Generative Modeling: A Review

Abstract:We organize the generative-modeling literature around three classes of generators, corresponding to three distinct inferential tasks: estimating counterfactual outcome distributions in causal inference, recovering posteriors from simulated parameter--outcome pairs, and forming predictive outcome distributions. The unifying representation relies on the noise outsourcing theorem of Kallenberg, which expresses a conditional distribution as a deterministic function of its inputs and an independent noise variable. Within this organization we develop generative Bayesian computation, a method in the parameter--outcome class: a quantile neural network, trained on simulated pairs under the pinball loss, that targets the posterior of the parameter directly, without invertible architectures or density evaluation, and that serves equally as a predictive generator once the roles of parameter and outcome are exchanged. We illustrate the framework on an agent-based Ebola transmission application, where generative Bayesian computation recovers accurate posteriors at substantially lower cost than rejection-based simulation inference, while avoiding the density-evaluation and invertibility constraints of competing generators.

arXiv admin note: substantial text overlap with arXiv:2305.14972

Computation (stat.CO); Machine Learning (cs.LG)

arXiv:2501.05458 [stat.CO]

(or arXiv:2501.05458v3 [stat.CO] for this version)

https://doi.org/10.48550/arXiv.2501.05458 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.