Uncertainty estimation aims to evaluate the confidence of a trained deep neural network.

The accurate predictions and principled uncertainty measures provided by GP regression incur $O(n^3)$ cost which is prohibitive for modern-day large-scale applications. This has motivated extensive work on computationally efficient approximations. We introduce a new perspective by exploring robustness properties and limiting behaviour of GP nearest-neighbour (GPnn) prediction. We demonstrate through theory and simulation that as the data-size $n$ increases, accuracy of estimated parameters and GP model assumptions become increasingly irrelevant to GPnn predictive accuracy. Consequently, it is sufficient to spend small amounts of work on parameter estimation in order to achieve high MSE accuracy, even in the presence of gross misspecification. In contrast, as $n \rightarrow \infty$, uncertainty calibration and NLL are shown to remain sensitive to just one parameter, the additive noise-variance; but we show that this source of inaccuracy can be corrected for, thereby achieving both well-calibrated uncertainty measures and accurate predictions at remarkably low computational cost. We exhibit a very simple GPnn regression algorithm with stand-out performance compared to other state-of-the-art GP approximations as measured on large UCI datasets. It operates at a small fraction of those other methods' training costs, for example on a basic laptop taking about 30 seconds to train on a dataset of size $n = 1.6 \times 10^6$.

Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. V arious uncertainty measures have been proposed for this purpose, typically claiming superiority over other measures. In this paper, we argue that there is no single best measure. Instead, uncertainty quantification should be tailored to the specific application. To this end, we use a flexible family of uncertainty measures that distinguishes between total, aleatoric, and epistemic uncertainty of second-order distributions. These measures can be instantiated with specific loss functions, so-called proper scoring rules, to control their characteristics, and we show that different characteristics are useful for different tasks. In particular, we show that, for the task of selective prediction, the scoring rule should ideally match the task loss. On the other hand, for out-of-distribution detection, our results confirm that mutual information, a widely used measure of epistemic uncertainty, performs best. Furthermore, in an active learning setting, epistemic uncertainty based on zero-one loss is shown to consistently outperform other uncertainty measures.

We address this shortcoming by proposing a novel loss function for DPN to maximize the representation gap between in-domain and OOD examples.

We address this shortcoming by proposing a novel loss function for DPN to maximize the representation gap between in-domain and OOD examples.

Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic uncertainty based on proper scoring rules, with a particular emphasis on kernel scores. The framework unifies several well-known measures and provides a principled recipe for designing new ones whose behavior, such as tail sensitivity, robustness, and out-of-distribution responsiveness, is governed by the choice of kernel. We prove explicit correspondences between kernel-score characteristics and downstream behavior, yielding concrete design guidelines for task-specific measures. Extensive experiments demonstrate that these measures are effective in downstream tasks and reveal clear trade-offs among instantiations, including robustness and out-of-distribution detection performance.

This paper investigates methods for estimating uncertainty in semantic segmentation predictions derived from satellite imagery. Estimating uncertainty for segmentation presents unique challenges compared to standard image classification, requiring scalable methods producing per-pixel estimates. While most research on this topic has focused on scene understanding or medical imaging, this work benchmarks existing methods specifically for remote sensing and Earth observation applications. Our evaluation focuses on the practical utility of uncertainty measures, testing their ability to identify prediction errors and noise-corrupted input image regions. Experiments are conducted on two remote sensing datasets, PASTIS and ForTy, selected for their differences in scale, geographic coverage, and label confidence. We perform an extensive evaluation featuring several models, such as Stochastic Segmentation Networks and ensembles, in combination with a number of neural architectures and uncertainty metrics. We make a number of practical recommendations based on our findings.