Diffusion posterior sampling for simulation-based inference in tall data
  settings
Julia Linhart Gabriel Victorino Cardoso Alexandre Gramfort Sylvain Le Corff Pedro L. C. Rodrigues
Determining which parameters of a non-linear model could best describe a set
of experimental data is a fundamental problem in science and it has gained much
traction lately with the rise of complex large-scale simulators (a.k.a.
black-box simulators). The likelihood of such models is typically intractable,
which is why classical MCMC methods can not be used. Simulation-based inference
(SBI) stands out in this context by only requiring a dataset of simulations to
train deep generative models capable of approximating the posterior
distribution that relates input parameters to a given observation. In this
work, we consider a tall data extension in which multiple observations are
available and one wishes to leverage their shared information to better infer
the parameters of the model. The method we propose is built upon recent
developments from the flourishing score-based diffusion literature and allows
us to estimate the tall data posterior distribution simply using information
from the score network trained on individual observations. We compare our
method to recently proposed competing approaches on various numerical
experiments and demonstrate its superiority in terms of numerical stability and
computational cost.