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UID:20250709T213913EDT-0950lN38eP@132.216.98.100
DTSTAMP:20250710T013913Z
DESCRIPTION:Title : The Connections Between Discrete Geometric Mechanics\, 
 Information Geometry and Machine Learning\n\nAbstract : Geometric mechanic
 s describes Lagrangian and Hamiltonian mechanics geometrically\, and infor
 mation geometry formulates statistical estimation\, inference\, and machin
 e learning in terms of geometry. A divergence function is an asymmetric di
 stance between two probability densities that induces differential geometr
 ic structures and yields efficient machine learning algorithms that minimi
 ze the duality gap. The connection between information geometry and geomet
 ric mechanics will yield a unified treatment of machine learning and struc
 ture-preserving discretizations. In particular\, the divergence function o
 f information geometry can be viewed as a discrete Lagrangian\, which is a
  generating function of a symplectic map\, that arise in discrete variatio
 nal mechanics. This identification allows the methods of backward error an
 alysis to be applied\, and the symplectic map generated by a divergence fu
 nction can be associated with the exact time-$h$ flow map of a Hamiltonian
  system on the space of probability distributions.\n
DTSTART:20191104T210000Z
DTEND:20191104T220000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Melvin Leok (University of California\, San Diego)
URL:/mathstat/channels/event/melvin-leok-university-ca
 lifornia-san-diego-302115
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