Uncertainty-Aware Out-of-Distribution Detection with Gaussian Processes

Arpan Kusari; Chih-Li Sung; Wenbo Sun; Xiaoyang Song; Yang Chen

REVIEW 4 major objections 4 minor 1 cited by

Uncertainty-Aware Out-of-Distribution Detection with Gaussian Processes

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A Gaussian process fitted only to in-distribution features can detect out-of-distribution inputs to deep classifiers, outperforming OOD detectors that require OOD data for tuning.

desk verdict The GP-OOD method is sensible and the MNIST experiments are decent, but the proof of Theorem 1 has a sign error that voids the theoretical guarantee, and the paper's own Table 4 undercuts its headline claim. read the letter →

arxiv 2412.20918 v1 pith:SWFGBDFC submitted 2024-12-30 stat.ML cs.LG

Yang Chen , Chih-Li Sung , Arpan Kusari , Xiaoyang Song , Wenbo Sun This is my paper · ORCID

classification stat.MLcs.LG MSC 62M4568T07

keywords out-of-distributiondetectionGaussianprocessesuncertaintyquantificationKullback-Leiblerdivergencedeepneuralnetworksin-distribution-onlycalibrationmulti-classGP

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Deep classifiers tend to make confident predictions even on inputs from outside their training distribution, and common safeguards need actual out-of-distribution (OOD) examples to tune thresholds. This paper proposes an OOD detector that never sees OOD data: it fits one Gaussian process per class to the intermediate-layer features of a pre-trained network, treating the network's unconstrained softmax scores as the GP responses, and then flags any test point whose average Kullback-Leibler divergence from the class-conditional predictive distributions exceeds a quantile threshold computed from in-distribution validation data. The paper argues that because GPs revert to their prior mean and inflate variance far from training data, OOD points generate larger scores than InD points, and it proves a sufficient distance condition under which detection is guaranteed. On MNIST-trained and ImageNet-trained classifiers, the method reports higher true-negative rates than several score-based detectors under the constraint that no OOD data are used for tuning.

What carries the argument

The carrying object is the multi-class Gaussian process predictive distribution. For class $k$, the GP maps the DNN's intermediate features to the unconstrained softmax score $f_k$ through a squared exponential kernel $\Phi_k(\xi(x),\xi(x')) = \exp\left(-\sum_{j=1}^p (\xi_j(x)-\xi_j(x'))^2/\theta_{k,j}\right)$. The mechanism does the work: away from the class training data the predictive mean decays toward the zero prior and the predictive variance grows, so the average KL divergence between a test point and the class's validation points becomes large exactly when the input is unlike that class. The threshold $\gamma_k$ is the $1-\alpha$ quantile of those InD validation scores, so no OOD sample enters the calibration. Theorem 1 converts this intuition into a sufficient condition on the scaled distance $\|\Theta_k^{-1}(\xi(x)-\xi(x'))\|_2$, using the minimum eigenvalue of the kernel matrix to control how far is far enough.

What would settle it

Take a fixed pre-trained classifier and a fixed intermediate layer, then evaluate the detector on a family of OOD sets ordered by similarity to the InD data, for example corrupted versions of the InD test set and a semantically similar but distinct dataset. Record the per-class threshold $\gamma_k$ and the GP score of every point: the paper's claim predicts that all points with $d_{\min,k}(x')^2$ above the Theorem 1 bound are flagged, so any such point that fails to be flagged would refute the sufficiency theorem, and an OOD set whose AUROC falls to chance while the InD true positive rate stays at 95% would refute the InD-only decision boundary.

