Bayesian Learning via Stochastic Gradient Langevin Dynamics

motivation

• emerge of large-scale datasets
• success of SGD
• left-behind: Bayesian methods
  • MCMC: requires whole dataset, time!

SGD methods

• var. in gardient cancelled out in the whole dataset
• step sizes: able to travel far and stay at stable point

Langevin dynamics

• insert gaussian noise in gard.
• matched step size and noise
• can be corrected using MH
  • as epsilon -> zero, no need to correct

this work

• change the gradient in Langevin dynamics to estimation by mini-batch
• injected noise after all dominated stochastic noise
• and will converge
• step size must goes to zero
  • or switch to a diff. algo. later
• adjust noise cov. to control var. of grad.
• est. by weighted sum.(weighted by step sizes)