# Improving Bridge estimators via f-GAN

arXiv: https://arxiv.org/abs/2106.07462 · HTML: https://mlsanity.com/paper/2106.07462/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 53 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Unrolled Generative Adversarial Networks](https://mlsanity.com/paper/1611.02163/) (2016)
- [Discrete Flows: Invertible Generative Models of Discrete Data](https://mlsanity.com/paper/1905.10347/) (2019)
- [Generative Adversarial Nets from a Density Ratio Estimation Perspective](https://mlsanity.com/paper/1610.02920/) (2016)
- [Accurate and Conservative Estimates of MRF Log-likelihood using Reverse Annealing](https://mlsanity.com/paper/1412.8566/) (2014)
- [Normalizing Constant Estimation with Gaussianized Bridge Sampling](https://mlsanity.com/paper/1912.06073/) (2019)
- [Warp Bridge Sampling: The Next Generation](https://mlsanity.com/paper/1609.07690/) (2016)

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

- [Provable benefits of annealing for estimating normalizing constants: Importance Sampling, Noise-Contrastive Estimation, and beyond](https://mlsanity.com/paper/2310.03902/) (2023)
- [Optimizing the Noise in Self-Supervised Learning: from Importance Sampling to Noise-Contrastive Estimation](https://mlsanity.com/paper/2301.09696/) (2023)

## Abstract (arXiv)

Bridge sampling is a powerful Monte Carlo method for estimating ratios of normalizing constants. Various methods have been introduced to improve its efficiency. These methods aim to increase the overlap between the densities by applying appropriate transformations to them without changing their normalizing constants. In this paper, we first give a new estimator of the asymptotic relative mean square error (RMSE) of the optimal Bridge estimator by equivalently estimating an f-divergence between the two densities. We then utilize this framework and propose f-GAN-Bridge estimator (f-GB) based on a bijective transformation that maps one density to the other and minimizes the asymptotic RMSE of the optimal Bridge estimator with respect to the densities. This transformation is chosen by minimizing a specific f-divergence between the densities using an f-GAN. We show f-GB is optimal in the sense that within any given set of candidate transformations, the f-GB estimator can asymptotically achieve an RMSE lower than or equal to that achieved by Bridge estimators based on any other transformed densities. Numerical experiments show that f-GB outperforms existing methods in simulated and real-world examples. In addition, we discuss how Bridge estimators naturally arise from the problem of f-divergence estimation.