Watch

Extended reading notes

Core claim

The central claim is that a multi-class Gaussian process emulator, trained and thresholded exclusively on in-distribution data, can draw a decision boundary that separates InD and OOD inputs and that transfers to unseen OOD test sets. For each class $k$, a zero-mean GP is trained on the DNN's intermediate features $\xi(x)$ and the unconstrained softmax score $f_k(x)$; the detection score $s_k(x')$ is the average KL divergence between the predictive distribution at $x'$ and at each InD validation point of the predicted class. Theorem 1 states that $x'$ is flagged as OOD whenever its scaled minimum feature distance satisfies $d_{\min,k}(x')^2 > -\frac{1}{2}\log\left(\frac{2 a_k \lambda_{\min}(\Phi_k)}{m_k^{GP}}\right)$, where $\lambda_{\min}(\Phi_k)$ is the smallest eigenvalue of the class kernel matrix and $a_k$ is defined from the threshold and the validation predictive variances. In the paper's experiments, this InD-only rule matches or beats ODIN, Mahalanobis distance, Energy, and VOS on MNIST-versus-other and ImageNet-versus-other benchmarks, with the largest advantage on FashionMNIST, the near-OOD set most similar to MNIST.

Load-bearing premise

The load-bearing premise is that any out-of-distribution input, once mapped to the chosen intermediate layer, will land far enough from the in-distribution points of the class it is assigned to that the Gaussian process becomes noticeably more uncertain; near-OOD inputs that embed close to in-distribution features would get confident predictions and slip past the threshold.

Editorial extensions

If this is right

A pre-trained classifier can be wrapped with this detector as a plug-in module; no re-training and no OOD collection is needed, so deployment becomes possible where OOD data are scarce or not yet defined.
The user can set the admissible false negative rate in advance: the threshold is fixed from the $1-\alpha$ quantile of InD validation scores, and the experiments report TNR and AUROC at 90% and 95% true positive rates.
For any test point whose scaled distance to the class-$k$ training set exceeds the Theorem 1 bound, being flagged as OOD is guaranteed rather than merely likely.
Near-OOD data are the hardest case, yet the method keeps a reported AUROC above 0.85 on FashionMNIST versus MNIST, where the comparators fall below 0.82 in the same no-OOD tuning setup.
On large-scale ImageNet-based problems, the reported TNR drops to roughly 30-70% at a 90% TPR, showing the boundary degrades when each InD class contains wide internal variation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper states the feature separation between InD and OOD as a goal rather than proving it for the chosen layer; a direct test would be to sweep the layer index of a fixed network and measure the GP score margin on a near-OOD set, predicting that the margin tracks the scaled distance of Theorem 1.
Theorem 1 is only sufficient, so the practical decision boundary may be looser than the theorem's bound; computing, for detected and missed OOD points, the empirical distance at which flagging begins would quantify how conservative the bound is.
Because $\gamma_k$ is estimated from a validation sample, the false-positive rate is only as reliable as that sample; small validation sets will make the quantile noisy, so a per-class sample-size correction is a natural follow-up.
The same decomposition could be applied to regression or time-series monitoring by replacing the unconstrained softmax response with a scalar target and using a single GP instead of one per class; the paper only gestures at this in its closing discussion.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's my take. The method—per-class GP on an intermediate DNN layer, KL-divergence score, InD-only quantile threshold—is a legitimate and reasonably clean construction. The paper is well organized, and on the MNIST-vs-everything setup it shows genuinely strong separation for Cifar10, SVHN, and ImageNet. That part of the empirical story is credible.

The problems are concentrated in the theory and the overclaiming. I checked the Appendix proof of Theorem 1. The stress-test note is right: the algebra reverses the inequality. The proof's final equivalence states phi(d_min)^2 < 2 a_k lambda_min / m_GP^k, but following their own inequalities gives m_GP^k phi(d_min)^2 / lambda_min < -2 a_k. Since a_k is positive by their own claim, no nonnegative B can satisfy that. So the sufficient condition is vacuous and the theorem, as stated, does not follow. That is a load-bearing flaw because the paper advertises statistical theory as a contribution and uses the theorem to motivate the distance-based score.

The empirical overreach is also real. Table 4, the large-scale ImageNet setup, shows the proposed method below ODIN on every OOD set, and often well below Mahalanobis. The paper acknowledges this but then falls back on Table 2, where ODIN and Mahalanobis are handicapped by averaging over untuned hyperparameters. That's not a fair comparison for the 'outperforms state-of-the-art' claim. And Section 4.1 says the intermediate layer dimension p=32 was 'validated' via UMAP on InD and OOD data, which leaks OOD information into model selection—minor, but it weakens the 'no OOD data' selling point. No code is provided.

