# Robust model training and generalisation with Studentising flows

arXiv: https://arxiv.org/abs/2006.06599 · HTML: https://mlsanity.com/paper/2006.06599/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2020.

## Built on by (most cited first, 10 of 10)

- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
- [FlowVQTalker: High-Quality Emotional Talking Face Generation through Normalizing Flow and Quantization](https://mlsanity.com/paper/2403.06375/) (2024)
- [t3-Variational Autoencoder: Learning Heavy-tailed Data with Student's t and Power Divergence](https://mlsanity.com/paper/2312.01133/) (2023)
- [Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference](https://mlsanity.com/paper/2310.04395/) (2023)
- [Amortized Bayesian Multilevel Models](https://mlsanity.com/paper/2408.13230/) (2024)
- [A Review of Change of Variable Formulas for Generative Modeling](https://mlsanity.com/paper/2308.02652/) (2023)
- [Marginal Tail-Adaptive Normalizing Flows](https://mlsanity.com/paper/2206.10311/) (2022)
- [Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data](https://mlsanity.com/paper/2501.13483/) (2025)
- [Copula-Based Normalizing Flows](https://mlsanity.com/paper/2107.07352/) (2021)
- [metabeta -- A fast neural model for Bayesian mixed-effects regression](https://mlsanity.com/paper/2510.07473/) (2025)

## Abstract (arXiv)

Normalising flows are tractable probabilistic models that leverage the power of deep learning to describe a wide parametric family of distributions, all while remaining trainable using maximum likelihood. We discuss how these methods can be further improved based on insights from robust (in particular, resistant) statistics. Specifically, we propose to endow flow-based models with fat-tailed latent distributions such as multivariate Student's t, as a simple drop-in replacement for the Gaussian distribution used by conventional normalising flows. While robustness brings many advantages, this paper explores two of them: 1) We describe how using fatter-tailed base distributions can give benefits similar to gradient clipping, but without compromising the asymptotic consistency of the method. 2) We also discuss how robust ideas lead to models with reduced generalisation gap and improved held-out data likelihood. Experiments on several different datasets confirm the efficacy of the proposed approach in both regards.