Symmetry and Convergence

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United States Simons Institute for the Theory of Computing
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Published on ● Video Link: https://www.youtube.com/watch?v=bGBh7pz7s6E


Duration: 47:56
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Peter Orbanz (University College London)
https://simons.berkeley.edu/node/22597
Graph Limits, Nonparametric Models, and Estimation

A random structure exhibits symmetry if its law remains invariant under a group of transformations. Exchangeability (of graphs, sequences, etc) and stationarity are examples. Under suitable conditions, the transformation group can be used to define an estimator that averages over an instance of the structure, and such estimators turn out to satisfy a law of large numbers, a central limit theorem, and further convergence results. Loosely speaking: The large-sample theory of i.i.d averages still holds if the i.i.d assumption is substituted by a suitable symmetry assumption.

Joint work with Morgane Austern.



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Tags:
Simons Institute
theoretical computer science
UC Berkeley
Computer Science
Theory of Computation
Theory of Computing
Graph Limits Nonparametric Models and Estimation
Peter Orbanz