So: the core idea is worth a serious look, but the theoretical guarantee is currently invalid and the performance claims need to be scaled back to 'competitive no-OOD baseline at best.' I'd send this to review only if the authors can fix the proof and re-frame the claims. As is, I would not cite it in my own work, and I wouldn't trust the abstract. But it's worth a reading-group discussion to see the sign error and debate the baseline comparison.

Referee Report

4 major / 4 minor

Summary. The paper proposes an OOD detection method for DNN classifiers that fits a separate Gaussian process to each class's unconstrained softmax scores using only in-distribution (InD) feature representations from an intermediate layer. A test point is scored by the average KL divergence between the GP predictive distribution at that point and the predictive distributions at InD validation points of the DNN's predicted class, and it is flagged as OOD when the score exceeds an InD-derived quantile threshold. The authors provide Theorem 1 as a sufficient-distance theoretical guarantee and report experiments on MNIST and ImageNet-based benchmarks, claiming state-of-the-art performance without using OOD data during training.

Significance. If the proposed method worked as advertised, it would offer a useful plug-in OOD detector that avoids using OOD data for training or threshold selection, and the GP uncertainty-quantification perspective is a natural and potentially appealing idea. The algorithm is clearly specified in Algorithm 1, the implementation relies on the standard laGP package, and the experiments use widely recognized benchmarks. However, the paper's central theoretical result is invalid as stated, the claim that no OOD data are used in validation is contradicted by the paper's own UMAP-based layer selection, and the real-world comparison in Table 4 does not support the abstract's claim of outperforming state-of-the-art methods. These are load-bearing issues rather than presentation concerns.

major comments (4)

[Appendix A, Theorem 1 proof] The proof of Theorem 1 contains a sign error that invalidates the stated sufficient condition. After bounding the left-hand side of the detection inequality by -log(tau_k^2) + (1 - B)/2 with B = m_GP^k * phi(d_min,k(x'))^2 / lambda_min(Phi_k), and writing the right-hand side as a_k + 1/2 - log(tau_k^2), the proof requires (1 - B)/2 > a_k + 1/2, which rearranges to B < -2a_k, not B < 2a_k. Since the paper correctly notes that a_k > 0, the condition B < -2a_k cannot hold for the nonnegative quantity B, so the claimed sufficient distance condition d_min,k(x')^2 > -1/2 log(2 a_k lambda_min(Phi_k) / m_GP^k) is not implied by the derivation. This error is load-bearing because Theorem 1 is the paper's only theoretical justification for separating InD and OOD inputs by the Mahalanobis-like distance in Eq. (7).
[Table 4 and Section 4.2] The abstract and Section 4.2 claim that the proposed method outperforms state-of-the-art OOD detection methods, but Table 4 shows that Multi-class GP underperforms both ODIN and Mahalanobis on every real-world dataset in both TNR and AUROC. For example, on DTD the reported values are 0.4168/0.6815 for Multi-class GP versus 0.4956/0.8017 for ODIN and 0.6100/0.9003 for Mahalanobis, and on SVHN the values are 0.1781/0.5631 versus 0.3095/0.6889 for ODIN and 0.6484/0.9383 for Mahalanobis. The text's characterization of the result as 'comparable TNR and AUROC with ODIN' is therefore inaccurate, and the central empirical claim of outperforming the state of the art is not supported by the paper's own data.
[Section 4.1 and Section 3.3] The paper states that 'All setups above ensure that OOD data was not involved in any training or validation process,' but earlier in Section 4.1 the dimension of the intermediate layer was 'validated' using UMAP visualization of InD and OOD data. This is a hyper-parameter choice informed by OOD data, which directly contradicts the central claim that the method requires no OOD samples for training or hyper-parameter tuning. Section 3.3 explicitly permits t-SNE or UMAP visualization only when OOD data are available, so the experimental setup in Section 4.1 is not a pure no-OOD validation procedure.
[Section 3.3, Eq. (7)] The detection mechanism relies on the assumption that OOD inputs are far from their predicted class's InD points in the feature space measured by the GP kernel metric, but the paper states this separability as a goal rather than proving or empirically validating it for near-OOD inputs. Because Theorem 1 is vacuous due to the sign error, the paper does not currently provide a theoretical rationale for why the GP-based score will separate InD from OOD when the OOD distribution is close to the InD distribution.

