Related papers: Exchangeable Variable Models
Sum-Product Networks (SPNs) are expressive probabilistic models that provide exact, tractable inference. They achieve this efficiency by making use of local independence. On the other hand, mixtures of exchangeable variable models (MEVMs)…
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…
Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…
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…
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…
There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…
A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any permutation of the indices. De Finetti's theorem characterizes all $\{0,1\}$-valued exchangeable sequences as a "mixture" of…
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…
We study random relational structures that are \emph{relatively exchangeable}---that is, whose distributions are invariant under the automorphisms of a reference structure $\mathfrak{M}$. When $\mathfrak{M}$ has {\em trivial definable…
Intelligent agents must be able to articulate its own uncertainty. In this work, we show that pre-trained sequence models are naturally capable of probabilistic reasoning over exchangeable data points -- forming informed beliefs and…
Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or…
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…
In scientific studies involving analyses of multivariate data, basic but important questions often arise for the researcher: Is the sample exchangeable, meaning that the joint distribution of the sample is invariant to the ordering of the…
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…
Permutation tests are a powerful and flexible approach to inference via resampling. As computational methods become more ubiquitous in the statistics curriculum, use of permutation tests has become more tractable. At the heart of the…
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…
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…
Exchangeable arrays are natural tools to model common forms of dependence between units of a sample. Jointly exchangeable arrays are well suited to dyadic data, where observed random variables are indexed by two units from the same…
Evolutionary accumulation models (EvAMs) are an emerging class of machine learning methods designed to infer the evolutionary pathways by which features are acquired. Applications include cancer evolution (accumulation of mutations),…
A general class of models is proposed that is able to estimate the whole predictive distribution of a dependent variable $Y$ given a vector of explanatory variables $\xb$. The models exploit that the strength of explanatory variables to…