Related papers: More Uses of Exchangeability: Representations of C…
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…
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments…
A relationally exchangeable structure is a random combinatorial structure whose law is invariant with respect to relabeling its relations, as opposed to its elements. Aside from exchangeable random partitions, examples include edge…
Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes…
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 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…
We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…
Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper…
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…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
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…
Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
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…
In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…
Analysis of multivariate data sets from e.g. microarray studies frequently results in lists of genes which are associated with some response of interest. The biological interpretation is often complicated by the statistical instability of…
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…
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…
We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with…