Related papers: Relative exchangeability with equivalence relation…
The Aldous-Hoover Theorem concerns an infinite matrix of random variables whose distribution is invariant under finite permutations of rows and columns. It states that, up to equality in distribution, each random variable in the matrix can…
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…
Exchangeability -- in which the distribution of an infinite sequence is invariant to reorderings of its elements -- implies the existence of a simple conditional independence structure that may be leveraged in the design of statistical…
It is often convenient to represent a process for randomly generating a graph as a graphon. (More precisely, these give \emph{vertex exchangeable} processes -- those processes in which each vertex is treated the same way.) Other structures…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…
We introduce the notion of a restricted exchangeable partition of $\mathbb{N}$. We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In…
There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various…
The theory of quasirandomness has greatly expanded from its inaugural graph theoretical setting to several different combinatorial objects such as hypergraphs, tournaments, permutations, etc. However, these quasirandomness variants have…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
Motivated by statistical practice, category theory terminology is used to introduce Borel data structures and study exchangeability in an abstract framework. A generalization of de Finetti's theorem is shown and natural transformations are…
We introduce the exchangeable rewiring process for modeling time-varying networks. The process fulfills fundamental mathematical and statistical properties and can be easily constructed from the novel operation of random rewiring. We derive…
In a general algebraic setting, we state some properties of commutators of reflexive admissible relations.
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
We study Markov processes with values in the space of general two-dimensional arrays whose distribution is exchangeable. The results of this paper are inspired by the theory of exchangeable dynamical random graphs developed by H. Crane…
We formulate and prove a very general relative version of the Dobrushin-Lanford-Ruelle theorem which gives conditions on constraints of configuration spaces over a finite alphabet such that for every absolutely summable relative…
Some practical results are derived for population inference based on a sample, under the two qualitative conditions of 'ignorability' and exchangeability. These are the 'Histogram Theorem', for predicting the outcome of a non-sampled member…
Self-similarity of systems is very popular and intensively developing field during last decades. To this field belong so-called stable distributions and their generalization. In Klebanov and Sl\'amov\'a (2014) there was given an approach to…
We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than…
The aim of this paper is to establish Hoeffding and Bernstein type concentration inequalities for weighted sums of exchangeable random variables. A special case is the i.i.d. setting, where random variables are sampled independently from…