Title: STACI: Spatio-Temporal Aleatoric Conformal Inference
Venue: NeurIPS 2025
Accepted: yes
Keywords: Gaussian Process

Spatio-Temporal

Conformal Inference

Deep Learning
Abstract: 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.


Peer reviews:
comments: SUMMARY:
This paper proposes a novel methodology for estimating non-stationary random fields using feature construction, BNNs, and conformal predictions. The methods is well validated on two good examples and properly compared to SOTA methods in the field with promising results.

STRENGTHS AND WEAKNESSES:
Strengths:
- The paper is well written, clear, and properly exposited. Shortcomings of other methods, and the proposed method, are well explained.
- The explanation on conformal predictions is succinct and clear.
- The numerics are well done and compare to many relevant methods.
- Overall the methods is quite original and tackles a challenging problem in spatio-temporal inference.


Weaknesses:
- In the numerics, the metrics for assessing performance are poorly explained, i.e.: Coverage, Interval, Score, Interval Width.
 Could these be elaborated on and explained how they are computed as they would help the reader.
-SVGD might suffer from mode-collapse in high dimensions, would this have a negative effect on the proposed methodology at test time on harder problems?

QUESTIONS:
- How would one perform model selection in this framework; as opposed to marginal likelihood maximization in GPs? Could this be elaborated on?

- The proposed method is, in some parts, complex. Which parts of the model could be simplified if the inference task at hand is perhaps simpler (for example not none-stationary)?

- What is the relation between (4) and Karhunen-Loeve expansions? If there is one, could this link be expanded on to help readers more familiar with these tools understand the proposed method?

LIMITATIONS:
Visual explanations of the use of conformal predictions could be helpful for readers less familiar with this class of methods.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 4
DATE: 2025-06-24

comments: SUMMARY:
The problem with Gaussian Process approximations is that they only work well in low data cases. In this work the authors merge a Bayesian neural network approximation with the newly emerged conformal inference algorithm. This allows them to both produce a good approximation of the spatio-temporal data whilst still being able to accurately predict uncertainty quantification. The authors compare their work (in terms of RMSE and negative Gaussian log likelihood) with three common approaches from the literature on two datasets.

STRENGTHS AND WEAKNESSES:
The paper is technically sound and covers the problem well. However, the clarity of the presentation could be improved to make the paper more approachable for those not closely working in this area. For example, there is a figure which provides an overview of the whole process, but this is not discussed or explained in the text; the concept of nugget variance is discussed but not defined.

QUESTIONS:
- Please provide a clear description of figure 1.

- Please ensure all concepts discussed in the paper are clearly defined before used.

- Figure 2 is quite hard to interpret. Please provide more guidance.

- Further consideration for the conclusions would help. Especially what to do next.

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 2
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-06-29

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes STACI, a novel two-stage framework that combines a Bayesian neural approximation of non-stationary spatio-temporal GP with a conformal inference algorithm for uncertainty quantification. The authors address three key challenges in spatio-temporal modeling: (1) scalability, (2) non-stationarity, and (3) valid uncertainty quantification. The model leverages spectral approximations and a dimension expansion technique to approximate non-stationary covariance functions. STACI also incorporates conformal prediction to correct potential under/over-confidence introduced by approximations.\n\nEmpirical evaluations on both synthetic and real-world datasets demonstrate that STACI achieves superior prediction accuracy and tighter, valid prediction intervals compared to deep GPs, sparse GPs, and Deep RF methods.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\n\n1.\tThe authors propose a novel, scalable method that provides valid uncertainty quantification for non-stationary spatio-temporal processes—an important and under-explored area of research.\n\n2.\tThe paper is well-written, and the methodology and preliminaries are clearly presented, making complex concepts easy to follow.\n\n3.\tThe authors provide thorough experimental details, including ablations, training procedures, and model architecture. The visualization and results presented are clear and informative.\n\nWeakness:\n\n1.\tAlthough the authors compared the proposed model with several GP-based models in the experiments, they did not include a comparison with DNN-based models.\n\n2.\tThere are some typos and glitches here and there. E.g., Eq 9. Duplicate “at” in line 269.\n\nQUESTIONS:\n1.\tWhile the proposed spectral approximation is theoretically justified, it would be helpful to understand the error bounds associated with the overall approximation. Specifically, how do factors such as the number of random features or SVGD particles affect the fidelity of the STGP approximation and the resulting prediction intervals?\n\n2.\tHave you tried to compare with the mixture model of local GPs in GPSat library?\n\n3.\tWhy not using Continuous Ranked Probability Score(CRPS) to evaluate the quality of predicted uncertainties?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

comments: SUMMARY:
The paper consider the problem of inferring GP models using a variational Bayesian neural network approximation. A conformal inference algorithm is proposed and compared with three baselines including SVGP, deep RF, and deep GP.

STRENGTHS AND WEAKNESSES:
+ The idea of using a variational Bayesian neural network to approximate non-stationary spatio-temporal GPs makes sense. 
+ The proposed solution is clearly described.
- The evaluation is quite limited and missed many important baselines, including both GP and more advanced Gaussian Cox process models, such as variational Bayesian approximation, mean-field approximation, path integral approximations of GP, and change of kernel in a reproducing kernel Hilbert space. Without a complete comparison, the benefit of the proposed method is hardly convincing.
- The pros and cons of the proposed algorithm compared to these baselines isn't clear.
- Can any guarantees be provided for the approximation methods used in this algorithm? Can any theoretical analysis on the improvement be provided?

QUESTIONS:
- How does the algorithm compare with baselines mentioned above, both theoretically and numerically?
- Can any guarantees be provided for the approximation methods used in this algorithm? 
- Can any theoretical analysis on the improvement be provided?

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 1
ORIGINALITY: 1
DATE: 2025-07-04