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Past seminars

Upcoming seminars

  • PVSeminar #27, 02 December 2021  / 10:00 AEDT (TBC)

Jay Rosen (The City University of New York, USA): Law of the iterated logarithm for permanental processes and the local times of associated Markov processes

Abstract: Permanental processes are a generalization of Gaussian processes. They are connected to the local times of Markov processes by an Isomorphism Theorem of Eisenbaum and Kaspi. We explain how we obtain LIL’s for non-symmetric permanental processes and use the Isomorphism Theorem to derive LIL’s for certain non-symmetric Markov processes.

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  • PVSeminar #28 (TBC), 16 December 2021  / 17:00 AEDT (TBC)

Paul Jung (KAIST, USA):  A Generalization of Hierarchical Exchangeability on Trees to Directed Acyclic Graphs

Abstract: A random array indexed by the paths of an infinitely-branching rooted tree of finite depth is hierarchically exchangeable if its joint distribution is invariant under rearrangements that preserve the tree structure underlying the index set. Austin and Panchenko (2014) prove that such arrays have de Finetti-type representations, and moreover, that an array indexed by a finite collection of such trees has an Aldous-Hoover-type representation.

Motivated by issues in Neural Networks and Bayesian nonparametric models used in probabilistic programming languages, we generalize hierarchical exchangeability to a new kind of partial exchangeability for random arrays which we call DAG-exchangeability. In our setting a random array is indexed by N^|V| for some DAG G=(V,E), and its exchangeability structure is governed by the edge set E. We will present a representation theorem for such arrays which generalizes the Aldous-Hoover and Austin-Panchenko representation theorems.

Based on joint work with Jiho Lee (KAIST Mathematics), Sam Staton (Oxford CS), and Hongseok Yang (KAIST CS).

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