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SUMMARY:Random Batch Methods for Interacting Particle Systems and Consensu
 s-based Global Non-convex  Optimization in High-dimensional Machine Learni
 ng (copy) - Shi Jin (Shanghai Jiao Tong University)
DTSTART:20191111T140000Z
DTEND:20191111T150000Z
UID:TALK134683@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We develop random batch methods for interacting particle syste
 ms with large number of particles. These methods <br>use small but random 
 batches for particle interactions\,<br>thus the computational cost is redu
 ced from O(N^2) per time step to O(N)\, for a<br>system with N particles w
 ith binary interactions.<br>For one of the methods\, we give a particle nu
 mber independent error estimate under some special interactions. <br>Then\
 , we apply these methods<br>to some representative problems in mathematics
 \, physics\, social and data sciences\, including the Dyson Brownian <br>m
 otion from random matrix theory\, Thomson&#39\;s problem\,<br>distribution
  of wealth\, opinion dynamics and clustering. Numerical results show that<
 br>the methods can capture both the transient solutions and the global equ
 ilibrium in<br>these problems.<br><br>We also apply this method and improv
 e the consensus-based global optimization algorithm for high <br>dimension
 al machine learning problems. This method does not require taking gradient
  in finding global <br>minima for non-convex functions in high dimensions.
 <br>
LOCATION:Seminar Room 2\, Newton Institute
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