minor comments (4)

[Section 4.1, Table 1] The text says that increasing 1-alpha from 0.9 to 0.95 improves TPR 'from 0.8795 to 0.9420', but the TPR values reported in Table 1 are 0.9036 and 0.9546, respectively; these numbers should be reconciled.
[Figure 3 and Section 4.1] The text says the intermediate-layer dimension was validated using UMAP, but the caption of Figure 3 says the visualization was produced with t-SNE; one of these statements is incorrect.
[Section 1] There is a typo in the discussion of ODIN: 'perturbations to the input data using a gradient-based method' appears in a sentence that refers to the 'DMM' instead of the DNN.
[Section 4.1, Table 1] The statement that FashionMNIST performance 'remains high' is relative: the AUROC values are 0.8661 and 0.8551, which are markedly lower than the values above 0.95 obtained on the other OOD datasets, so the wording could be more precise.

Circularity Check

1 steps flagged · score 3.0 of 10

Core GP score and threshold are InD-only and not circular; the no-OOD evaluation is partially compromised because the intermediate-layer dimension was validated using UMAP on OOD data. Theorem 1's reversed inequality is a correctness error, not circularity.

fitted input called prediction [Section 4.1, 'Conventional Image Classification Datasets'; see also Section 3.3]
"Following Subsection 3.3, the intermediate layer of dimension 32 was chosen to balance the computational efficiency and fitting accuracy of the multi-class GP. We further validated the dimension of the intermediate layer using UMAP visualization as shown in Figure 3, where ξ of InD and OOD data were projected and visualized in a two-dimensional space. ... All setups above ensure that OOD data was not involved in any training or validation process."

The intermediate-layer dimension p is a hyperparameter of the detector. Section 3.3 explicitly says UMAP can be applied to InD and OOD data to enable an informed choice of ξ(x) that maximizes InD/OOD separation. The experiments then use OOD data to validate or select p=32 while claiming that OOD data were not involved in any training or validation. The reported OOD detection accuracy is therefore not a clean evaluation of an OOD-free procedure: the feature extractor was chosen with knowledge of the OOD test distribution, so part of the separation on which the GP score relies was selected using the target data rather than predicted from InD alone.

full rationale

The proposed detection score s_k(x') is the average KL divergence between the GP predictive distributions at x' and at InD validation points, and gamma_k is a quantile of those InD-only scores; neither the GP hyperparameters nor the threshold are fitted to OOD values. This part of the derivation is self-contained and does not reduce to its inputs. The distance-based sufficient condition in Theorem 1 is a genuine derived statement, not a restatement of the detection rule; however, the Appendix algebra appears to reverse the inequality: the proof's chain gives B < -2a_k (with B = m_GP phi(d_min)^2 / lambda_min(Phi_k)), not B < 2a_k, so the stated threshold does not follow. That is a serious correctness problem, but it is not circularity. The one circular element is the model-selection step: the intermediate-layer dimension was validated using UMAP projections of InD and OOD data, and the paper simultaneously asserts OOD data were not involved in any training or validation. This weakens the headline no-OOD claim, but the core GP/threshold construction remains InD-only, so the overall circularity is partial rather than wholesale.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central machinery is standard GP regression on DNN features; no new physical or mathematical entities are introduced. The method's load-bearing assumptions are domain-level: feature-space separation and GP extrapolation uncertainty as a detector.

free parameters (4)

