Quasi-Monte Carlo Flows

Abstract

Normalizing flows provide a general approach to construct flexible variational posteriors. The parameters are learned by stochastic optimization of the variational bound, but inference can be slow due to high variance of the gradient estimator. We propose Quasi-Monte Carlo (QMC) flows which reduce the variance of the gradient estimator by one order of magnitude. First results show that QMC flows lead to faster inference and samples from the variational posterior cover the target space more evenly.

Machine learning Post-Minkowskian integrals

“…We hence expect that a QMC integrator could be combined with improved NN phase-space sampling to reach an even better performance (see e.g. [155]). We leave that for future work.…”

Measure Transport with Kernel Stein Discrepancy

“…As one might hope, these approximations were successful in finding each of the modes in p 3 , but fared relatively worse for p 1 and p 2 . Second, since in Adam we are using a Monte Carlo estimator of the gradient, it is natural to ask whether a quasi Monte Carlo estimator would offer an improvement [Wenzel et al, 2018]. This was investigated and our results are reported in Appendix C.3.…”

“…To reduce the variance of the Monte-Carlo based gradient estimators, it was put forward in Buchholz et al [2018] and Wenzel et al [2018], to instead use randomised Quasi-Monte Carlo (QMC) in constructing an unbiased estimator of the gradient. This is achieved by simply replacing the Monte-Carlo samples from the base distribution with samples from a (randomised) QMC sequence in a principled manner.…”

“…We first, however, briefly outline the rudimentary idea. Refer to Buchholz et al [2018] and Wenzel et al [2018] for the full detail.…”

“…These negative findings dissuaded us from further exploring QMC in this work. However, it remains to be seen whether more advanced randomised QMC sequences, such as the scrambled Sobol sequence that was used in Wenzel et al [2018], provide performance gains relative to standard Monte Carlo.…”