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CATEGORIES:Machine Learning Reading Group @ CUED
SUMMARY:Information Geometry — Natural Gradient Descent - 
 Andy Lin\, MLG
DTSTART;TZID=Europe/London:20221123T110000
DTEND;TZID=Europe/London:20221123T123000
UID:TALK192956AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/192956
DESCRIPTION:Information geometry applies fundamental concepts 
 of differential geometry to probability theory and
  statistics to study statistical manifolds\, which
  are Riemannian manifolds in which each point in t
 he manifold corresponds to a probability distribut
 ion.\nThe perhaps most prominent application of in
 formation geometry in machine learning is natural 
 gradient descent (NGD)\, which can be described as
  'gradient descent which respects the curvature of
  the statistical manifold'.\nIn this session\, we 
 will be looking at NGD from different perspectives
 .\nIn particular\, we will consider NGD as 1) prec
 onditioning the gradient with the inverse Fisher i
 nformation matrix\, 2) second-order optimisation w
 ith Newton's method\, 3) the result of stating gra
 dient descent as a valid tensor equation\, and (bo
 nus) *) mirror descent in a dual Riemannian manifo
 ld.\nPrevious knowledge of differential geometry i
 s NOT required.\n\nReading (suggested\, but not re
 quired):\nMartens\, J. (2020). “New Insights and P
 erspectives on the Natural Gradient Method”.
 Jour
 nal of Machine Learning Research\, Volume 21\, Iss
 ue 146.\n(Sections 5\, 8 - 8.1\, 9.2\, ~6 pages)\n
 \nRaskutti\, G.\, Mukherjee\, S. (2015). “The info
 rmation geometry of mirror descent”.
 IEEE Transac
 tions on Information Theory\, Volume 61\, Issue 3.
 \n(Sections 1\, 2\, ~3 pages)
LOCATION:Cambridge University Engineering Department\, CBL 
 Seminar room BE4-38.
CONTACT:
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