GP kernel lengthscales θ_k,j = estimated via MLE, p=32 per class
One lengthscale per feature dimension per class, fit to predict the DNN's logits on InD data; these determine the metric in the detection score.
GP scale τ_k^2 = estimated via MLE (Equation 3)
Per-class output scale of the GP, fit to InD data.
Intermediate layer dimension p = 32
Chosen by hand to balance GP fitting accuracy and computational cost; Section 4.1 says it was 'validated' with UMAP on both InD and OOD data.
InD train/validation split ratio = 80%/20%
Chosen by hand in Section 3.2 and Algorithm 1; the validation split is used to set the thresholds γ_k.

assumptions (4)

domain assumption The GP trained on InD logits is an accurate emulator of the DNN's unconstrained softmax scores for InD data, and its extrapolation behavior (variance growth, mean reverting to zero) is a reliable signal for OOD.
Sections 3.1 and 3.2 rely on this property to separate InD from OOD; it is standard GP behavior but not guaranteed for a given DNN feature space.
domain assumption An intermediate layer ξ(x) exists such that the minimum distance between InD and OOD feature sets is positive and OOD samples are far from their predicted class's InD points under the metric ∥Θ_k^{-1}(ξ(x)-ξ(x'))∥.
Section 3.3 states this separation as a goal; Theorem 1 quantifies a sufficient condition using this distance, but the existence is not proven.
domain assumption The threshold γ_k as a quantile of validation scores provides the desired true positive rate control while keeping OOD unused.
Algorithm 1 uses this, and the paper reports TPR values near the nominal levels, but this holds only if the validation distribution is representative.
standard math The DNN's logits are a smooth function of the chosen features, so a squared exponential kernel is appropriate.
Equation (2) assumes smoothness; the MLE lengthscales partly compensate for violations.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Uncertainty-Aware Out-of-Distribution Detection with Gaussian Processes." pith.science (2026). https://pith.science/paper/SWFGBDFC

@misc{pith2026241220918,
  author       = {Pith},
  title        = {Pith review of: Uncertainty-Aware Out-of-Distribution Detection with Gaussian Processes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SWFGBDFC}},
  note         = {Machine review of arXiv:2412.20918}
}

read the original abstract

Deep neural networks (DNNs) are often constructed under the closed-world assumption, which may fail to generalize to the out-of-distribution (OOD) data. This leads to DNNs producing overconfident wrong predictions and can result in disastrous consequences in safety-critical applications. Existing OOD detection methods mainly rely on curating a set of OOD data for model training or hyper-parameter tuning to distinguish OOD data from training data (also known as in-distribution data or InD data). However, OOD samples are not always available during the training phase in real-world applications, hindering the OOD detection accuracy. To overcome this limitation, we propose a Gaussian-process-based OOD detection method to establish a decision boundary based on InD data only. The basic idea is to perform uncertainty quantification of the unconstrained softmax scores of a DNN via a multi-class Gaussian process (GP), and then define a score function to separate InD and potential OOD data based on their fundamental differences in the posterior predictive distribution from the GP. Two case studies on conventional image classification datasets and real-world image datasets are conducted to demonstrate that the proposed method outperforms the state-of-the-art OOD detection methods when OOD samples are not observed in the training phase.

Figures

Figures reproduced from arXiv: 2412.20918 by the authors.

**Figure 2.** Illustration of InD (in-distribution) predictive distributions (blue, solid lines) with smaller [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Visualization of the InD and OOD data from the conventional image classification [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Visualization of the InD and OOD data from the large-scale OOD learning studies [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models
cs.LG 2025-06 reject novelty 5.0 of 10

Attention and layer propagation in Transformers are recast as operations in free probability, yielding spectral and entropy-based claims that rest on unjustified assumptions and contain mathematical errors.

