from Electronic Health Records (EHR), Case Report Forms (CRF), web questionnaires with other data sources like primary care databases and genetic data repositories is necessary for research purposes. This joining of healthcare and research processes results in challenges for the privacy protection framework of the LHS. Based on an exploration of EU legal requirements for data protection and privacy, different data access policies of data provider organizations as well as existing privacy frameworks of research projects, basic privacy principles and privacy requirements were extracted. Based on privacy principles and legal requirements a graphical model to display privacy protection requirements was created. This graphical model is based on concepts of requirements engineering and can be used like a model kit to create new privacy frameworks and to ease knowledge exchange with stakeholders of the LHS. Our model is built upon the concept of three privacy zones (Care Zone, Non-Care Zone and Research Zone) representing areas where similar legal requirements and rules apply. These zones contain databases, data transformation operators, such as data linkers and privacy filters and graphs to indicate the data flow necessary for research processes. The aim of the model is to help arrange its components in a way that creates a risk gradient for the data flow from a zone of high risk for patient identification to a zone of low risk. The model is applied to the analysis of several general clinical research usage scenarios and two research use cases from the TRANSFoRm project (finding patients for clinical research and linkage of databases). Both use cases represent different data collection aspects of the LHS. The model was used during discussions with data managers from the NIVEL Primary Care Database in the Netherlands and validated by representing an approved research case of using primary care data employing NIVEL services. Experiences with the graphic privacy model used to improve the privacy framework of TRANSFoRm and with the presentation of the model to LHS stakeholders and the research community are discussed.

Recently, there has been an explosive growth in graphical modeling approaches for estimating brain functional networks. In a detailed study, we show that surprisingly, standard graphical modeling approaches for fMRI data may not yield accurate estimates of the brain network due to the inability to suitably account for temporal correlations. We propose a novel Bayesian matrix normal graphical model that jointly models the temporal covariance and the brain network under a separable structure for the covariance to obtain improved estimates. The approach is implemented via an efficient optimization algorithm that computes the maximum-a-posteriori network estimates having desirable theoretical properties and which is scalable to high dimensions. The proposed method leads to substantial gains in network estimation accuracy compared to standard brain network modeling approaches as illustrated via extensive simulations. We apply the method to resting state fMRI data from the Human Connectome Project involving a large number of time scans and brain regions, to study the relationships between fluid intelligence and functional connectivity, where it is not computationally feasible to apply existing matrix normal graphical models. Our proposed approach led to the detection of differences in connectivity between high and low fluid intelligence groups, whereas these differences were less pronounced or absent using the graphicallasso.

Structural-graphic modelling is considered: concept, connections, classification and application in cartographic research. The principles of modelling in cartography (the possibility of using maps using common epistemological categories; the use of general scientific methods of modelling and rational forms and variants of contacts with other types of modelling; the etymology of the term indicates the place of cartographic modelling as a means of research in the general system of cognition). The functions of structural-graphical modelling are defined. Functions of structural and graphical modelling are determined, and they are investigated, which allow: to carry out the selection of existing maps necessary for research; identify elements of systems that have not yet been mapped; determine the topic of maps and their placement within the complex cartographic works; use maps of other elements of the system when creating a series of maps of each specific element; ensure that the maps of this element are those of other elements; change the complex maps and their groups; determine the main columns of tables for collecting information in relational or electronic databases; identify sections of map legends; present legends in the form of graphical link models of lower-ranking system elements. Spatial modeling is investigated, the types and models of real-world spatial models are substantiated and identified, in particular: analogue (an analog model is defined as a large-scale model, representation of the real-world system, in which each part of the real system is modeled in miniature, very popular analog models of the real world are paper topographic, geographic and thematic maps); digital models (all operations are carried out using a computer, data is collected in the data model and encoded using different coding schemes that reduce the relevant aspects of the real world to structures of zeros and ones); discrete (models imitate the processes that occur between discrete entities, such as the forces acting between celestial bodies and controlling their movement, or the behavior of humans or animals when they interact in space); continuous models (on the other hand, are models in terms of variables that are continuous space functions, for example, atmospheric pressure or temperature, soil acidity or humidity. The concept of a continuous field describes the geographic world with a series of continuous maps, each of which represents the changes of a definite variable over the surface of the Earth); individual (you can model any system with a set of rules on the mechanical behavior of the main objects of the system); aggregate models (approach is to merge (aggregate) individual objects into a single whole and model the system through the behavior of these aggregates); static model (models can be static if the input and output are the same at the same time point, or dynamic, if the output represents a later time point than the input); dynamic models (dynamic models, on the other hand, constitute a process that changes or transforms some aspects of the Earth’s surface over time); cellular vending machines (in cellular automaton spatial variations are represented as a raster of fixed resolution, each cell of which is assigned one of a finite set of certain states); agent models (agent model is a series of interacting active objects that reflect objects and relationships in the real world, from the point of view of practical application, agent modeling can be defined as a modeling method that investigates the behavior of decentralized agents and how this behavior determines the behavior of the whole system as a whole).

