Stein Self-Repulsive Dynamics: Benefits From Past Samples
This addresses the problem of sample inefficiency and poor uncertainty estimation in sampling from complex distributions for researchers and practitioners in machine learning and statistics, representing a novel method rather than an incremental improvement.
The paper tackles the problem of obtaining diversified samples from intractable un-normalized distributions by proposing Stein self-repulsive dynamics, which introduces Stein variational gradient as a repulsive force to push samples away from past trajectories in Langevin dynamics. This approach significantly decreases auto-correlation, increases effective sample size, and yields much higher sample efficiency and better uncertainty estimation than vanilla Langevin dynamics.
We propose a new Stein self-repulsive dynamics for obtaining diversified samples from intractable un-normalized distributions. Our idea is to introduce Stein variational gradient as a repulsive force to push the samples of Langevin dynamics away from the past trajectories. This simple idea allows us to significantly decrease the auto-correlation in Langevin dynamics and hence increase the effective sample size. Importantly, as we establish in our theoretical analysis, the asymptotic stationary distribution remains correct even with the addition of the repulsive force, thanks to the special properties of the Stein variational gradient. We perform extensive empirical studies of our new algorithm, showing that our method yields much higher sample efficiency and better uncertainty estimation than vanilla Langevin dynamics.