Reference graph

Works this paper leans on

49 extracted references · 36 canonical work pages · cited by 1 Pith paper

[1]

Alvarez, M. A. and Lawrence, N. D. (2011). Computationally efficient convolved multiple output G aussian processes. The Journal of Machine Learning Research , 12:1459--1500

work page 2011
[2]

Combining additivity and active subspaces for high-dimensional Gaussian process modeling

Binois, M. and Picheny, V. (2024). Combining additivity and active subspaces for high-dimensional G aussian process modeling. arXiv preprint arXiv:2402.03809

work page Pith review arXiv 2024
[3]

and Wycoff, N

Binois, M. and Wycoff, N. (2022). A survey on high-dimensional G aussian process modeling with application to bayesian optimization. ACM Transactions on Evolutionary Learning and Optimization , 2(2):1--26

work page 2022
[4]

H., Lu, P., Nocedal, J., and Zhu, C

Byrd, R. H., Lu, P., Nocedal, J., and Zhu, C. (1995). A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing , 16(5):1190--1208

work page 1995
[5]

Chen, Y.-A., Wang, Y.-X., and Duvenaud, D. (2021). Enhancing calibration of deep neural networks using a rank-one modification to the empirical loss. In International Conference on Learning Representations

work page 2021
[6]

Cimpoi, M., Maji, S., Kokkinos, I., Mohamed, S., and Vedaldi, A. (2014). The describable textures dataset (dtd): A texture database for the detailed and categorical study of texture description. Proceedings of the IEEE conference on computer vision and pattern recognition , pages 382--391

work page 2014
[7]

G., Dow, E., and Wang, Q

Constantine, P. G., Dow, E., and Wang, Q. (2014). Active subspace methods in theory and practice: applications to kriging surfaces. SIAM Journal on Scientific Computing , 36(4):A1500--A1524

work page 2014
[8]

Deng, J., Dong, W., Socher, R., Li, L.-J., Li, K., and Fei-Fei, L. (2009a). Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition , pages 248--255. Ieee

work page 2009

Show all 49 references

[9]

Deng, J., Dong, W., Socher, R., Li, L.-J., Li, K., and Fei-Fei, L. (2009b). Imagenet: A large-scale hierarchical image database. 2009 IEEE conference on computer vision and pattern recognition , pages 248--255

2009
[10]

Du, X., Wang, Z., Cai, M., and Li, Y. (2022). Vos: Learning what you don't know by virtual outlier synthesis. arXiv preprint arXiv:2202.01197

2022 arXiv
[11]

Durrande, N., Ginsbourger, D., and Roustant, O. (2012). Additive kernels for G aussian process modeling. Annales de la Facult \'e e de Sciences de Toulouse , page 17

2012
[12]

K., Nickisch, H., and Rasmussen, C

Duvenaud, D. K., Nickisch, H., and Rasmussen, C. E. (2011). Additive G aussian processes. In Advances in Neural Information Processing Systems , pages 226--234

2011
[13]

A., and Hennig, P

Garnett, R., Osborne, M. A., and Hennig, P. (2014). Active learning of linear embeddings for G aussian processes. In Proceedings of the Thirtieth Conference on Uncertainty in Artificial Intelligence , pages 230--239. AUAI Press

2014
[14]

Gramacy, R. B. (2016). laGP : large-scale spatial modeling via local approximate G aussian processes in R . Journal of Statistical Software , 72(1):1--46

2016
[15]

Gramacy, R. B. (2020). Surrogates: G aussian Process Modeling, Design, and Optimization for the Applied Sciences . CRC press

2020
[16]

Gramacy, R. B. and Apley, D. W. (2015). Local G aussian process approximation for large computer experiments. Journal of Computational and Graphical Statistics , 24(2):561--578

2015
[17]

Gramacy, R. B. and Lee, H. K. H. (2008). Bayesian treed G aussian process models with an application to computer modeling. Journal of the American Statistical Association , 103(483):1119--1130

2008
[18]

He, K., Zhang, X., Ren, S., and Sun, J. (2016). Deep residual learning for image recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , pages 770--778

2016
[19]

and Lee, K

Hendrycks, D. and Lee, K. (2019). Using self-supervised learning can improve model robustness and uncertainty. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops

2019
[20]

O rsmark, O., and Toft s, M. \

Henriksson, J., Ursing, S., Erdogan, M., Warg, F., Thors \'e n, A., Jaxing, J., \"O rsmark, O., and Toft s, M. \"O . (2023). Out-of-distribution detection as support for autonomous driving safety lifecycle. In International Working Conference on Requirements Engineering: Found...

