# Variational Inference based on Robust Divergences

arXiv: https://arxiv.org/abs/1710.06595 · HTML: https://mlsanity.com/paper/1710.06595/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2017.

## Built on by (most cited first, 15 of 15)

- [Heavy-Tailed Diffusion Models](https://mlsanity.com/paper/2410.14171/) (2024)
- [t3-Variational Autoencoder: Learning Heavy-tailed Data with Student's t and Power Divergence](https://mlsanity.com/paper/2312.01133/) (2023)
- [Robust and Scalable Bayesian Online Changepoint Detection](https://mlsanity.com/paper/2302.04759/) (2023)
- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [Robust PACm: Training Ensemble Models Under Misspecification and Outliers](https://mlsanity.com/paper/2203.01859/) (2022)
- [Overcoming the Limitations of Localization Uncertainty: Efficient & Exact Non-Linear Post-Processing and Calibration](https://mlsanity.com/paper/2306.08981/) (2023)
- [Weakly Augmented Variational Autoencoder in Time Series Anomaly Detection](https://mlsanity.com/paper/2401.03341/) (2024)
- [Stein Variational Evolution Strategies](https://mlsanity.com/paper/2410.10390/) (2024)
- [Multi-Output Robust and Conjugate Gaussian Processes](https://mlsanity.com/paper/2510.26401/) (2025)
- [Generalized Munchausen Reinforcement Learning using Tsallis KL Divergence](https://mlsanity.com/paper/2301.11476/) (2023)
- [Minimizing robust density power-based divergences for general parametric density models](https://mlsanity.com/paper/2307.05251/) (2023)
- [R'enyi Neural Processes](https://mlsanity.com/paper/2405.15991/) (2024)
- [Robust and Scalable Variational Bayes](https://mlsanity.com/paper/2504.12528/) (2025)
- [Robust computation of optimal transport by β-potential regularization](https://mlsanity.com/paper/2212.13251/) (2022)
- [Rethinking Likelihood distributions: Student's t Likelihood Boosts Bayesian Neural Network Performance](https://mlsanity.com/paper/2607.25376/) (2026)

## Abstract (arXiv)

Robustness to outliers is a central issue in real-world machine learning applications. While replacing a model to a heavy-tailed one (e.g., from Gaussian to Student-t) is a standard approach for robustification, it can only be applied to simple models. In this paper, based on Zellner's optimization and variational formulation of Bayesian inference, we propose an outlier-robust pseudo-Bayesian variational method by replacing the Kullback-Leibler divergence used for data fitting to a robust divergence such as the beta- and gamma-divergences. An advantage of our approach is that superior but complex models such as deep networks can also be handled. We theoretically prove that, for deep networks with ReLU activation functions, the influence function in our proposed method is bounded, while it is unbounded in the ordinary variational inference. This implies that our proposed method is robust to both of input and output outliers, while the ordinary variational method is not. We experimentally demonstrate that our robust variational method outperforms ordinary variational inference in regression and classification with deep networks.