Topic
Graphoid
About: Graphoid is a research topic. Over the lifetime, 82 publications have been published within this topic receiving 2787 citations.
Papers published on a yearly basis
Papers
TL;DR: This article characterizes all independence assertions that logically follow from the topology of a network and develops a linear time algorithm that identifies these assertions and is shown to work for a broad class of nonprobabilistic independencies.
Abstract: An important feature of Bayesian networks is that they facilitate explicit encoding of information about independencies in the domain, information that is indispensable for efficient inferencing. This article characterizes all independence assertions that logically follow from the topology of a network and develops a linear time algorithm that identifies these assertions. The algorithm's correctness is based on the soundness of a graphical criterion, called d-separation, and its optimality stems from the completeness of d-separation. An enhanced version of d-separation, called D-separation, is defined, extending the algorithm to networks that encode functional dependencies. Finally, the algorithm is shown to work for a broad class of nonprobabilistic independencies.
635 citations
TL;DR: It is shown how the concept of separoid unifies a variety of notions of ‘irrelevance’ arising out of different formalisms for representing uncertainty in Probability, Statistics, Artificial Intelligence, and other fields.
Abstract: We introduce an axiomatic definition of a mathematical structure that we term a i>separoid. We develop some general mathematical properties of separoids and related axiom systems, as well as connections with other mathematical structures, such as distributive lattices, Hilbert spaces, and graphs. And we show, by means of a detailed account of a number of models of the separoid axioms, how the concept of separoid unifies a variety of notions of ‘irrelevance’ arising out of different formalisms for representing uncertainty in Probability, Statistics, Artificial Intelligence, and other fields.
98 citations
TL;DR: In this paper, a new class of graphical models capturing the dependence structure of events that occur in time is proposed, where the graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some (but not necessarilly all) events in the past.
Abstract: Summary. A new class of graphical models capturing the dependence structure of events that occur in time is proposed.The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some (but not necessarilly all) events in the past. This dynamic concept of independence is asymmetric, similar to Granger non-causality, so the corresponding local independence graphs differ considerably from classical graphical models. Hence a new notion of graph separation, which is called δ-separation, is introduced and implications for the underlying model as well as for likelihood inference are explored. Benefits regarding facilitation of reasoning about and understanding of dynamic dependences as well as computational simplifications are discussed.
97 citations
TL;DR: In this article, the authors unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such graphs are compositional graphoids.
Abstract: In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such graphs are compositional graphoids. We focus in particular on the subclass of ribbonless graphs which as special cases include undirected graphs, bidirected graphs, and directed acyclic graphs, as well as ancestral graphs and summary graphs. We define maximality of such graphs as well as a pairwise and a global Markov property. We prove that the global and pairwise Markov properties of a maximal ribbonless graph are equivalent for any independence model that is a compositional graphoid.
58 citations
TL;DR: This paper investigates Walley's concepts of epistemic irrelevance and epistemic independence for imprecise probability models, and their relation to the graphoid axioms.
Abstract: This paper investigates Walley's concepts of epistemic irrelevance and epistemic independence for imprecise probability models. We study the mathematical properties of irrelevance and independence, and their relation to the graphoid axioms. Examples are given to show that epistemic irrelevance can violate the symmetry, contraction and intersection axioms, that epistemic independence can violate contraction and intersection, and that this accords with informal notions of irrelevance and independence.
58 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 1 |
| 2019 | 3 |
| 2018 | 3 |
| 2017 | 2 |
| 2016 | 4 |