<p>Global or large-scale hydrological forecasting systems covering entire countries, continents and even the entire planet are growing in popularity. As more large-scale hydrological forecasting systems emerge, it is likely that they will co-exist with pre-existing local forecasting systems. It is the case for instance in Canada, where most provinces have their own streamflow forecasting system, while the new NSRPS will eventually cover the whole country using a 1km by 1km grid. Those province, for instance Quebec, built their own forecasting systems on hydrological models configured for river catchments rather than a regular grid. Using this situation as a starting point and a case study, we propose a Bayesian framework for merging the forecasts from two systems. Within this Bayesian framework, the large-scale prior information comes from the NSRPS. This prior information is then updated using forecasts from the government of Quebec and the associated likelihood. In order to account for forecast uncertainty, this work is carried out using a probabilistic approach for both the NSRPS and Quebec’s Système de Prévision Hydrologique (SPH). While SPH produces probabilistic forecasts by default, the preliminary version of the NSRPS that we had access to is deterministic. Consequently, forecasts from the NSRPS had to be dressed into an ensemble in order to use them as prior distribution within the Bayesian merging framework. Alternative prior distributions (climatology, Markov chain) are also considered instead of those obtained from the NSRPS. Since both forecasting systems include ungauged sites, a version of this Bayesian merging framework based on regional statistics was also developed and tested using cross-validation. Our results show that the merged forecasts perform at least as well as the best individual system, for both gauged and ungauged basins. For longer lead times, merged forecasts can even outperform individual systems. Considering that the NSRPS relies on a non-calibrated model with no data assimilation, those results show that there could be important practical gains in merging large scale hydrological forecasts with local scale forecasts.</p>

A Two-Year cohort study examining the impact of cytokines and chemokines on cognitive and psychiatric outcomes in Long-COVID-19 patients.

SUMMARY Bayesian graphical modelling represents the synthesis of several recent developments in applied complex modelling. After describing a moderately challenging real example, we show how graphical models and Markov chain Monte Carlo methods naturally provide a direct path between model specification and the computational means of making inferences on that model. These ideas are illustrated with a range of modelling issues related to our example. An appendix discusses the BUGS software.

Today we are witnessing the necessity to align Business and Information Technology (IT) as well as a change in the role of IT from an enabler to an industrial sector in its own right. Based on the assumption that businesses in different sectors of the economy will require IT for different reasons and in different ways, this article introduces the EU project plugIT that aspires to develop an IT-Socket that will realize the vision of businesses "plugging-in" to IT. Three demonstration scenarios deal with: (1) "Certification" of IT infrastructure to stay compliant with regulations, (2) "Virtual Organisation" by evolving the current service orientation to a higher and more business driven abstraction as well as, (3) "Governance" of IT infrastructure introducing business context into highly distributed and complex systems. The IT-Socket follows a model-driven approach by introducing graphical modelling languages as mediators between the domain experts and IT. The research challenge is to link human interpretable graphical models – partly semi-formal – with machine interpretable semantic formalisms to enable: (1) a tighter involvement of domain experts when expressing formal knowledge specifying business requirements on IT infrastructure and services, (2) different graphical modelling languages for different views on the IT-Socket to provide modelling languages the domain expert is used to work with as well as, (3) a domain specific notation for semantics by integrating formal concepts of semantics with the graphic notation from modelling languages.

