# Tackling Incomplete Data in Air Quality Prediction: A Bayesian Deep Learning Framework for Uncertainty Quantification

arXiv: https://arxiv.org/abs/2511.02175 · HTML: https://mlsanity.com/paper/2511.02175/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 4 Nov 2025.

## Builds on (most cited first, 12 of 12)

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Stabilizing Generative Adversarial Networks: A Survey](https://mlsanity.com/paper/1910.00927/) (2019)
- [Quantifying Uncertainty in Deep Spatiotemporal Forecasting](https://mlsanity.com/paper/2105.11982/) (2021)
- [Spatio-Temporal Variational Gaussian Processes](https://mlsanity.com/paper/2111.01732/) (2021)
- [Graph-based Forecasting with Missing Data through Spatiotemporal Downsampling](https://mlsanity.com/paper/2402.10634/) (2024)
- [Guaranteed Coverage Prediction Intervals with Gaussian Process Regression](https://mlsanity.com/paper/2310.15641/) (2023)
- [Scalable Spatiotemporal Prediction with Bayesian Neural Fields](https://mlsanity.com/paper/2403.07657/) (2024)
- [Spatial-temporal Forecasting for Regions without Observations](https://mlsanity.com/paper/2401.10518/) (2024)
- [An Efficient Implementation for Spatial-Temporal Gaussian Process Regression and Its Applications](https://mlsanity.com/paper/2209.12565/) (2022)
- [Multiple Imputation with Neural Network Gaussian Process for High-dimensional Incomplete Data](https://mlsanity.com/paper/2211.13297/) (2022)

## Abstract (arXiv)

Accurate air quality forecasts are vital for public health alerts, exposure assessment, and emissions control. In practice, observational data are often missing in varying proportions and patterns due to collection and transmission issues. These incomplete spatiotemporal records impede reliable inference and risk assessment and can lead to overconfident extrapolation. To address these challenges, we propose an end to end framework, the channel gated learning unit based spatiotemporal bayesian neural field (CGLUBNF). It uses Fourier features with a graph attention encoder to capture multiscale spatial dependencies and seasonal temporal dynamics. A channel gated learning unit, equipped with learnable activations and gated residual connections, adaptively filters and amplifies informative features. Bayesian inference jointly optimizes predictive distributions and parameter uncertainty, producing point estimates and calibrated prediction intervals. We conduct a systematic evaluation on two real world datasets, covering four typical missing data patterns and comparing against five state of the art baselines. CGLUBNF achieves superior prediction accuracy and sharper confidence intervals. In addition, we further validate robustness across multiple prediction horizons and analysis the contribution of extraneous variables. This research lays a foundation for reliable deep learning based spatio-temporal forecasting with incomplete observations in emerging sensing paradigms, such as real world vehicle borne mobile monitoring.