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PRODID:UW-Madison-Physics-Events
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SEQUENCE:2
UID:UW-Physics-Event-7952
DTSTART:20221102T160000Z
DTEND:20221102T171500Z
DTSTAMP:20260414T153415Z
LAST-MODIFIED:20221031T034555Z
LOCATION:Online Seminar: Please sign up for our mailing list at www.ph
 ysicsmeetsml.org for zoom link
SUMMARY:Bayesian Updating and dynamical flows\, Physics ∩ ML Seminar
 \, David Berman\, Queen Mary University
DESCRIPTION:Statistical Inference is the process of determining a prob
 ability distribution over the space of parameters of a model given a d
 ata set. As more data becomes available this probability distribution 
 becomes updated via the application of Bayes’ theorem. We present a 
 treatment of this Bayesian updating process as a continuous dynamical 
 system. Statistical inference is then governed by a first order differ
 ential equation describing a trajectory or flow in the information geo
 metry determined by a parametric family of models. We solve this equat
 ion for some simple models and show that when the Cram´er-Rao bound i
 s saturated the learning rate is governed by a simple 1/T power-law\, 
 with T a time-like variable denoting the quantity of data. We illustra
 te this with both analytic and numerical examples based on Gaussians a
 nd the inference of the coupling constant in the Ising model. Finally 
 we compare the qualitative behaviour exhibited by Bayesian flows to th
 e training of various neural networks on benchmarked data sets such as
  MNIST and CIFAR10 and show how that for networks exhibiting small fin
 al losses the simple power-law is also satisfied.
URL:https://www.physics.wisc.edu/events/?id=7952
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