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Nonparametric Bayesian statistics with exchangeable random structures

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If you have a question about this talk, please contact Gintare Karolina Dziugaite.

Most of nonparametric Bayesian statistics is focused on the settings of “i.i.d. data” and “regression with i.i.d. noise”. What of problems that don’t fit into one of these molds? I’ll introduce exchangeability (and other invariance principles) as a general guiding principle for constructing statistical models, and in particular identifying appropriate parameter spaces. The main focus will be on networks and graphs, where exchangeability of vertices is shown by Aldous-Hoover to give a natural parameter space of “graphons”, i.e., measurable functions from [0,1]^2 to [0,1]. I’ll give a few more examples of exchangeability, including Markov exchangeability and rotatability. I’ll start with the sequence case to explain how to interpret/understand the later theorems.

This talk is part of the Machine Learning @ CUED series.

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