# Probabilistic Deep Learning to Quantify Uncertainty in Air Quality Forecasting

arXiv: https://arxiv.org/abs/2112.02622 · HTML: https://mlsanity.com/paper/2112.02622/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 81 references that are in the map.
- First posted on arXiv 5 Dec 2021.

## Builds on (most cited first, 30 of 30)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [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)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Adversarial Training for Free!](https://mlsanity.com/paper/1904.12843/) (2019)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [Exploring the Limits of Language Modeling](https://mlsanity.com/paper/1602.02410/) (2016)
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](https://mlsanity.com/paper/1512.05287/) (2015)
- [Multiplicative Normalizing Flows for Variational Bayesian Neural Networks](https://mlsanity.com/paper/1703.01961/) (2017)
- [Analyzing Uncertainty in Neural Machine Translation](https://mlsanity.com/paper/1803.00047/) (2018)
- [Bayesian Graph Neural Networks with Adaptive Connection Sampling](https://mlsanity.com/paper/2006.04064/) (2020)
- [Quantifying Uncertainties in Natural Language Processing Tasks](https://mlsanity.com/paper/1811.07253/) (2018)
- [A Farewell to the Bias-Variance Tradeoff? An Overview of the Theory of Overparameterized Machine Learning](https://mlsanity.com/paper/2109.02355/) (2021)
- [Deep and Confident Prediction for Time Series at Uber](https://mlsanity.com/paper/1709.01907/) (2017)
- [Learning an Uncertainty-Aware Object Detector for Autonomous Driving](https://mlsanity.com/paper/1910.11375/) (2019)

## Built on by (most cited first, 3 of 3)

- [MVG-CRPS: A Robust Loss Function for Multivariate Probabilistic Forecasting](https://mlsanity.com/paper/2410.09133/) (2024)
- [Scoring rule nets: beyond mean target prediction in multivariate regression](https://mlsanity.com/paper/2409.14456/) (2024)
- [Bayesian Generative Adversarial Networks via Gaussian Approximation for Tabular Data Synthesis](https://mlsanity.com/paper/2602.21948/) (2026)

## Abstract (arXiv)

Data-driven forecasts of air quality have recently achieved more accurate short-term predictions. Despite their success, most of the current data-driven solutions lack proper quantifications of model uncertainty that communicate how much to trust the forecasts. Recently, several practical tools to estimate uncertainty have been developed in probabilistic deep learning. However, there have not been empirical applications and extensive comparisons of these tools in the domain of air quality forecasts. Therefore, this work applies state-of-the-art techniques of uncertainty quantification in a real-world setting of air quality forecasts. Through extensive experiments, we describe training probabilistic models and evaluate their predictive uncertainties based on empirical performance, reliability of confidence estimate, and practical applicability. We also propose improving these models using "free" adversarial training and exploiting temporal and spatial correlation inherent in air quality data. Our experiments demonstrate that the proposed models perform better than previous works in quantifying uncertainty in data-driven air quality forecasts. Overall, Bayesian neural networks provide a more reliable uncertainty estimate but can be challenging to implement and scale. Other scalable methods, such as deep ensemble, Monte Carlo (MC) dropout, and stochastic weight averaging-Gaussian (SWAG), can perform well if applied correctly but with different tradeoffs and slight variations in performance metrics. Finally, our results show the practical impact of uncertainty estimation and demonstrate that, indeed, probabilistic models are more suitable for making informed decisions. Code and dataset are available at urlhttps://github.com/Abdulmajid-Murad/deepprobabilisticforecast