A generalization of hierarchical exchangeability on trees to directed acyclic graphs
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)....
| Main Authors: | , , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
ENS Rennes
2021
|
| Summary: | 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 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. |
|---|