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SUMMARY:Information Geometry: From Divergence Functions to Geometric Struc
 tures - Jun Zhang\, University of Michigan-Ann Arbor
DTSTART:20140509T150000Z
DTEND:20140509T160000Z
UID:TALK52254@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:Information Geometry is the differential geometric study of th
 e manifold of probability density functions. Divergence functions (such as
  KL divergence)\, as measure of proximity on this manifold\, play an impor
 tant role in machine learning\, statistical inference\, optimization\, etc
 . This talk will review the various geometric structures induced from any 
 divergence function. Most importantly\, a Riemannian metric (Fisher inform
 ation) with a family of torsion-free affine connections (alpha-\nconnectio
 ns) can be induced on the manifold\, this is the so-called the “statisti
 cal structure” in Information Geometry. Divergence functions can induce 
 other important structures/quantities\, such as bi-orthogonal coordinates 
 (namely expectation and natural parameters)\, parallel volume form (in mod
 eling Bayesian priors)\, symplectic structure (for Hamiltonian systems).
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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