# The Inductive Bias of Restricted f-GANs

arXiv: https://arxiv.org/abs/1809.04542 · HTML: https://mlsanity.com/paper/1809.04542/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2018.

## Built on by (most cited first, 5 of 5)

- [Distributionally Robust Bayesian Optimization with varphi-divergences](https://mlsanity.com/paper/2203.02128/) (2022)
- [Approximate Data Deletion in Generative Models](https://mlsanity.com/paper/2206.14439/) (2022)
- [Statistical Error Bounds for GANs with Nonlinear Objective Functionals](https://mlsanity.com/paper/2406.16834/) (2024)
- [Density-Ratio Losses for Post-Hoc Learning to Defer](https://mlsanity.com/paper/2605.19557/) (2026)
- [Seasoning Generative Models for a Generalization Aftertaste](https://mlsanity.com/paper/2603.18817/) (2026)

## Abstract (arXiv)

Generative adversarial networks are a novel method for statistical inference that have achieved much empirical success; however, the factors contributing to this success remain ill-understood. In this work, we attempt to analyze generative adversarial learning -- that is, statistical inference as the result of a game between a generator and a discriminator -- with the view of understanding how it differs from classical statistical inference solutions such as maximum likelihood inference and the method of moments. Specifically, we provide a theoretical characterization of the distribution inferred by a simple form of generative adversarial learning called restricted f-GANs -- where the discriminator is a function in a given function class, the distribution induced by the generator is restricted to lie in a pre-specified distribution class and the objective is similar to a variational form of the f-divergence. A consequence of our result is that for linear KL-GANs -- that is, when the discriminator is a linear function over some feature space and f corresponds to the KL-divergence -- the distribution induced by the optimal generator is neither the maximum likelihood nor the method of moments solution, but an interesting combination of both.