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Accelerating the diffusion-based ensemble sampling by non-reversible dynamics
Futoshi Futami · Issei Sato · Masashi Sugiyama

Tue Jul 14 06:00 PM -- 06:45 PM & Wed Jul 15 04:00 AM -- 04:45 AM (PDT) @ None #None

Posterior distribution approximation is a central task in Bayesian inference. Stochastic gradient Langevin dynamics (SGLD) and its extensions have been widely used practically and studied theoretically. While SGLD updates a single particle at a time, ensemble methods that update multiple particles simultaneously have been recently gathering attention. Compared with the naive parallel-chain SGLD that updates multiple particles independently, ensemble methods update particles with their interactions. Thus, these methods are expected to be more particle-efficient than the naive parallel-chain SGLD because particles can be aware of other particles’ behavior through their interactions. Although ensemble methods demonstrated their superior performance numerically, no theoretical guarantee exists to assure such particle-efficiency and it is unclear whether those ensemble methods are really superior to the naive parallel-chain SGLD in the non-asymptotic settings. To cope with this problem, we propose a novel ensemble method that uses a non-reversible Markov chain for the interaction, and we present a non-asymptotic theoretical analysis for our method. Our analysis shows that, for the first time, the interaction causes a faster convergence rate than the naive parallel-chain SGLD in the non-asymptotic setting if the discretization error is appropriately controlled. Numerical experiments show that we can control the discretization error by tuning the interaction appropriately.

Author Information

Futoshi Futami (NTT)
Issei Sato (University of Tokyo / RIKEN)
Masashi Sugiyama (RIKEN / The University of Tokyo)

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