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SUMMARY:Nonlinear Dynamics of Learning - Prof. Max Welling (UC Irvine)
DTSTART:20110321T110000Z
DTEND:20110321T120000Z
UID:TALK30259@talks.cam.ac.uk
CONTACT:Zoubin Ghahramani
DESCRIPTION:We describe a class of deterministic weakly chaotic dynamical 
 systems with infinite memory. These ``herding systems'' combine learning a
 nd inference into one algorithm. They convert moments directly into a sequ
 ence of pseudo-samples without learning an explicit model. Using the "perc
 eptron cycling theorem" we can show that Monte Carlo estimates based on th
 ese pseudo-samples converge at an optimal rate of O(1/T)\, due to infinite
  range negative auto-correlations. We show that the information content of
  these sequences\, as measured by sub-extensive entropy\, can grow as fast
  as K*log(N). In continuous spaces we can control an infinite number of mo
 ments by formulating herding in a Hilbert space. Also in this case sample 
 averages over arbitrary functions in the Hilbert space will converge at an
  optimal rate of O(1/T). More generally\, we advocate the application of t
 he rich theoretical framework of nonlinear dynamical systems and chaos the
 ory to statistical learning.
LOCATION:Engineering Department\, CBL Room 438
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