Generative Modeling: A Review
stat.CO, cs.LG
Submitted: 2024-12-24
Updated: 2026-08-24
Comments: arXiv admin note: substantial text overlap with arXiv:2305.14972
License: http://creativecommons.org/publicdomain/zero/1.0/
The gist: We organize the generative-modeling literature around three classes of generators, corresponding to three distinct inferential tasks: estimating counterfactual outcome distributions in causal
Terminology
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.
Sources
- Guided Image Generation with Conditional Invertible Neural Networks
- Merging Two Cultures: Deep and Statistical Learning
- NICE: Non-linear Independent Components Estimation
- Deep Learning in Finance
- i-RevNet: Deep Invertible Networks
- Conditional Generative Adversarial Nets
- Deep Learning Partial Least Squares
- Variational Inference with Normalizing Flows
- Bayesian Calibration for Activity Based Models
- MintNet: Building Invertible Neural Networks with Masked Convolutions
- Conditional Density Estimation with Bayesian Normalising Flows
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