# A General Framework for Uncertainty Quantification via Neural SDE-RNN

arXiv: https://arxiv.org/abs/2306.01189 · HTML: https://mlsanity.com/paper/2306.01189/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 18 of 18)

- [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)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Modeling Missing Data in Clinical Time Series with RNNs](https://mlsanity.com/paper/1606.04130/) (2016)
- [SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates](https://mlsanity.com/paper/2008.10546/) (2020)
- [Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filtering](https://mlsanity.com/paper/2006.04727/) (2020)
- [A General Framework for quantifying Aleatoric and Epistemic uncertainty in Graph Neural Networks](https://mlsanity.com/paper/2205.09968/) (2022)
- [Deep learning with differential Gaussian process flows](https://mlsanity.com/paper/1810.04066/) (2018)
- [Neural ODEs for Informative Missingness in Multivariate Time Series](https://mlsanity.com/paper/2005.10693/) (2020)
- [Robust Learning of Recurrent Neural Networks in Presence of Exogenous Noise](https://mlsanity.com/paper/2105.00996/) (2021)
- [Latent Neural ODE for Integrating Multi-timescale measurements in Smart Distribution Grids](https://mlsanity.com/paper/2211.03882/) (2022)
- [Recursive Gaussian Process over graphs for Integrating Multi-timescale Measurements in Low-Observable Distribution Systems](https://mlsanity.com/paper/2209.01703/) (2022)
- [Multi Time-scale Imputation aided State Estimation in Distribution System](https://mlsanity.com/paper/2011.10738/) (2020)

## Built on by (most cited first, 2 of 2)

- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [SDE-Attention: Latent Attention in SDE-RNNs for Irregularly Sampled Time Series with Missing Data](https://mlsanity.com/paper/2511.23238/) (2025)

## Abstract (arXiv)

Uncertainty quantification is a critical yet unsolved challenge for deep learning, especially for the time series imputation with irregularly sampled measurements. To tackle this problem, we propose a novel framework based on the principles of recurrent neural networks and neural stochastic differential equations for reconciling irregularly sampled measurements. We impute measurements at any arbitrary timescale and quantify the uncertainty in the imputations in a principled manner. Specifically, we derive analytical expressions for quantifying and propagating the epistemic and aleatoric uncertainty across time instants. Our experiments on the IEEE 37 bus test distribution system reveal that our framework can outperform state-of-the-art uncertainty quantification approaches for time-series data imputations.