# Deep Generative Quantile-Copula Models for Probabilistic Forecasting

arXiv: https://arxiv.org/abs/1907.10697 · HTML: https://mlsanity.com/paper/1907.10697/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2019.

## Built on by (most cited first, 18 of 18)

- [Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting](https://mlsanity.com/paper/2111.06581/) (2021)
- [TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series](https://mlsanity.com/paper/2310.01327/) (2023)
- [Deep Inventory Management](https://mlsanity.com/paper/2210.03137/) (2022)
- [Deep Time Series Forecasting with Shape and Temporal Criteria](https://mlsanity.com/paper/2104.04610/) (2021)
- [From Samples to Scenarios: A New Paradigm for Probabilistic Forecasting](https://mlsanity.com/paper/2509.19975/) (2025)
- [MQRetNN: Multi-Horizon Time Series Forecasting with Retrieval Augmentation](https://mlsanity.com/paper/2207.10517/) (2022)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)
- [Learning an Inventory Control Policy with General Inventory Arrival Dynamics](https://mlsanity.com/paper/2310.17168/) (2023)
- [Efficiently Generating Correlated Sample Paths from Multi-step Time Series Foundation Models](https://mlsanity.com/paper/2510.02224/) (2025)
- [Learning to Simulate: Generative Metamodeling via Quantile Regression](https://mlsanity.com/paper/2311.17797/) (2023)
- [C2VAE: Gaussian Copula-based VAE Differing Disentangled from Coupled Representations with Contrastive Posterior](https://mlsanity.com/paper/2309.13303/) (2023)
- [Deep Generative Quantile Bayes](https://mlsanity.com/paper/2410.08378/) (2024)
- [GEANN: Scalable Graph Augmentations for Multi-Horizon Time Series Forecasting](https://mlsanity.com/paper/2307.03595/) (2023)
- [Creating Probabilistic Forecasts from Arbitrary Deterministic Forecasts using Conditional Invertible Neural Networks](https://mlsanity.com/paper/2302.01800/) (2023)
- [AutoPQ: Automating Quantile estimation from Point forecasts in the context of sustainability](https://mlsanity.com/paper/2412.00419/) (2024)
- [A Data-driven Dynamic Temporal Correlation Modeling Framework for Renewable Energy Scenario Generation](https://mlsanity.com/paper/2501.14233/) (2025)
- [Gaussian Mixture Copula Processes for Irregular Time Series](https://mlsanity.com/paper/2605.23632/) (2026)
- [Interweaving Marginals into Multivariate Sample Paths: Training-Free Dependence Construction for Probabilistic Time Series Foundation Models](https://mlsanity.com/paper/2609.25980/) (2026)

## Abstract (arXiv)

We introduce a new category of multivariate conditional generative models and demonstrate its performance and versatility in probabilistic time series forecasting and simulation. Specifically, the output of quantile regression networks is expanded from a set of fixed quantiles to the whole Quantile Function by a univariate mapping from a latent uniform distribution to the target distribution. Then the multivariate case is solved by learning such quantile functions for each dimension's marginal distribution, followed by estimating a conditional Copula to associate these latent uniform random variables. The quantile functions and copula, together defining the joint predictive distribution, can be parameterized by a single implicit generative Deep Neural Network.