Sebastian Gruber

Sebastian G. Gruber, Florian Buettner

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the reliability of probabilistic predictions but their estimators are usually biased and inconsistent. In this work, we introduce the framework of proper calibration errors, which relates every calibration error to a proper score and provides a respective upper bound with optimal estimation properties. This relationship can be used to reliably quantify the model calibration improvement. We theoretically and empirically demonstrate the shortcomings of commonly used estimators compared to our approach. Due to the wide applicability of proper scores, this gives a natural extension of recalibration beyond classification.

Sebastian G. Gruber, Florian Buettner

Reliably estimating the uncertainty of a prediction throughout the model lifecycle is crucial in many safety-critical applications. The most common way to measure this uncertainty is via the predicted confidence. While this tends to work well for in-domain samples, these estimates are unreliable under domain drift and restricted to classification. Alternatively, proper scores can be used for most predictive tasks but a bias-variance decomposition for model uncertainty does not exist in the current literature. In this work we introduce a general bias-variance decomposition for proper scores, giving rise to the Bregman Information as the variance term. We discover how exponential families and the classification log-likelihood are special cases and provide novel formulations. Surprisingly, we can express the classification case purely in the logit space. We showcase the practical relevance of this decomposition on several downstream tasks, including model ensembles and confidence regions. Further, we demonstrate how different approximations of the instance-level Bregman Information allow reliable out-of-distribution detection for all degrees of domain drift.

Tim J. Adler, Jan-Hinrich Nölke, Annika Reinke et al.

Current deep learning-based solutions for image analysis tasks are commonly incapable of handling problems to which multiple different plausible solutions exist. In response, posterior-based methods such as conditional Diffusion Models and Invertible Neural Networks have emerged; however, their translation is hampered by a lack of research on adequate validation. In other words, the way progress is measured often does not reflect the needs of the driving practical application. Closing this gap in the literature, we present the first systematic framework for the application-driven validation of posterior-based methods in inverse problems. As a methodological novelty, it adopts key principles from the field of object detection validation, which has a long history of addressing the question of how to locate and match multiple object instances in an image. Treating modes as instances enables us to perform mode-centric validation, using well-interpretable metrics from the application perspective. We demonstrate the value of our framework through instantiations for a synthetic toy example and two medical vision use cases: pose estimation in surgery and imaging-based quantification of functional tissue parameters for diagnostics. Our framework offers key advantages over common approaches to posterior validation in all three examples and could thus revolutionize performance assessment in inverse problems.

Sebastian G. Gruber, Pascal Tobias Ziegler, Florian Buettner

The evaluation of image generators remains a challenge due to the limitations of traditional metrics in providing nuanced insights into specific image regions. This is a critical problem as not all regions of an image may be learned with similar ease. In this work, we propose a novel approach to disentangle the cosine similarity of mean embeddings into the product of cosine similarities for individual pixel clusters via central kernel alignment. Consequently, we can quantify the contribution of the cluster-wise performance to the overall image generation performance. We demonstrate how this enhances the explainability and the likelihood of identifying pixel regions of model misbehavior across various real-world use cases.

Sebastian G. Gruber, Florian Buettner

Generative models, like large language models, are becoming increasingly relevant in our daily lives, yet a theoretical framework to assess their generalization behavior and uncertainty does not exist. Particularly, the problem of uncertainty estimation is commonly solved in an ad-hoc and task-dependent manner. For example, natural language approaches cannot be transferred to image generation. In this paper, we introduce the first bias-variance-covariance decomposition for kernel scores. This decomposition represents a theoretical framework from which we derive a kernel-based variance and entropy for uncertainty estimation. We propose unbiased and consistent estimators for each quantity which only require generated samples but not the underlying model itself. Based on the wide applicability of kernels, we demonstrate our framework via generalization and uncertainty experiments for image, audio, and language generation. Specifically, kernel entropy for uncertainty estimation is more predictive of performance on CoQA and TriviaQA question answering datasets than existing baselines and can also be applied to closed-source models.

David Haag, Devender Kumar, Sebastian Gruber et al.

