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Combining Normalizing Flows and Quasi-Monte Carlo

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arxiv 2401.05934 v1 pith:HHQSORYT submitted 2024-01-11 stat.CO stat.ML

Charly Andral This is my paper · ORCID
classification stat.COstat.ML
keywords carlomontemethodsflowsnormalizingquasi-montedistributionflow
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Recent advances in machine learning have led to the development of new methods for enhancing Monte Carlo methods such as Markov chain Monte Carlo (MCMC) and importance sampling (IS). One such method is normalizing flows, which use a neural network to approximate a distribution by evaluating it pointwise. Normalizing flows have been shown to improve the performance of MCMC and IS. On the other side, (randomized) quasi-Monte Carlo methods are used to perform numerical integration. They replace the random sampling of Monte Carlo by a sequence which cover the hypercube more uniformly, resulting in better convergence rates for the error that plain Monte Carlo. In this work, we combine these two methods by using quasi-Monte Carlo to sample the initial distribution that is transported by the flow. We demonstrate through numerical experiments that this combination can lead to an estimator with significantly lower variance than if the flow was sampled with a classic Monte Carlo.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Transport Quasi-Monte Carlo

    math.NA 2024-12 conditional novelty 6.0 of 10

    A transport-map estimator built from composed autoregressive layers and randomized quasi-Monte Carlo points achieves O(n^{-1+ε}) error for general target distributions under stated growth conditions.

  2. Error estimation for quasi-Monte Carlo

    math.NA 2024-12 accept novelty 2.0 of 10

    A review of uncertainty quantification for quasi-Monte Carlo that recommends Student's t intervals from at least 10 randomized replicates and identifies near-symmetry of RQMC errors as a promising but unproven basis f...

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