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Extra Colloquium Mathematics - Max Welling

17 March 2011

Join us for coffee and tea at 15.45 p.m.


Date: Thursday, March 17th 2011

Speaker: Max Welling

Room: 5161.0289 (Bernoulliborg),

Time: 16.15



Title: Herding: Learning with Weakly Chaotic Nonlinear Dynamical Systems



We describe a class of deterministic weakly chaotic dynamical systems with infinite memory. These ``herding systems'' combine learning and inference into one algorithm. They convert moments directly into a sequence of pseudo-samples without learning an explicit model. Using the "perceptron cycling theorem" we can easily show that Monte Carlo estimates based on these 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), which is faster than the usual 1/2 K log(N) for sequences generated by random posterior sampling from a Bayesian posterior model. In continuous spaces we can control an infinite number of moments
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 the rich theoretical framework of nonlinear dynamical systems and chaos theory to statistical learning.





Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : and

Dr. M. Dür (e-mail:

Last modified:06 June 2018 2.04 p.m.

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