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21
Representation of Irrelevance Relations By Annotated Graphs
, 2000
"... Irrelevance relations are sets of statements of the form: given that the `value' of Z is known, the `values' of Y can add no further information about the `values' of X. Undirected Graphs (UGs), Directed Acyclic Graphs (DAGs) and Chain Graphs (CGs) were used and investigated as sch ..."
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Irrelevance relations are sets of statements of the form: given that the `value' of Z is known, the `values' of Y can add no further information about the `values' of X. Undirected Graphs (UGs), Directed Acyclic Graphs (DAGs) and Chain Graphs (CGs) were used and investigated as schemes for the purpose of representing irrelevance relations. It is known that, although all three schemes can approximate irrelevance, they are inadequate in the sense that there are relations which cannot be fully represented by anyone of them. In this paper annotated graphs are defined and suggested as a new model for graphical representation. It is shown that this new model is a proper generalization of the former
Structural Learning of Chain Graphs via Decomposition
"... Chain graphs present a broad class of graphical models for description of conditional independence structures, including both Markov networks and Bayesian networks as special cases. In this paper, we propose a computationally feasible method for the structural learning of chain graphs based on the i ..."
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Chain graphs present a broad class of graphical models for description of conditional independence structures, including both Markov networks and Bayesian networks as special cases. In this paper, we propose a computationally feasible method for the structural learning of chain graphs based on the idea of decomposing the learning problem into a set of smaller scale problems on its decomposed subgraphs. The decomposition requires conditional independencies but does not require the separators to be complete subgraphs. Algorithms for both skeleton recovery and complex arrow orientation are presented. Simulations under a variety of settings demonstrate the competitive performance of our method, especially when the underlying graph is sparse.
S.: Directed cycles in Bayesian belief networks: probabilistic semantics and consistency checking complexity
 MICAI 2005: Advances in Artificial Intelligence
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Random Effects Graphical Models for Multiple Site Sampling
, 2003
"... We propose a two component graphical chain model, the discrete regression distribution, in which a set of categorical (or discrete) random variables is modeled as a response to a set of categorical and continuous covariates. We examine necessary and sufficient conditions for a discrete regression di ..."
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We propose a two component graphical chain model, the discrete regression distribution, in which a set of categorical (or discrete) random variables is modeled as a response to a set of categorical and continuous covariates. We examine necessary and sufficient conditions for a discrete regression distribution to be described by a given graph. The discrete regression formulation is extended to a statespace representation for the analysis of data collected at many random sites. In addition, some new results concerning marginalization in chain graph models are explored. Using the new results, we examine the Markov properties of the extended model as well as the marginal model of covariates and responses.
An Algorithm for Reading Dependencies from the Minimal Undirected Independence Map of a Graphoid that Satisfies Weak Transitivity
"... We present a sound and complete graphical criterion for reading dependencies from the minimal undirected independence map G of a graphoid M that satisfies weak transitivity. Here, complete means that it is able to read all the dependencies in M that can be derived by applying the graphoid properties ..."
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We present a sound and complete graphical criterion for reading dependencies from the minimal undirected independence map G of a graphoid M that satisfies weak transitivity. Here, complete means that it is able to read all the dependencies in M that can be derived by applying the graphoid properties and weak transitivity to the dependencies used in the construction of G and the independencies obtained from G by vertex separation. We argue that assuming weak transitivity is not too restrictive. As an intermediate step in the derivation of the graphical criterion, we prove that for any undirected graph G there exists a strictly positive discrete probability distribution with the prescribed sample spaces that is faithful to G. We also report an algorithm that implements the graphical criterion and whose running time is considered to be at most O(n 2 (e+n)) for n nodes and e edges. Finally, we illustrate how the graphical criterion can be used within bioinformatics to identify biologically meaningful gene dependencies.
A Note on Nonsymmetric Independence Models
"... Some independence models not necessarily closed with respect to symmetry property are briefly recalled and they arise in different framework. The Lseparation criterion for directed acyclic graphs is useful for effective description of such models. Since independence structures are richer than the g ..."
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Some independence models not necessarily closed with respect to symmetry property are briefly recalled and they arise in different framework. The Lseparation criterion for directed acyclic graphs is useful for effective description of such models. Since independence structures are richer than the graphical ones, the notion of minimal Imap has been redefined in this context and its properties are detected. 1
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"... Probabilistic graphical models, such as Bayesian networks, allow representing conditional independence information of random variables. These relations are graphically represented by the presence and absence of arcs and edges between vertices. Probabilistic graphical models are nonunique representat ..."
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Probabilistic graphical models, such as Bayesian networks, allow representing conditional independence information of random variables. These relations are graphically represented by the presence and absence of arcs and edges between vertices. Probabilistic graphical models are nonunique representations of the independence information of a joint probability distribution. However, the concept of Markov equivalence of probabilistic graphical models is able to offer unique representations, called essential graphs. In this survey paper the theory underlying these concepts is reviewed.
Clinical Decision Support
, 2006
"... Within orthopædics, clinicians routinely take multiple measurements on patients during the course of their treatment, often repeating the same measurements before and after operations, and subsequently at periodic followup consultations. This data combined with additional factors gives a wealth of ..."
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Within orthopædics, clinicians routinely take multiple measurements on patients during the course of their treatment, often repeating the same measurements before and after operations, and subsequently at periodic followup consultations. This data combined with additional factors gives a wealth of information, resulting in a highdimensional data set with a mixture of data types and a longitudinal aspect; all of which can be problematic in statistical analysis. Therefore, general statistical methods for the investigation and analysis of a generic medical data set are presented and developed. Methods are proposed for supporting exploratory analysis of the data via novel visualisations of the patient’s status over time across multiple variables, thus giving an easily interpretable overview of this evolution. To address the problem of high dimensionality of the data, a new approach to variable selection is proposed and developed using principal variables. The method is further extended by the use of temporal smoothing to tackle data with this repeated measures aspect allowing for the simultaneous reduction of the patient status variables over time. The ultimate goal of these analyses is to determine an appropriate model for the orthopædic data, with a focus on the modelling of the time series of patient progress. The techniques of graphical modelling and, in particular, those of chain graphs lend themselves to this problem. Additionally, they have the added benefit of a simple and intuitive visualisation which is of benefit to clinicians. All of these methods are illustrated via their application to two largescale case study data sets concerning total joint replacement.