2023
[21]

H., Wang, W., Xu, J., Yang, X., et al

Hong, Z., Yue, Y., Chen, Y., Cong, L., Lin, H., Luo, Y., Wang, M. H., Wang, W., Xu, J., Yang, X., et al. (2024). Out-of-distribution detection in medical image analysis: A survey. arXiv preprint arXiv:2404.18279

2024 arXiv
[22]

Huang, G., Liu, Z., Van Der Maaten, L., and Weinberger, K. Q. (2017). Densely connected convolutional networks. In Proceedings of the IEEE conference on computer vision and pattern recognition , pages 4700--4708

2017
[23]

and Guinness, J

Katzfuss, M. and Guinness, J. (2021). A general framework for vecchia approximations of G aussian processes. Statistical Science , 36(1):124--141

2021
[24]

Krizhevsky, A. (2009). Learning multiple layers of features from tiny images. Technical report, University of Toronto

2009
[25]

LeCun, Y., Bottou, L., Bengio, Y., and Haffner, P. (1998). Gradient-based learning applied to document recognition. Proceedings of the IEEE , 86(11):2278--2324

1998
[26]

Lee, K., Lee, K., Lee, H., and Shin, J. (2018). A simple unified framework for detecting out-of-distribution samples and adversarial attacks. In Advances in Neural Information Processing Systems , pages 7167--7177

2018
[27]

Liang, S., Li, Y., and Srikant, R. (2018). Enhancing the reliability of out-of-distribution image detection in neural networks. In International Conference on Learning Representations

2018
[28]

Liu, W., Wang, X., Owens, J., and Li, Y. (2020). Energy-based out-of-distribution detection. Advances in neural information processing systems , 33:21464--21475

2020
[29]

McInnes, L., Healy, J., and Melville, J. (2018). Umap: Uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv:1802.03426

2018 arXiv
[30]

Ming, D., Williamson, D., and Guillas, S. (2023). Deep G aussian process emulation using stochastic imputation. Technometrics , 65(2):150--161

2023
[31]

Montgomery, D. C. (2020). Introduction to statistical quality control . John Wiley & Sons

2020
[32]

Netzer, Y., Wang, T., Coates, A., Bissacco, A., Wu, B., and Ng, A. Y. (2011). Reading digits in natural images with unsupervised feature learning. In NIPS Workshop on Deep Learning and Unsupervised Feature Learning

2011
[33]

Nguyen, A., Yosinski, J., and Clune, J. (2015). Deep neural networks are easily fooled: High confidence predictions for unrecognizable images. In CVPR

2015
[34]

R: A Language and Environment for Statistical Computing

R Core Team (2023). R: A Language and Environment for Statistical Computing . R Foundation for Statistical Computing, Vienna, Austria

2023
[35]

Rasmussen, C. E. and Williams, C. K. I. (2006). Gaussian Processes for Machine Learning . MIT Press

2006
[36]

J., Williams, B

Santner, T. J., Williams, B. J., and Notz, W. I. (2018). The Design and Analysis of Computer Experiments . Springer New York

2018
[37]

Sauer, A., Cooper, A., and Gramacy, R. B. (2023a). Vecchia-approximated deep G aussian processes for computer experiments. Journal of Computational and Graphical Statistics , 32(3):824--837

2023
[38]

B., and Higdon, D

Sauer, A., Gramacy, R. B., and Higdon, D. (2023b). Active learning for deep G aussian process surrogates. Technometrics , 65(1):4--18

2023
[39]

Stork, J., Friese, M., Zaefferer, M., Bartz-Beielstein, T., Fischbach, A., Breiderhoff, B., Naujoks, B., and Tu s ar, T. (2020). Open issues in surrogate-assisted optimization. High-performance simulation-based optimization , pages 225--244

2020
[40]

