2021/06/21 by Jian Huang, Huang, Jian, Yuling Jiao +9 · 1 citation
Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2106.10880
openalex publication_date 2021/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Schrödinger-Föllmer sampler (SFS), a novel approach for sampling from possibly unnormalized distributions. The proposed SFS is based on the Schrödinger-Föllmer 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. Comparing with the existing Markov chain Monte Carlo samplers that require ergodicity, no such requirement is needed for SFS. Computationally, SFS can be easily implemented using the Euler-Maruyama discretization. In theoretical analysis, we establish non-asymptotic error bounds for the sampling distribution of SFS in the Wasserstein distance under suitable 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.