# Fisher Auto-Encoders

@inproceedings{Elkhalil2020FisherA, title={Fisher Auto-Encoders}, author={Khalil Elkhalil and Ali Hasan and Jie Ding and Sina Farsiu and Vahid Tarokh}, booktitle={International Conference on Artificial Intelligence and Statistics}, year={2020} }

It has been conjectured that the Fisher divergence is more robust to model uncertainty than the conventional Kullback-Leibler (KL) divergence. This motivates the design of a new class of robust generative auto-encoders (AE) referred to as Fisher auto-encoders. Our approach is to design Fisher AEs by minimizing the Fisher divergence between the intractable joint distribution of observed data and latent variables, with that of the postulated/modeled joint distribution. In contrast to KL-based…

## 5 Citations

### On the failure of variational score matching for VAE models

- Computer ScienceArXiv
- 2022

A critical study of existing variational SM objectives is presented, showing catastrophic failure on a wide range of datasets and network architectures and suggesting that only ELBO and the baseline objective robustly produce expected results, while previously proposed SM methods do not.

### Skewed Jensen—Fisher Divergence and Its Bounds

- Computer ScienceFoundations
- 2021

A skewed Jensen-Fisher divergence is introduced based on relative Fisher information, and some bounds are provided in terms of the skewed Jensen–Shannon divergence and of the variational distance.

### Probabilistic Autoencoder Using Fisher Information

- Computer ScienceEntropy
- 2021

In this work, an extension to the autoencoder architecture is introduced, the FisherNet, which has advantages from a theoretical point of view as it provides a direct uncertainty quantification derived from the model and also accounts for uncertainty cross-correlations.

### Fast approximations of the Jeffreys divergence between univariate Gaussian mixture models via exponential polynomial densities

- Computer ScienceArXiv
- 2021

This work proposes a simple yet fast heuristic to approximate the Jeffreys divergence between two GMMs of arbitrary number of components and considers Polynomial Exponential Densities, and designs a goodness-of-fit criterion to measure the dissimilarity between a GMM and a PED which is a generalization of the Hyvärinen divergence.

### Fast Approximations of the Jeffreys Divergence between Univariate Gaussian Mixtures via Mixture Conversions to Exponential-Polynomial Distributions

- Computer ScienceEntropy
- 2021

This paper proposes a simple yet fast heuristic to approximate the Jeffreys divergence between two univariate Gaussian mixtures with arbitrary number of components and demonstrates that this heuristic improves over the computational time of stochastic Monte Carlo estimations by several orders of magnitude.

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