We evaluated the viability of using Large Language Models (LLMs) to trigger and personalize content in Just-in-Time Adaptive Interventions (JITAIs) in digital health. As an interaction pattern representative of context-aware computing, JITAIs are being explored for their potential to support sustainable behavior change, adapting interventions to an individual's current context and needs. Challenging traditional JITAI implementation models, which face severe scalability and flexibility limitations, we tested GPT-4 for suggesting JITAIs in the use case of heart-healthy activity in cardiac rehabilitation. Using three personas representing patients affected by CVD with varying severeness and five context sets per persona, we generated 450 JITAI decisions and messages. These were systematically evaluated against those created by 10 laypersons (LayPs) and 10 healthcare professionals (HCPs). GPT-4-generated JITAIs surpassed human-generated intervention suggestions, outperforming both LayPs and HCPs across all metrics (i.e., appropriateness, engagement, effectiveness, and professionalism). These results highlight the potential of LLMs to enhance JITAI implementations in personalized health interventions, demonstrating how generative AI could revolutionize context-aware computing.

Teodora Popordanoska, Sebastian G. Gruber, Aleksei Tiulpin et al.

Proper scoring rules evaluate the quality of probabilistic predictions, playing an essential role in the pursuit of accurate and well-calibrated models. Every proper score decomposes into two fundamental components -- proper calibration error and refinement -- utilizing a Bregman divergence. While uncertainty calibration has gained significant attention, current literature lacks a general estimator for these quantities with known statistical properties. To address this gap, we propose a method that allows consistent, and asymptotically unbiased estimation of all proper calibration errors and refinement terms. In particular, we introduce Kullback--Leibler calibration error, induced by the commonly used cross-entropy loss. As part of our results, we prove the relation between refinement and f-divergences, which implies information monotonicity in neural networks, regardless of which proper scoring rule is optimized. Our experiments validate empirically the claimed properties of the proposed estimator and suggest that the selection of a post-hoc calibration method should be determined by the particular calibration error of interest.

Han Zhou, Sebastian G. Gruber, Teodora Popordanoska et al.

Several variants of reweighted risk functionals, such as focal loss, inverse focal loss, and the Area Under the Risk--Coverage Curve (AURC), have been proposed for improving model calibration, yet their theoretical connections to calibration errors remain unclear. In this paper, we revisit a broad class of weighted risk functions commonly used in deep learning and establish a principled connection between calibration error and selective classification. We show that minimizing calibration error is closely linked to the selective classification paradigm and demonstrate that optimizing selective risk in low-confidence region naturally leads to improved calibration. This loss shares a similar reweighting strategy with dual focal loss but offers greater flexibility through the choice of confidence score functions (CSFs). Our approach uses a bin-based cumulative distribution function (CDF) approximation, enabling efficient gradient-based optimization without requiring expensive sorting and achieving $O(nK)$ complexity. Empirical evaluations demonstrate that our method achieves competitive calibration performance across a range of datasets and model architectures.

Jiameng Li, Teodora Popordanoska, Aleksei Tiulpin et al.

Ratio-based biomarkers -- such as the proportion of necrotic tissue within a tumor -- are widely used in clinical practice to support diagnosis, prognosis, and treatment planning. These biomarkers are typically estimated from soft segmentation outputs by computing region-wise ratios. Despite the high-stakes nature of clinical decision making, existing methods provide only point estimates, offering no measure of uncertainty. In this work, we propose a unified confidence-aware framework for estimating ratio-based biomarkers. Our uncertainty analysis stems from two observations: i) the probability ratio estimator inherently admits a statistical confidence interval regarding local randomness (bias and variance), ii) the segmentation network is not perfectly calibrated. We conduct a systematic analysis of error propagation in the segmentation-to-biomarker pipeline and identify model miscalibration as the dominant source of uncertainty. We leverage tunable parameters to control the confidence level of the derived bounds, allowing adaptation towards clinical practice. Extensive experiments show that our method produces statistically sound confidence intervals, with tunable confidence levels, enabling more trustworthy application of predictive biomarkers in clinical workflows.

Christian Tomani, Sebastian Gruber, Muhammed Ebrar Erdem et al.

We address the problem of uncertainty calibration. While standard deep neural networks typically yield uncalibrated predictions, calibrated confidence scores that are representative of the true likelihood of a prediction can be achieved using post-hoc calibration methods. However, to date the focus of these approaches has been on in-domain calibration. Our contribution is two-fold. First, we show that existing post-hoc calibration methods yield highly over-confident predictions under domain shift. Second, we introduce a simple strategy where perturbations are applied to samples in the validation set before performing the post-hoc calibration step. In extensive experiments, we demonstrate that this perturbation step results in substantially better calibration under domain shift on a wide range of architectures and modelling tasks.