# Deep classifier kriging for probabilistic spatial prediction of air quality index

arXiv: https://arxiv.org/abs/2512.23474 · HTML: https://mlsanity.com/paper/2512.23474/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 37 references that are in the map.
- First posted on arXiv 29 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [A Random Forest Guided Tour](https://mlsanity.com/paper/1511.05741/) (2015)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [Permutation and Grouping Methods for Sharpening Gaussian Process Approximations](https://mlsanity.com/paper/1609.05372/) (2016)
- [DeepKriging: Spatially Dependent Deep Neural Networks for Spatial Prediction](https://mlsanity.com/paper/2007.11972/) (2020)
- [Deep Air Learning: Interpolation, Prediction, and Feature Analysis of Fine-grained Air Quality](https://mlsanity.com/paper/1711.00939/) (2017)
- [Spatio-temporal DeepKriging for Interpolation and Probabilistic Forecasting](https://mlsanity.com/paper/2306.11472/) (2023)
- [Bivariate DeepKriging for Large-scale Spatial Interpolation of Wind Fields](https://mlsanity.com/paper/2307.08038/) (2023)

## Abstract (arXiv)

Accurate spatial interpolation of the air quality index (AQI), computed from concentrations of multiple air pollutants, is essential for regulatory decision-making, yet AQI fields are inherently non-Gaussian and often exhibit complex nonlinear spatial structure. Classical spatial prediction methods such as kriging are linear and rely on Gaussian assumptions, which limits their ability to capture these features and to provide reliable predictive distributions. In this study, we propose textitdeep classifier kriging (DCK), a flexible, distribution-free deep learning framework for estimating full predictive distribution functions for univariate and bivariate spatial processes, together with a textitdata fusion mechanism that enables modeling of non-collocated bivariate processes and integration of heterogeneous air pollution data sources. Through extensive simulation experiments, we show that DCK consistently outperforms conventional approaches in predictive accuracy and uncertainty quantification. We further apply DCK to probabilistic spatial prediction of AQI by fusing sparse but high-quality station observations with spatially continuous yet biased auxiliary model outputs, yielding spatially resolved predictive distributions that support downstream tasks such as exceedance and extreme-event probability estimation for regulatory risk assessment and policy formulation.