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20
A Transformational Characterization of Equivalent Bayesian Network Structures
, 1995
"... We present a simple characterization of equivalentBayesian network structures based on local transformations. The significance of the characterization is twofold. First, we are able to easily proveseveral new invariant properties of theoretical interest for equivalent structures. Second, we ..."
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Cited by 89 (1 self)
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We present a simple characterization of equivalentBayesian network structures based on local transformations. The significance of the characterization is twofold. First, we are able to easily proveseveral new invariant properties of theoretical interest for equivalent structures. Second, we use the characterization to derive an efficient algorithm that identifies all of the compelled edges in a structure. Compelled edge identification is of particular importance for learning Bayesian network structures from data because these edges indicate causal relationships when certain assumptions hold. 1
dseparation: From theorems to algorithms
 in Uncertainty in Articial Intelligence 5
, 1990
"... Bayesian networks encode properties of a probability distribution using directed acycIic graphs (dags). queries can, in principle, be computed directly from ..."
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Cited by 40 (1 self)
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Bayesian networks encode properties of a probability distribution using directed acycIic graphs (dags). queries can, in principle, be computed directly from
Belief Networks Revisited
, 1994
"... this paper, Rumelhart presented compelling evidence that text comprehension must be a distributed process that combines both topdown and bottomup inferences. Strangely, this dual mode of inference, so characteristic of Bayesian analysis, did not match the capabilities of either the "certainty fact ..."
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Cited by 36 (6 self)
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this paper, Rumelhart presented compelling evidence that text comprehension must be a distributed process that combines both topdown and bottomup inferences. Strangely, this dual mode of inference, so characteristic of Bayesian analysis, did not match the capabilities of either the "certainty factors" calculus or the inference networks of PROSPECTOR  the two major contenders for uncertainty management in the 1970s. I thus began to explore the possibility of achieving distributed computation in a "pure" Bayesian framework, so as not to compromise its basic capacity to combine bidirectional inferences (i.e., predictive and abductive) . Not caring much about generality at that point, I picked the simplest structure I could think of (i.e., a tree) and tried to see if anything useful can be computed by assigning each variable a simple processor, forced to communicate only with its neighbors. This gave rise to the treepropagation algorithm reported in [15] and, a year later, the KimPearl algorithm [12], which supported not only bidirectional inferences but also intercausal interactions, such as "explainingaway." These two algorithms were described in Section 2 of Fusion.
A Computational Theory of Decision Networks
 International Journal of Approximate Reasoning
, 1994
"... This paper is about how to represent and solve decision problems in Bayesian decision theory (e.g. [6]). A general representation named decision networks is proposed based on influence diagrams [10]. This new representation incorporates the idea, from Markov decision process (e.g. [5]), that a decis ..."
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Cited by 33 (2 self)
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This paper is about how to represent and solve decision problems in Bayesian decision theory (e.g. [6]). A general representation named decision networks is proposed based on influence diagrams [10]. This new representation incorporates the idea, from Markov decision process (e.g. [5]), that a decision may be conditionally independent of certain pieces of available information. It also allows multiple cooperative agents and facilitates the exploitation of separability in the utility function. Decision networks inherit the advantages of both influence diagrams and Markov decision processes, which makes them a better representation framework for decision analysis, planning under uncertainty, medical diagnosis and treatment.
Remarks concerning graphical models for time series and point processes
 Revista de Econometria
, 1996
"... Uma rede estatística é uma cole,cão de nós representando variáveis aleatórias e um conjunto de arestas que ligam os nós. Um modelo estocástico por isso e chamado um modelo gráfico. Estes modelos, de gráficos e redes, sáo particularmente úteis para examinar as dependéncias estatísticas baseadas em co ..."
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Cited by 21 (3 self)
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Uma rede estatística é uma cole,cão de nós representando variáveis aleatórias e um conjunto de arestas que ligam os nós. Um modelo estocástico por isso e chamado um modelo gráfico. Estes modelos, de gráficos e redes, sáo particularmente úteis para examinar as dependéncias estatísticas baseadas em condi,coes do tipo das que ocorrem frequentemente em economia e estatística. Neste artigo as variáveis aleatórias dos nós serão séries temporais ou processos pontuais. Os casos de gráfos direcionados e nãodirecionados são apresentados. A statistical network is a collection of nodes representing random variables and a set of edges that connect the nodes. A probabilistic model for such is called a graphical model. These models, graphs and networks are particularly useful for examining statistical dependencies based on conditioning as often occurs in economics and statistics. In this paper the nodal random variables will be time series or point proceses. The cases of undirected and directed graphs are focussed on.
