# Asymptotic Statistical Analysis of f-divergence GAN

arXiv: https://arxiv.org/abs/2209.06853 · HTML: https://mlsanity.com/paper/2209.06853/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 37 references that are in the map.
- First posted on arXiv 14 Sep 2022.

## Builds on (most cited first, 22 of 22)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Self-Attention Generative Adversarial Networks](https://mlsanity.com/paper/1805.08318/) (2018)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [MoCoGAN: Decomposing Motion and Content for Video Generation](https://mlsanity.com/paper/1707.04993/) (2017)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [Generalization and Equilibrium in Generative Adversarial Nets (GANs)](https://mlsanity.com/paper/1703.00573/) (2017)
- [MuseGAN: Multi-track Sequential Generative Adversarial Networks for Symbolic Music Generation and Accompaniment](https://mlsanity.com/paper/1709.06298/) (2017)
- [Stability and Generalization of Learning Algorithms that Converge to Global Optima](https://mlsanity.com/paper/1710.08402/) (2017)
- [How Well Generative Adversarial Networks Learn Distributions](https://mlsanity.com/paper/1811.03179/) (2018)
- [On the Discrimination-Generalization Tradeoff in GANs](https://mlsanity.com/paper/1711.02771/) (2017)
- [Approximation and Convergence Properties of Generative Adversarial Learning](https://mlsanity.com/paper/1705.08991/) (2017)
- [Approximability of Discriminators Implies Diversity in GANs](https://mlsanity.com/paper/1806.10586/) (2018)
- [Some Theoretical Properties of GANs](https://mlsanity.com/paper/1803.07819/) (2018)
- [Dualing GANs](https://mlsanity.com/paper/1706.06216/) (2017)

## Built on by (most cited first, 2 of 2)

- [Engression: Extrapolation through the Lens of Distributional Regression](https://mlsanity.com/paper/2307.00835/) (2023)
- [Generative Adversarial Network based Voice Conversion: Techniques, Challenges, and Recent Advancements](https://mlsanity.com/paper/2504.19197/) (2025)

## Abstract (arXiv)

Generative Adversarial Networks (GANs) have achieved great success in data generation. However, its statistical properties are not fully understood. In this paper, we consider the statistical behavior of the general f-divergence formulation of GAN, which includes the Kullback--Leibler divergence that is closely related to the maximum likelihood principle. We show that for parametric generative models that are correctly specified, all f-divergence GANs with the same discriminator classes are asymptotically equivalent under suitable regularity conditions. Moreover, with an appropriately chosen local discriminator, they become equivalent to the maximum likelihood estimate asymptotically. For generative models that are misspecified, GANs with different f-divergences converge to different estimators, and thus cannot be directly compared. However, it is shown that for some commonly used f-divergences, the original f-GAN is not optimal in that one can achieve a smaller asymptotic variance when the discriminator training in the original f-GAN formulation is replaced by logistic regression. The resulting estimation method is referred to as Adversarial Gradient Estimation (AGE). Empirical studies are provided to support the theory and to demonstrate the advantage of AGE over the original f-GANs under model misspecification.