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Random Batch Methods for Interacting Particle Systems and Consensus-based Global Non-convex Optimization in High-dimensional Machine Learning (copy)

Presented by: 
Shi Jin Shanghai Jiao Tong University
Date: 
Monday 11th November 2019 - 14:00 to 15:00
Venue: 
INI Seminar Room 2
Abstract: 
We develop random batch methods for interacting particle systems with large number of particles. These methods
use small but random batches for particle interactions,
thus the computational cost is reduced from O(N^2) per time step to O(N), for a
system with N particles with binary interactions.
For one of the methods, we give a particle number independent error estimate under some special interactions.
Then, we apply these methods
to some representative problems in mathematics, physics, social and data sciences, including the Dyson Brownian
motion from random matrix theory, Thomson's problem,
distribution of wealth, opinion dynamics and clustering. Numerical results show that
the methods can capture both the transient solutions and the global equilibrium in
these problems.

We also apply this method and improve the consensus-based global optimization algorithm for high
dimensional machine learning problems. This method does not require taking gradient in finding global
minima for non-convex functions in high dimensions.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons