# STACI: Spatio-Temporal Aleatoric Conformal Inference

arXiv: https://arxiv.org/abs/2505.21658 · HTML: https://mlsanity.com/paper/2505.21658/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 59 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Exact and Robust Conformal Inference Methods for Predictive Machine Learning With Dependent Data](https://mlsanity.com/paper/1802.06300/) (2018)
- [Non-Stationary Spectral Kernels](https://mlsanity.com/paper/1705.08736/) (2017)
- [Spatio-Temporal Variational Gaussian Processes](https://mlsanity.com/paper/2111.01732/) (2021)
- [Compressing multidimensional weather and climate data into neural networks](https://mlsanity.com/paper/2210.12538/) (2022)
- [Variational Inference for Gaussian Process Modulated Poisson Processes](https://mlsanity.com/paper/1411.0254/) (2014)
- [Missing Data Reconstruction in Remote Sensing image with a Unified Spatial-Temporal-Spectral Deep Convolutional Neural Network](https://mlsanity.com/paper/1802.08369/) (2018)
- [Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networks](https://mlsanity.com/paper/2401.11611/) (2024)
- [Valid model-free spatial prediction](https://mlsanity.com/paper/2006.15640/) (2020)
- [A test case for application of convolutional neural networks to spatio-temporal climate data: Re-identifying clustered weather patterns](https://mlsanity.com/paper/1811.04817/) (2018)
- [Spatio-temporal DeepKriging for Interpolation and Probabilistic Forecasting](https://mlsanity.com/paper/2306.11472/) (2023)
- [Gaussian Process Learning via Fisher Scoring of Vecchia's Approximation](https://mlsanity.com/paper/1905.08374/) (2019)
- [Spatial Conformal Inference through Localized Quantile Regression](https://mlsanity.com/paper/2412.01098/) (2024)
- [Deep Random Features for Scalable Interpolation of Spatiotemporal Data](https://mlsanity.com/paper/2412.11350/) (2024)
- [An Efficient Implementation for Spatial-Temporal Gaussian Process Regression and Its Applications](https://mlsanity.com/paper/2209.12565/) (2022)
- [Learning Non-Stationary Space-Time Models for Environmental Monitoring](https://mlsanity.com/paper/1804.10535/) (2018)

## Built on by (most cited first, 1 of 1)

- [Safe Urban Traffic Control via Uncertainty-Aware Conformal Prediction and World-Model Reinforcement Learning](https://mlsanity.com/paper/2602.04821/) (2026)

## Abstract (arXiv)

Fitting Gaussian Processes (GPs) provides interpretable aleatoric uncertainty quantification for estimation of spatio-temporal fields. Spatio-temporal deep learning models, while scalable, typically assume a simplistic independent covariance matrix for the response, failing to capture the underlying correlation structure. However, spatio-temporal GPs suffer from issues of scalability and various forms of approximation bias resulting from restrictive assumptions of the covariance kernel function. We propose STACI, a novel framework consisting of a variational Bayesian neural network approximation of non-stationary spatio-temporal GP along with a novel spatio-temporal conformal inference algorithm. STACI is highly scalable, taking advantage of GPU training capabilities for neural network models, and provides statistically valid prediction intervals for uncertainty quantification. STACI outperforms competing GPs and deep methods in accurately approximating spatio-temporal processes and we show it easily scales to datasets with millions of observations.