A hierarchical version of the de Finetti and Aldous-Hoover representations
By Tim Austin, Dmitry Panchenko. 2013
34 citations recorded by the source corpus.
We consider random arrays indexed by the leaves of an infinitary rooted tree of finite depth, with the distribution invariant under the rearrangements that preserve the tree structure. We call such arrays hierarchically exchangeable and prove that they satisfy an analogue of de Finetti’s theorem. We also prove a more general result for arrays indexed by several trees, which includes a hierarchical version of the Aldous-Hoover representation.
Subfields: Artificial Intelligence, Mathematical Physics
How researchers see this paper
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In Artificial Intelligence
- Jan Gasthaus
- Tim Januschowski
- Bernie Wang
- Danielle C. Maddix
- Dean Phillips Foster
- Alex Smola
- Arthur Gretton
- Bernhard Schölkopf
In Mathematical Physics
Citations in the corpus
- Deep Factors for Forecasting (2019, methodology): “The proof is analogous to that of Theorem 1, and follows from a hierarchical extension of de Finetti’s theorem (Austin & Panchenko, 2014).”