An end-to-end framework for uncertainty-aware validation of generative models

Giada Badaracco, Sean Benevedes, Christina Reissel, Philip Harris, Gaia Grosso

Density estimation with generative models is a common task in the physical sciences, for example in background estimation in particle physics. Existing machine learning techniques, however, lack methods to quantify uncertainties that can be propagated into a statistical test. That limits the validation of generative models to standard goodness-of-fit tests, in which the generative model is treated as exact (point-null hypothesis). But a model fitted to a finite training set is never exact, so if its uncertainties are neglected, any sufficiently powerful goodness-of-fit test will eventually reject it once the test set is large enough to resolve this estimation error. We propose SIGMA, an end-to-end framework combining density estimation with principled uncertainty quantification. We use Gaussian mixture models, for which uncertainties are tractable, and further construct a new goodness-of-fit test in which these uncertainties are profiled as nuisance parameters to account for the statistical error of the fit, promoting the conventional point-null test to a composite one. A rejection then signals genuine mismodeling rather than a test set large enough to resolve the error of the…