Partial inversion for linear systems and partial closure of independence graphs
 BIT, Numer. Math
"... We introduce and study a calculus for realvalued square matrices, called partial inversion, and an associated calculus for binary square matrices. The first, applied to systems of recursive linear equations, generates new sets of parameters for different types of statistical joint response models. ..."
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Cited by 14 (11 self)
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We introduce and study a calculus for realvalued square matrices, called partial inversion, and an associated calculus for binary square matrices. The first, applied to systems of recursive linear equations, generates new sets of parameters for different types of statistical joint response models. The corresponding generating graphs are directed and acyclic. The second calculus, applied to matrix representations of independence graphs, gives chain graphs induced by such a generating graph. Chain graphs are more complex independence graphs associated with recursive joint response models. Missing edges in independence graphs coincide with structurally zero parameters in linear systems. A wide range of consequences of an assumed independence structure can be derived by partial closure, but computationally efficient algorithms still need to be developed for applications to very large graphs.
Semigraphoids and Structures of Probabilistic Conditional Independence
, 1997
"... this paper, the semigraphoid closure of every couple of CIstatements is proved to be a CImodel. The substantial step to it is to show that every probabilistically sound inference rule for axiomatic characterization of CI properties (= axiom), having at most two antecedents, is a consequence of the ..."
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Cited by 12 (0 self)
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this paper, the semigraphoid closure of every couple of CIstatements is proved to be a CImodel. The substantial step to it is to show that every probabilistically sound inference rule for axiomatic characterization of CI properties (= axiom), having at most two antecedents, is a consequence of the semigraphoid inference rules. Moreover, all potential dominant triplets of the mentioned semigraphoid closure are found.
Matrix representations and independencies in directed acyclic graphs
 Ann. Statist
, 2008
"... For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria becau ..."
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Cited by 10 (9 self)
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For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs in which zeros indicate independence statements. A matrix condition is shown to give a new path criterion for separation and to be equivalent to each of the previous two path criteria. 1. Introduction. We
Multiscale Graphical Modeling in Space: Applications to Command and Control
, 2000
"... Recently, a class of multiscale treestructured models was introduced in terms of scalerecursive dynamics defined on trees. The main advantage of these models is their association with a fast, recursive, Kalmanfilter prediction algorithm. In this article, we propose a more general class of multisca ..."
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Cited by 9 (1 self)
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Recently, a class of multiscale treestructured models was introduced in terms of scalerecursive dynamics defined on trees. The main advantage of these models is their association with a fast, recursive, Kalmanfilter prediction algorithm. In this article, we propose a more general class of multiscale graphical models over acyclic directed graphs, for use in command and control problems. Moreover, we derive the generalizedKalmanfilter algorithm for graphical Markov models, which can be used to obtain the optimal predictors and prediction variances for multiscale graphical models. 1 Introduction Almost every aspect of command and control (C2) involves dealing with information in the presence of uncertainty. Since information in a battlefield is never precise, its status is rarely known exactly. In the face of this uncertainty, commanders must make decisions, issue orders, and monitor the consequences. The uncertainty may come from noisy data or, indeed, regions of the battle space whe...
Conditional independence and chain event graphs
, 2005
"... Graphs provide an excellent framework for interrogating symmetric models of measurement random variables and discovering their implied conditional independence structure. However, it is not unusual for a model to be specified from a description of how a process unfolds (i.e. via its event tree), rat ..."
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Cited by 7 (2 self)
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Graphs provide an excellent framework for interrogating symmetric models of measurement random variables and discovering their implied conditional independence structure. However, it is not unusual for a model to be specified from a description of how a process unfolds (i.e. via its event tree), rather than through relationships between a given set of measurements. Here we introduce a new mixed graphical structure called the chain event graph that is a function of this event tree and a set of elicited equivalence relationships. This graph is more expressive and flexible than either the Bayesian network — equivalent in the symmetric case — or the probability decision graph. Various separation theorems are proved for the chain event graph. These enable implied conditional independencies to be read from the graph’s topology. We also show how the topology can be exploited to tease out the interesting conditional independence structure of functions of random variables associated with the underlying event tree.