# GPDFlow: Generative Multivariate Threshold Exceedance Modeling via Normalizing Flows

arXiv: https://arxiv.org/abs/2503.11822 · HTML: https://mlsanity.com/paper/2503.11822/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 14 Mar 2025.

## Builds on (most cited first, 9 of 9)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependence](https://mlsanity.com/paper/2205.01224/) (2022)
- [Modeling spatial processes with unknown extremal dependence class](https://mlsanity.com/paper/1703.06031/) (2017)
- [Multivariate peaks over thresholds models](https://mlsanity.com/paper/1603.06619/) (2016)
- [Automated threshold selection and associated inference uncertainty for univariate extremes](https://mlsanity.com/paper/2310.17999/) (2023)

## Built on by (most cited first, 5 of 5)

- [Generative Machine Learning for Multivariate Angular Simulation](https://mlsanity.com/paper/2504.21505/) (2025)
- [Simulation of Multivariate Extremes: a Wasserstein-Aitchison GAN approach](https://mlsanity.com/paper/2504.21438/) (2025)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)
- [Canonical Tail Dependence for Soft Extremal Clustering of Multichannel Brain Signals](https://mlsanity.com/paper/2512.06435/) (2025)
- [Q-Edge: Symmetry-Reduced Quantum Simulation of Structured Extreme Dependence](https://mlsanity.com/paper/2609.03706/) (2026)

## Abstract (arXiv)

The multivariate generalized Pareto distribution (mGPD) is a common method for modeling extreme threshold exceedance probabilities in environmental and financial risk management. Despite its broad applicability, mGPD faces challenges due to the infinite possible parametrizations of its dependence function, with only a few parametric models available in practice. To address this limitation, we introduce GPDFlow, an innovative mGPD model that leverages normalizing flows to flexibly represent the dependence structure. Unlike traditional parametric mGPD approaches, GPDFlow does not impose explicit parametric assumptions on dependence, resulting in greater flexibility and enhanced performance. Additionally, GPDFlow allows direct inference of marginal parameters, providing insights into marginal tail behavior. We derive tail dependence coefficients for GPDFlow, including a bivariate formulation, a d-dimensional extension, and an alternative measure for partial exceedance dependence. A general relationship between the bivariate tail dependence coefficient and the generative samples from normalizing flows is discussed. Through simulations and a practical application analyzing the risk among five major US banks, we demonstrate that GPDFlow significantly improves modeling accuracy and flexibility compared to traditional parametric methods.