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X-WR-CALNAME:Statistical implications of group invariance of distributions
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UID:2022-11-21-peter-orbanz@cml.ics.uci.edu
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SUMMARY:[CML Seminar] Peter Orbanz: Statistical implications of group invar
iance of distributions
LOCATION:Donald Bren Hall 4011
DESCRIPTION:Peter Orbanz\, Professor of Machine Learning\, Gatsby Computati
onal Neuroscience Unit\, University College London\n\nTitle: Statistical i
mplications of group invariance of distributions\n\nAbstract: Consider a l
arge random structure — a random graph\, a stochastic process on the lin
e\, a random field on the grid — and a function that depends only on a s
mall part of the structure. Use a family of transformations to move the do
main of the function over the structure\, collect each function value\, an
d average. Under suitable conditions\, the law of large numbers generalize
s to such averages. My recent work with Morgane Austern shows that central
limit theorems and other higher-order properties also hold: if the i.i.d.
assumption of classical statistics is substituted by suitable properties
formulated in terms of groups\, the fundamental theorems of inference stil
l hold.\n\nhttps://cml.ics.uci.edu/seminars/2022-11-21-peter-orbanz
X-ALT-DESC;FMTTYPE=text/html:Peter Orbanz\, Professor of
Machine Learning\, Gatsby Computational Neuroscience Unit\, University Co
llege London
Title: Statistical implications of group invari
ance of distributions
Abstract: Consider a large random stru
cture — a random graph\, a stochastic process on the line\, a random fie
ld on the grid — and a function that depends only on a small part of the
structure. Use a family of transformations to move the domain of the func
tion over the structure\, collect each function value\, and average. Under
suitable conditions\, the law of large numbers generalizes to such averag
es. My recent work with Morgane Austern shows that central limit theorems
and other higher-order properties also hold: if the i.i.d. assumption of c
lassical statistics is substituted by suitable properties formulated in te
rms of groups\, the fundamental theorems of inference still hold.
<
a href="https://cml.ics.uci.edu/seminars/2022-11-21-peter-orbanz">https://
cml.ics.uci.edu/seminars/2022-11-21-peter-orbanz
URL:https://cml.ics.uci.edu/seminars/2022-11-21-peter-orbanz
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