A Generalization of Hierarchical Exchangeability on Trees to Directed Acyclic Graphs

Paul Jung; Jiho Lee; Sam Staton; Hongseok Yang

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arXiv · 1812.06282

A Generalization of Hierarchical Exchangeability on Trees to Directed Acyclic Graphs

Paul Jung·Jiho Lee·Sam Staton·Hongseok Yang

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Abstract

Motivated by the problem of designing inference-friendly Bayesian nonparametric models in probabilistic programming languages, we introduce a general class of partially exchangeable random arrays which generalizes the notion of hierarchical exchangeability introduced in Austin and Panchenko (2014). We say that our partially exchangeable arrays are DAG-exchangeable since their partially exchangeable structure is governed by a collection of Directed Acyclic Graphs. More specifically, such a random array is indexed by $\mathbb{N}^{|V|}$ for some DAG $G=(V,E)$, and its exchangeability structure is governed by the edge set $E$. We prove a representation theorem for such arrays which generalizes the Aldous-Hoover and Austin-Panchenko representation theorems.

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BibTeX RIS

Paul Jung, Jiho Lee, Sam Staton, Hongseok Yang. 2018-12-15. A Generalization of Hierarchical Exchangeability on Trees to Directed Acyclic Graphs. https://arxiv.org/abs/1812.06282

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