منابع مشابه
Sparse graphs using exchangeable random measures
Statistical network modelling has focused on representing the graph as a discrete structure, namely the adjacency matrix. When assuming exchangeability of this array-which can aid in modelling, computations and theoretical analysis-the Aldous-Hoover theorem informs us that the graph is necessarily either dense or empty. We instead consider representing the graph as an exchangeable random measur...
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We introduce a class of random graphs that we argue meets many of the desiderata one would demand of a model to serve as the foundation for a statistical analysis of real-world networks. The class of random graphs is defined by a probabilistic symmetry: invariance of the distribution of each graph to an arbitrary relabelings of its vertices. In particular, following Caron and Fox, we interpret ...
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Let Ω be a Borel subset of SN where S is countable. A measure is called exchangeable on Ω, if it is supported on Ω and is invariant under every Borel automorphism of Ω which permutes at most finitely many coordinates. De-Finetti’s theorem characterizes these measures when Ω = SN. We apply the ergodic theory of equivalence relations to study the case Ω 6= SN, and obtain versions of this theorem ...
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Call a random partition of the positive integers partially exchangeable if for each finite sequence of positive integers n l , . . . , nk, the probability that the partition breaks the first nl + . . . § nk integers into k particular classes, of sizes nl . . . . , nk in order of their first elements, has the same value p(na . . . . . nk) for every possible choice of classes subject to the sizes...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
سال: 2015
ISSN: 0246-0203
DOI: 10.1214/13-aihp584