Parametric Modelling of Multivariate Count Data Using Probabilistic Graphical Models

Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial issue in numerous modelling problems, particularly in the fields of biology and ecology (where the data can represent, for example, children counts associated with multitype branching processes), sociology and econometrics. We focus on I) Identifying categories that appear simultaneously, or on the contrary that are mutually exclusive. This is achieved by identifying conditional independence relationships between the variables; II)Building parsimonious parametric models consistent with these relationships; III) Characterising and testing the effects of covariates on the joint distribution of the counts. To achieve these goals, we propose an approach based on graphical probabilistic models, and more specifically partially directed acyclic graphs

Enumeration of labelled chain graphs and labelled essential directed acyclic graphs

AbstractA chain graph is a digraph whose strong components are undirected graphs and a directed acyclic graph (ADG or DAG) G is essential if the Markov equivalence class of G consists of only one element. We provide recurrence relations for counting labelled chain graphs by the number of chain components and vertices; labelled essential DAGs by the number of vertices. The second one is a lower bound for the number of labelled essential graphs. The formula for labelled chain graphs can be extended in such a way, that allows us to count digraphs with two additional properties, which essential graphs have

Particle Swarm Optimisation for learning Bayesian Networks

This paper discusses the potential of Particle Swarm Optimisation (PSO) for inducing Bayesian Networks (BNs). Specifically, we detail two methods which adopt the search and score approach to BN learning. The two algorithms are similar in that they both use PSO as the search algorithm, and the K2 metric to score the resulting network. The difference lies in the way networks are constructed. The CONstruct And Repair (CONAR) algorithm generates structures, validates, and repairs if required, and the REstricted STructure (REST) algorithm, only permits valid structures to be developed. Initial experiments indicate that these approaches produce promising results when compared to other BN learning strategies

A methodology for developing local smart diagnostic models using expert knowledge

© 2015 IEEE. This paper describes an innovative modular component-based modelling approach for diagnostics and condition-monitoring of manufacturing equipment. The approach is based on the use of object-oriented Bayesian networks, which supports a natural decomposition of a large and complex system into a set of less complex components. The methodology consists of six steps supporting the development process: Begin, Design, Implement, Test, Analyse, and Deploy. The process is iterative and the steps should be repeated until a satisfactory model has been achieved. The paper describes the details of the methodology as well as illustrates the use of the component-based modelling approach on a linear axis used in manufacturing. This application demonstrates the power and flexibility of the approach for diagnostics and condition-monitoring and shows a significant potential of the approach for modular component-based modelling in manufacturing and other domains