mlsanityData to 14 Oct 2026

Marginal Tail-Adaptive Normalizing Flows

arXiv 2206.10311 ↗First posted 21 Jun 2022cs.LG math.ST stat.MLcited by 12

Not on the map. Why?

Abstract (arXiv)

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled via the tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improves on the accuracy -- especially on the tails of the distribution -- and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 22 of its 57 references that are in the map. First posted on arXiv 21 Jun 2022.

Builds on

22 of 57 references.

References · 22

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2015Variational Inference with Normalizing Flowscited by 2,170
  3. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  4. 2014NICE: Non-linear Independent Components Estimationcited by 1,058
  5. 2017Masked Autoregressive Flow for Density Estimationcited by 684
  6. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 640
  7. 2019Neural Spline Flowscited by 596
  8. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 594
  9. 2018Invertible Residual Networkscited by 365
  10. 2015A note on the evaluation of generative modelscited by 292
  11. 2019Residual Flows for Invertible Generative Modelingcited by 257
  12. 2018Neural Autoregressive Flowscited by 208
10 more
  1. 2018i-RevNet: Deep Invertible Networkscited by 137
  2. 2020Understanding and Mitigating Exploding Inverses in Invertible Neural Networkscited by 71
  3. 2018Transformation Autoregressive Networkscited by 27
  4. 2013High-Dimensional Probability Estimation with Deep Density Modelscited by 17
  5. 2019Copula & Marginal Flows: Disentangling the Marginal from its Jointcited by 17
  6. 2020Robust model training and generalisation with Studentising flowscited by 10
  7. 2022COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependencecited by 8
  8. 2018Scale-free Networks Well Donecited by 7
  9. 2020Copula-based synthetic data augmentation for machine-learning emulatorscited by 6
  10. 2021Copula-Based Normalizing Flowscited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 5; 2024: 3; 2025: 1; 2026: 3.

12 papers.

  1. 2024Heavy-Tailed Diffusion Modelscited by 40
  2. 2024On the Challenges and Opportunities in Generative AIcited by 31
  3. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23
  4. 2023t3-Variational Autoencoder: Learning Heavy-tailed Data with Student's t and Power Divergencecited by 18
  5. 2024Flexible Tails for Normalizing Flowscited by 12
  6. 2023A VAE Approach to Sample Multivariate Extremescited by 10
  7. 2023Flexible Tails for Normalising Flows, with Application to the Modelling of Financial Return Datacited by 2
  8. 2023Efficient Epistemic Uncertainty Estimation in Regression Ensemble Models Using Pairwise-Distance Estimatorscited by 1
  9. 2025Stick-Breaking Mixture Normalizing Flows with Component-Wise Tail Adaptation for Variational Inferencecited by 0
  10. 2026Reducing Estimation Uncertainty Using Normalizing Flows and Stratificationcited by 0
  11. 2026Correcting Source Mismatch in Flow Matching with Radial-Angular Transportcited by 0
  12. 2026Tail Annealing for Heavy-Tailed Flow Matchingcited by 0