Adaptive MC w/ normalizing flows

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New paper turned up on PNAS about normalizing flows in Monte Carlo,

May be of interest?

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Cool! It seems related (in spirit) to the NeuTra HMC paper from a few years ago ([1903.03704] NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport). My 2 cents: attacking difficult posterior distributions this way is really helpful when you have moderate dimensionality (100 < d < 10000) and high correlations. My (limited) knowledge on this is that the compute cost incurred by the NF is at least linear in d so the payoff might not always be worth it.

Unfortunately, this is also kind of a mismatch to the problem space many advanced modelers face because you either have something with d >> 10000 like regression or Bayesian machine learning with many groups / covariates, or you have small d with extremely difficult posterior geometries from highly nonlinear models like ODE/PDEs from physics/ecology/etc in which case you can use Riemannian HMC.

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Thanks for the good remarks. I agree that it’s not a giant hammer to squash all problems. But I suspect in complex models it could help address certain difficult or inexistant reparametrizations.

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Slightly tangential question, but how often you you think sampling difficulty arises from multi-modality, as opposed to difficult or degenerate posterior geometry? In my own work (economics) I see the latter much more often than the former, although I admittedly don’t work much with mixture models.

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Slightly tangential question, but how often you you think sampling difficulty arises from multi-modality, as opposed to difficult or degenerate posterior geometry? In my own work (economics) I see the latter much more often than the former, although I admittedly don’t work much with mixture models.

Multimodality is definitely less of an issue than it used to be, since the implementation of features like the ordered transform and mixture classes have made label switching much less common. Variational inference has also been pretty helpful too, since it typically just picks a single mode for the approximate posterior though that’s more or less just shoving the issue under the rug so it doesn’t show up in the convergence diagnostics.

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