# DeepL'evy: Learning Heavy-Tailed Uncertainty in Highly Volatile Time Series

arXiv: https://arxiv.org/abs/2605.10364 · HTML: https://mlsanity.com/paper/2605.10364/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 43 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Regularizing Neural Networks by Penalizing Confident Output Distributions](https://mlsanity.com/paper/1701.06548/) (2017)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [A Survey of Deep Learning and Foundation Models for Time Series Forecasting](https://mlsanity.com/paper/2401.13912/) (2024)
- [Explainable AI for clinical and remote health applications: a survey on tabular and time series data](https://mlsanity.com/paper/2209.06528/) (2022)
- [COVID-19 Modeling: A Review](https://mlsanity.com/paper/2104.12556/) (2021)
- [Generative neural networks for characteristic functions](https://mlsanity.com/paper/2401.04778/) (2024)
- [Improving probabilistic forecasts of extreme wind speeds by training statistical post-processing models with weighted scoring rules](https://mlsanity.com/paper/2407.15900/) (2024)
- [CF-GO-Net: A Universal Distribution Learner via Characteristic Function Networks with Graph Optimizers](https://mlsanity.com/paper/2409.12610/) (2024)
- [STOAT: Spatial-Temporal Probabilistic Causal Inference Network](https://mlsanity.com/paper/2506.09544/) (2025)

## Abstract (arXiv)

Modeling uncertainty in heavy-tailed time series remains a critical challenge for deep probabilistic forecasting models, which often struggle to capture abrupt, extreme events. While L'evy stable distributions offer a natural framework for modeling such non-Gaussian behaviors, the intractability of their probability density functions severely limits conventional likelihood-based inference. To address this, we introduce DeepL'evy, a neural framework that learns mixtures of L'evy stable distributions by minimizing the discrepancy between empirical and parametric characteristic functions. DeepL'evy incorporates a mixture mechanism that adaptively learns context-dependent weights and parameters over multiple L'evy components, enabling flexible multi-horizon uncertainty modeling. Evaluations on both real and synthetic datasets demonstrate that DeepL'evy outperforms state-of-the-art deep probabilistic forecasting approaches in tail risk metrics, especially under extreme volatility.