Process knowledge is the most reliable resource for qualitative modeling of complex industrial processes, which is typically expressed in natural language and stored in human brains. We thus need to capture useful connectivity and causality from such resources and convert the information into computer accessible formats. From first-principle structural models, causality can be captured and expressed as structural equations. From unstructured process knowledge and dynamic and algebraic equations, graphical models, in particular signed directed graphs and variants, can be obtained. Graphic models are widely used due to their computer tractability and human readability. Rule-based models are another alternative, which is used in expert systems. When the process information is accessible in web language, connectivity can be retrieved by query.

Graphs are used effectively in representing model structures in a variety of research fields such as statistics, artificial intelligence, data mining, biological science, medicine, decision science, educational science, etc. We use different forms of graphs according to the nature of the random variables involved. For instance, arrows are used when the relationship is asymmetric as when it is causal or temporal, and undirected edges are used when the relationship is associative. When a random field is Markov with respect to a triangulated graph, i.e., a decomposable graph, which does not have a cycle of length 4 or larger, its corresponding probability model is expressed in a factorized form which facilitates computation over the probability distribution of the random field (Kemeny et al., 1976). This computational feasibility, among others, makes such a Markov random field a most favored random field. Literature is abound in regard to the properties of theMarkov randomfield which isMarkov with respect to a decomposable graph (see Chapter 12 of Whittaker (1990) and Lauritzen (1996)). We call such a random field a decomposable graphical model. There have been remarkable improvements in learning graphical models in the form of a Bayesian network (Pearl, 1986 & 1988; Heckerman et al., 1995; Friedman & Goldszmidt, 1998; Neil et al., 1999; Neapolitan, 2004) from data. This learning however is mainly instrumented by heuristic searching algorithms and the model searching is usually NP-hard [Chickering (1996)]. A good review is given in Cooper (1999) and Neopolitan (2004) on structural discovery of Bayesian or causal networks from data. Since a Bayesian network can be transformed into a decomposable graph [Lauritzen and Spiegelhalter (1988)], the method of model combination which is proposed in this paper would lead to an improvement in graphical modelling from data. This method would be useful when we don’t have data which are large enough for the number of the random variables that are involved in the data. In this situation, it is desirable to develop marginal models of manageable sizes for subsets of variables and then search for a model for the whole set of variables based on the marginal models. The main idea of the method to be proposed is similar to constraint-based learning as described in Neapolitan (2004) (also see Meek (1995) and Spirtes et al. (2000)) where we

Graphical models are omnipresent in the software engineering field, but most current graphical modeling languages do not scale with the increasing size and complexity of today’s systems. The navigation in the diagrams becomes a major problem especially if different aspects of the system are scattered over multiple, only loosely coupled diagrams. 
\nIn this paper we present the hierarchical navigation capabilities of the Adora modeling tool. The user of this tool can freely control the level of detail in different parts of the model to reduce the size and complexity of the diagrams being displayed. Our fisheye visualization technique makes it possible to integrate all modeling aspects (structure, data, behavior, etc.) in one coherent model while keeping the size and complexity of the diagrams within reasonable limits.

Background: At present, there is an urgent problem of renovation of rolling stock characterized by a high degree in Russia. The leading position in the country's transport system belongs to railway transport. In the context of declining demand for transportation investments in railcars, which represent a significant amount of capital investment, require reasonable management decisions.
 Aim: is to work out a decision-making model for renewal the transport organization's railway rolling stock.
 Methods: of technical, economic, investment and financial analysis, decision tree, graphical modeling, system approach.
 Results: The basic components of the decision-making model are determined. The key indicators of railway rolling stock renewal are defined, reflecting the criteria for making managerial decisions in the field of operational, investment and financial activities. A graphical model is proposed that interprets the decision support system for purchasing new railcars.
 Conclusion: Using the proposed model of decision-making in the field of renovation of rolling stock allows to transfer this process to a qualitatively new level, based on the results of an objective assessment of the current and forecast state of the management object according to various alternative scenarios and based on the selection of the rational decision by comparing the expected results for each of the considered alternatives and analysis degree of their compliance with the determined goals due to its versatility and complexity.