# When in Doubt: Neural Non-Parametric Uncertainty Quantification for Epidemic Forecasting

arXiv: https://arxiv.org/abs/2106.03904 · HTML: https://mlsanity.com/paper/2106.03904/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 7 Jun 2021.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Multiplicative Normalizing Flows for Variational Bayesian Neural Networks](https://mlsanity.com/paper/1703.01961/) (2017)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates](https://mlsanity.com/paper/2008.10546/) (2020)
- [The Functional Neural Process](https://mlsanity.com/paper/1906.08324/) (2019)
- [Bayesian Recurrent Neural Networks](https://mlsanity.com/paper/1704.02798/) (2017)
- [Recurrent Attentive Neural Process for Sequential Data](https://mlsanity.com/paper/1910.09323/) (2019)
- [When and How to Lift the Lockdown? Global COVID-19 Scenario Analysis and Policy Assessment using Compartmental Gaussian Processes](https://mlsanity.com/paper/2005.08837/) (2020)
- [Steering a Historical Disease Forecasting Model Under a Pandemic: Case of Flu and COVID-19](https://mlsanity.com/paper/2009.11407/) (2020)
- [A Framework for Evaluating Epidemic Forecasts](https://mlsanity.com/paper/1703.09828/) (2017)

## Built on by (most cited first, 16 of 16)

- [Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysis](https://mlsanity.com/paper/2406.08627/) (2024)
- [Time-Series Forecasting for Out-of-Distribution Generalization Using Invariant Learning](https://mlsanity.com/paper/2406.09130/) (2024)
- [Large Pre-trained time series models for cross-domain Time series analysis tasks](https://mlsanity.com/paper/2311.11413/) (2023)
- [EINNs: Epidemiologically-informed Neural Networks](https://mlsanity.com/paper/2202.10446/) (2022)
- [How Can Time Series Analysis Benefit From Multiple Modalities? A Survey and Outlook](https://mlsanity.com/paper/2503.11835/) (2025)
- [End-to-End Stochastic Optimization with Energy-Based Model](https://mlsanity.com/paper/2211.13837/) (2022)
- [CAMul: Calibrated and Accurate Multi-view Time-Series Forecasting](https://mlsanity.com/paper/2109.07438/) (2021)
- [MUBen: Benchmarking the Uncertainty of Molecular Representation Models](https://mlsanity.com/paper/2306.10060/) (2023)
- [Data-Centric Epidemic Forecasting: A Survey](https://mlsanity.com/paper/2207.09370/) (2022)
- [When Rigidity Hurts: Soft Consistency Regularization for Probabilistic Hierarchical Time Series Forecasting](https://mlsanity.com/paper/2206.07940/) (2022)
- [PEMS: Pre-trained Epidemic Time-series Models](https://mlsanity.com/paper/2311.07841/) (2023)
- [Large Scale Hierarchical Industrial Demand Time-Series Forecasting incorporating Sparsity](https://mlsanity.com/paper/2407.02657/) (2024)
- [Tackling Time-Series Forecasting Generalization via Mitigating Concept Drift](https://mlsanity.com/paper/2510.14814/) (2025)
- [Machine Learning for Infectious Disease Risk Prediction: A Survey](https://mlsanity.com/paper/2308.03037/) (2023)
- [When Rigidity Hurts: Soft Consistency Regularization for Probabilistic Hierarchical Time Series Forecasting](https://mlsanity.com/paper/2310.11569/) (2023)
- [Learning Graph Structures and Uncertainty for Accurate and Calibrated Time-series Forecasting](https://mlsanity.com/paper/2407.02641/) (2024)

## Abstract (arXiv)

Accurate and trustworthy epidemic forecasting is an important problem that has impact on public health planning and disease mitigation. Most existing epidemic forecasting models disregard uncertainty quantification, resulting in mis-calibrated predictions. Recent works in deep neural models for uncertainty-aware time-series forecasting also have several limitations; e.g. it is difficult to specify meaningful priors in Bayesian NNs, while methods like deep ensembling are computationally expensive in practice. In this paper, we fill this important gap. We model the forecasting task as a probabilistic generative process and propose a functional neural process model called EPIFNP, which directly models the probability density of the forecast value. EPIFNP leverages a dynamic stochastic correlation graph to model the correlations between sequences in a non-parametric way, and designs different stochastic latent variables to capture functional uncertainty from different perspectives. Our extensive experiments in a real-time flu forecasting setting show that EPIFNP significantly outperforms previous state-of-the-art models in both accuracy and calibration metrics, up to 2.5x in accuracy and 2.4x in calibration. Additionally, due to properties of its generative process,EPIFNP learns the relations between the current season and similar patterns of historical seasons,enabling interpretable forecasts. Beyond epidemic forecasting, the EPIFNP can be of independent interest for advancing principled uncertainty quantification in deep sequential models for predictive analytics