# Retrospective Uncertainties for Deep Models using Vine Copulas

arXiv: https://arxiv.org/abs/2302.12606 · HTML: https://mlsanity.com/paper/2302.12606/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 44 references that are in the map.
- First posted on arXiv 24 Feb 2023.

## Builds on (most cited first, 19 of 19)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Training independent subnetworks for robust prediction](https://mlsanity.com/paper/2010.06610/) (2020)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [TACTiS: Transformer-Attentional Copulas for Time Series](https://mlsanity.com/paper/2202.03528/) (2022)
- [Copulas as High-Dimensional Generative Models: Vine Copula Autoencoders](https://mlsanity.com/paper/1906.05423/) (2019)
- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [Nonparametric estimation of simplified vine copula models: comparison of methods](https://mlsanity.com/paper/1701.00845/) (2017)
- [Deep Non-Crossing Quantiles through the Partial Derivative](https://mlsanity.com/paper/2201.12848/) (2022)
- [Probit transformation for nonparametric kernel estimation of the copula density](https://mlsanity.com/paper/1404.4414/) (2014)
- [Modelling heterogeneous distributions with an Uncountable Mixture of Asymmetric Laplacians](https://mlsanity.com/paper/1910.12288/) (2019)
- [Model selection in sparse high-dimensional vine copula models with application to portfolio risk](https://mlsanity.com/paper/1801.09739/) (2018)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)
- [Solving estimating equations with copulas](https://mlsanity.com/paper/1801.10576/) (2018)
- [Uncertainty Modelling in Deep Networks: Forecasting Short and Noisy Series](https://mlsanity.com/paper/1807.09011/) (2018)

## Built on by (most cited first, 7 of 7)

- [BOtied: Multi-objective Bayesian optimization with tied multivariate ranks](https://mlsanity.com/paper/2306.00344/) (2023)
- [Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies](https://mlsanity.com/paper/2509.19707/) (2025)
- [CLEAR: Calibrated Learning for Epistemic and Aleatoric Risk](https://mlsanity.com/paper/2507.08150/) (2025)
- [Vine Copulas as Differentiable Computational Graphs](https://mlsanity.com/paper/2506.13318/) (2025)
- [2-Cats: 2D Copula Approximating Transforms](https://mlsanity.com/paper/2309.16391/) (2023)
- [Stepwise Variational Inference with Vine Copulas](https://mlsanity.com/paper/2603.22959/) (2026)
- [Dynamic Vine Copulas: Detecting and Quantifying Time-Varying Higher-Order Interactions](https://mlsanity.com/paper/2605.03061/) (2026)

## Abstract (arXiv)

Despite the major progress of deep models as learning machines, uncertainty estimation remains a major challenge. Existing solutions rely on modified loss functions or architectural changes. We propose to compensate for the lack of built-in uncertainty estimates by supplementing any network, retrospectively, with a subsequent vine copula model, in an overall compound we call Vine-Copula Neural Network (VCNN). Through synthetic and real-data experiments, we show that VCNNs could be task (regression/classification) and architecture (recurrent, fully connected) agnostic while providing reliable and better-calibrated uncertainty estimates, comparable to state-of-the-art built-in uncertainty solutions.