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Adaptation of the Independent Metropolis-Hastings Sampler with Normalizing Flow Proposals.
James A Brofos1, Marylou Gabrié2, Marcus A Brubaker3
1Yale University.
Proceedings of Machine Learning Research
|February 15, 2023
Summary
Adaptive Markov Chain Monte Carlo (MCMC) methods improve parameter tuning for complex distributions. This study extends convergence theory to normalizing flows, enhancing MCMC sampling performance.
Area of Science:
- Computational Statistics
- Machine Learning
- Bayesian Inference
Background:
- Markov Chain Monte Carlo (MCMC) methods are essential for complex probability distributions.
- MCMC performance relies heavily on parameter tuning, which is often challenging.
- Adaptive MCMC methods adjust parameters during sampling but require new convergence analyses.
Purpose of the Study:
- To extend the convergence theory of adaptive MCMC methods.
- To introduce a new class of adaptive MCMC methods using normalizing flows.
- To analyze the practical performance of these novel methods.
Main Methods:
- Developed an adaptive MCMC method using normalizing flows as proposal distributions.
- Employed stochastic gradient descent for updating normalizing flow parameters.
- Applied the method to synthetic datasets and a physical field system.
Main Results:
- Successfully extended the convergence theory for adaptive MCMC with normalizing flows.
- Demonstrated practical performance on synthetic and real-world data.
- Compared the proposed method against existing adaptive and non-adaptive MCMC techniques.
Conclusions:
- The proposed adaptive MCMC method using normalizing flows is theoretically sound and practically effective.
- This approach offers a promising advancement for sampling complex distributions.
- Further research can explore broader applications in statistical modeling and scientific computation.
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