| Abstract: |
| Sampling from probability distributions is an important problem in statistics
and machine learning, specially in Bayesian inference when integration with respect
to posterior distribution is intractable and sampling from the posterior is the only
viable option for inference. In this paper, we propose Schrodinger-Follmer sampler
(SFS), a novel approach to sampling from possibly unnormalized distributions.
The proposed SFS is based on the Schrodinger-Follmer diffusion process on the unit
interval with a time-dependent drift term, which transports the degenerate distribution
at time zero to the target distribution at time one. Compared with the existing
Markov chain Monte Carlo samplers that require ergodicity, SFS does not need to
have the property of ergodicity. Computationally, SFS can be easily implemented
using the Euler-Maruyama discretization. In theoretical analysis, we establish nonasymptotic
error bounds for the sampling distribution of SFS in the Wasserstein
distance under reasonable conditions. We conduct numerical experiments to evaluate
the performance of SFS and demonstrate that it is able to generate samples
with better quality than several existing methods. |
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