B., and Haaland, B

Sung, C.-L., Gramacy, R. B., and Haaland, B. (2018). Exploiting variance reduction potential in local G aussian process search. Statistica Sinica , 28(2):577--600

2018
[41]

Sung, C.-L., Haaland, B., Hwang, Y., and Lu, S. (2023). A clustered G aussian process model for computer experiments. Statistica Sinica , 33(2):893--918

2023
[42]

Tao, L., Du, X., Zhu, X., and Li, Y. (2023). Non-parametric outlier synthesis. arXiv preprint arXiv:2303.02966

2023 arXiv
[43]

and Joseph, V

Vakayil, A. and Joseph, V. R. (2024). A global-local approximation framework for large-scale G aussian process modeling. Technometrics , 66(2):295--305

2024
[44]

W., and Gal, Y

Van Amersfoort, J., Smith, L., Teh, Y. W., and Gal, Y. (2020). Uncertainty estimation using a single deep deterministic neural network. In ICML , pages 7, 10. PMLR

2020
[45]

and Hinton, G

Van der Maaten, L. and Hinton, G. (2008). Visualizing data using t-SNE . Journal of Machine Learning Research , 9(11)

2008
[46]

Xiao, H., Rasul, K., and Vollgraf, R. (2017). Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747

2017 arXiv
[47]

A., Zhang, Y., Finkelstein, A., Kulkarni, S

Xu, P., Ehinger, K. A., Zhang, Y., Finkelstein, A., Kulkarni, S. R., and Xiao, J. (2015). Turkergaze: Crowdsourcing saliency with webcam based eye tracking. arXiv preprint arXiv:1504.06755

2015 arXiv
[48]

Yu, F., Zhang, Y., Song, S., Seff, A., and Xiao, J. (2015). Lsun: Construction of a large-scale image dataset using deep learning with humans in the loop. In arXiv preprint arXiv:1506.03365

2015 arXiv
[49]

Zhou, B., Lapedriza, A., Xiao, J., Torralba, A., and Oliva, A. (2017). Places: A 10 million image database for scene recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence

2017

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Alvarez, M. A. and Lawrence, N. D. (2011). Computationally efficient convolved multiple output G aussian processes. The Journal of Machine Learning Research , 12:1459--1500

work page 2011

[2] [2]

Combining additivity and active subspaces for high-dimensional Gaussian process modeling

Binois, M. and Picheny, V. (2024). Combining additivity and active subspaces for high-dimensional G aussian process modeling. arXiv preprint arXiv:2402.03809

work page Pith review arXiv 2024

[3] [3]

and Wycoff, N

Binois, M. and Wycoff, N. (2022). A survey on high-dimensional G aussian process modeling with application to bayesian optimization. ACM Transactions on Evolutionary Learning and Optimization , 2(2):1--26

work page 2022

[4] [4]

H., Lu, P., Nocedal, J., and Zhu, C

Byrd, R. H., Lu, P., Nocedal, J., and Zhu, C. (1995). A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing , 16(5):1190--1208

work page 1995

[5] [5]

Chen, Y.-A., Wang, Y.-X., and Duvenaud, D. (2021). Enhancing calibration of deep neural networks using a rank-one modification to the empirical loss. In International Conference on Learning Representations

work page 2021

[6] [6]

Cimpoi, M., Maji, S., Kokkinos, I., Mohamed, S., and Vedaldi, A. (2014). The describable textures dataset (dtd): A texture database for the detailed and categorical study of texture description. Proceedings of the IEEE conference on computer vision and pattern recognition , pages 382--391

work page 2014

[7] [7]

G., Dow, E., and Wang, Q

Constantine, P. G., Dow, E., and Wang, Q. (2014). Active subspace methods in theory and practice: applications to kriging surfaces. SIAM Journal on Scientific Computing , 36(4):A1500--A1524

work page 2014

[8] [8]

Deng, J., Dong, W., Socher, R., Li, L.-J., Li, K., and Fei-Fei, L. (2009a). Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition , pages 248--255. Ieee

work page 2009