Spectrum Exchangeability, Sx, is an irrelevance principle of Pure Inductive Logic, and arguably the most natural (but not the only) extension of Atom Exchangeability to polyadic languages. It has been shown1 that all probability functions which satisfy Sx are comprised of a mixture of two essential types of probability functions; heterogeneous and homogeneous functions. We determine the theory ...

A general inductive Bayesian classification framework is introduced for data from multiple finite alphabets using predictive representations based on random urn models and generalized exchangeability. We develop a novel principle of generative supervised and semi-supervised probabilistic classification based on marginalizing simultaneous predictive classification probabilities for all test item...

We show that a finite Markov exchangeable sequence of random variables with finite state space is a signed mixture of Markov chains. This is shown to partially generalize earlier work by Fortini et al. and Freedman under the added condition of stationarity. Associated statistical issues are discussed and a test of Markov exchangeability is proposed.

We study some percolation problems on the complete graph over N. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability, such as independency, is made. The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.

The majority of theoretical work in machine learning is done under the assumption of exchangeability: essentially, it is assumed that the examples are generated from the same probability distribution independently. This paper is concerned with the problem of testing the exchangeability assumption in the on-line mode: examples are observed one by one and the goal is to monitor on-line the streng...

Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of its finite classes and directing measures of its infinite ones (given by the de Finetti Theorem), corresponds to sampling independently from each class, with...

A known failing of many popular random graph models is that the Aldous–Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is considered unrealistic in observed graphs. We define a notion of edge exchangeability for random graphs in contrast to the established notion of infinite exchangea...

For positive q, the q-exchangeability is introduced as quasi-invariance under permutations, with a special cocycle. This allows us to extend the q-analogue of de Finetti’s theorem for binary sequences [GO2] to the general real-valued sequences. In contrast to the classical case with q = 1, the order on R plays for the q-analogues a significant role. An explicit construction of ergodic q-exchang...