Jump-Diffusion Langevin Dynamics for Multimodal Posterior Sampling

• URL: http://arxiv.org/abs/2211.01774v1
• Date: Wed, 2 Nov 2022 17:35:04 GMT
• Title: Jump-Diffusion Langevin Dynamics for Multimodal Posterior Sampling
• Authors: Jacopo Guidolin, Vyacheslav Kungurtsev, Ond\v{r}ej Ku\v{z}elka
• Abstract summary: We investigate the performance of a hybrid Metropolis and Langevin sampling method akin to Jump Diffusion on a range of synthetic and real data. We find that careful calibration of mixing sampling jumps with gradient based chains significantly outperforms both pure gradient-based or sampling based schemes.
• Score: 3.4483987421251516
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bayesian methods of sampling from a posterior distribution are becoming increasingly popular due to their ability to precisely display the uncertainty of a model fit. Classical methods based on iterative random sampling and posterior evaluation such as Metropolis-Hastings are known to have desirable long run mixing properties, however are slow to converge. Gradient based methods, such as Langevin Dynamics (and its stochastic gradient counterpart) exhibit favorable dimension-dependence and fast mixing times for log-concave, and "close" to log-concave distributions, however also have long escape times from local minimizers. Many contemporary applications such as Bayesian Neural Networks are both high-dimensional and highly multimodal. In this paper we investigate the performance of a hybrid Metropolis and Langevin sampling method akin to Jump Diffusion on a range of synthetic and real data, indicating that careful calibration of mixing sampling jumps with gradient based chains significantly outperforms both pure gradient-based or sampling based schemes.

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