Exchangeable random hypergraphs
نویسنده
چکیده
A hypergraph is a generalization of a graph in which an edge may contain more than two vertices. Hereditary hypergraphs are particularly important because they arise in mathematics as the class of monotone subsets, in statistics as the class of factorial models, in topology as simplicial complexes and in algebra as the free distributive lattice. An exchangeable random hypergraph consists of a projective system and a probability distribution that is consistent with the projections in the system. The Indian buffet process is one instance. Three projective systems are defined. A specific sub-class of Poissongenerated hereditary hypergraphs is studied.
منابع مشابه
On exchangeable random variables and the statistics of large graphs and hypergraphs
De Finetti’s classical result of [18] identifying the law of an exchangeable family of random variables as a mixture of i.i.d. laws was extended to structure theorems for more complex notions of exchangeability by Aldous [1, 2, 3], Hoover [41, 42], Kallenberg [44] and Kingman [47]. On the other hand, such exchangeable laws were first related to questions from combinatorics in an independent ana...
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