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Poster
Local-Global MCMC kernels: the best of both worlds
Sergey Samsonov · Evgeny Lagutin · Marylou Gabrié · Alain Durmus · Alexey Naumov · Eric Moulines

Tue Nov 29 02:00 PM -- 04:00 PM (PST) @ Hall J #143
in Poster Session 2 »
Recent works leveraging learning to enhance sampling have shown promising results, in particular by designing effective non-local moves and global proposals. However, learning accuracy is inevitably limited in regions where little data is available such as in the tails of distributions as well as in high-dimensional problems. In the present paper we study an Explore-Exploit Markov chain Monte Carlo strategy ($\operatorname{Ex^2MCMC}$) that combines local and global samplers showing that it enjoys the advantages of both approaches. We prove $V$-uniform geometric ergodicity of $\operatorname{Ex^2MCMC}$ without requiring a uniform adaptation of the global sampler to the target distribution. We also compute explicit bounds on the mixing rate of the Explore-Exploit strategy under realistic conditions. Moreover, we propose an adaptive version of the strategy ($\operatorname{FlEx^2MCMC}$) where a normalizing flow is trained while sampling to serve as a proposal for global moves. We illustrate the efficiency of $\operatorname{Ex^2MCMC}$ and its adaptive version on classical sampling benchmarks as well as in sampling high-dimensional distributions defined by Generative Adversarial Networks seen as Energy Based Models.
Keywords: MCMC · Markov chains · adaptive MCMC

Author Information

Sergey Samsonov (National Research University Higher School of Economics)
Evgeny Lagutin (Moscow Institute of Physics and Technology)
Marylou Gabrié (NYU / Flatiron Institute)
Alain Durmus (Ecole polytechnique)
Alexey Naumov (HSE University)
Eric Moulines (Ecole Polytechnique)

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