Related papers: Exchangeable Trait Allocations
The problem of inferring a clustering of a data set has been the subject of much research in Bayesian analysis, and there currently exists a solid mathematical foundation for Bayesian approaches to clustering. In particular, the class of…
We introduce a general framework for de Finetti reduction results, applicable to various notions of partially exchangeable probability distributions. Explicit statements are derived for the cases of exchangeability, Markov exchangeability,…
The exchange graph of a cluster algebra encodes the combinatorics of mutations of clusters. Through the recent "categorifications" of cluster algebras using representation theory one obtains a whole variety of exchange graphs associated…
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…
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…
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…
To allow for tractable probabilistic inference with respect to domain sizes, lifted probabilistic inference exploits symmetries in probabilistic graphical models. However, checking whether two factors encode equivalent semantics and hence…
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…
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…
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
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…
Standard clustering techniques assume a common configuration for all features in a dataset. However, when dealing with multi-view or longitudinal data, the clusters' number, frequencies, and shapes may need to vary across features to…
Feature and trait allocation models are fundamental objects in Bayesian nonparametrics and play a prominent role in several applications. Existing approaches, however, typically assume full exchangeability of the data, which may be…
We review the class of species sampling models (SSM). In particular, we investigate the relation between the exchangeable partition probability function (EPPF) and the predictive probability function (PPF). It is straightforward to define a…
Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…
Clustering a graph, i.e., assigning its nodes to groups, is an important operation whose best known application is the discovery of communities in social networks. Graph clustering and community detection have traditionally focused on…
We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of…
We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…
We propose a general framework for modelling network data that is designed to describe aspects of non-exchangeable networks. Conditional on latent (unobserved) variables, the edges of the network are generated by their finite growth history…
In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud…