arXiv subjects

Nina Maria Gottschling

Publications and source records attributed to Nina Maria Gottschling.

4 recordsLinked to original sources

arXiv2026

Hoeffding-Type Concentration Bounds for Exchangeable Random Variables

We establish Hoeffding-type concentration inequalities for empirical means of bounded infinitely exchangeable sequences. Using the unique de Finetti mixing measure, we identify the appropriate concentration set as the collection of means of the component distributions in the support of the mixing law. The empirical mean concentrates exponentially around this set, with the same exponential rate as in the classical Hoeffding inequality. More sharply, the empirical mean concentrates directly around its random almost sure de Finetti limit. This also yields one sided bounds relative to the smallest and largest component means. When the mixing measure is concentrated at a single distribution, the sequence is independent and identically distributed, and our result recovers the classical Hoeffding inequality.

math.OC↗

arXiv2026

On the existence of optimal multi-valued decoders and their accuracy bounds for ill-posed inverse problems

Ill-posed inverse problems occur everywhere in the sciences including medical imaging, radar, astronomy etc., yielding underdetermined or ill-posed linear (non-linear) reconstruction problems. There are now a myriad of techniques to design decoders/reconstruction-methods that can tackle such problems, ranging from optimization based approaches, such as compressed sensing, to data-driven techniques such as deep learning (DL), and variants in between the two techniques. The variety of methods begs for a unifying approach to determine the existence of optimal decoders and fundamental accuracy bounds, in order to facilitate a theoretical and empirical understanding of the performance of existing and future methods. Such a theory must allow for both single-valued and set-valued decoders, as underdetermined and ill-posed inverse problems typically have multiple solutions. Indeed, set-valued decoders arise due to non-uniqueness of minimizers in optimisation problems, such as in compressed sensing, and for DL based decoders in generative adversarial models, such as diffusion models and ensemble models. In this work we provide a framework for assessing the lowest possible reconstruction accuracy in terms of worst-case and average errors. The universal bounds only depend on the measurement model $F$, the model class $\mathcal{M}_1$ and the noise model $\mathcal{E}$. For linear $F$ these bounds depend on its kernel, and in the non-linear case the concept of kernel is generalized for undersampled and ill-posed settings. Additionally, we provide set-valued variational solutions that obtain the lowest possible reconstruction error.

math.OC↗

arXiv2024

Lightning UQ Box: A Comprehensive Framework for Uncertainty Quantification in Deep Learning

Uncertainty quantification (UQ) is an essential tool for applying deep neural networks (DNNs) to real world tasks, as it attaches a degree of confidence to DNN outputs. However, despite its benefits, UQ is often left out of the standard DNN workflow due to the additional technical knowledge required to apply and evaluate existing UQ procedures. Hence there is a need for a comprehensive toolbox that allows the user to integrate UQ into their modelling workflow, without significant overhead. We introduce \texttt{Lightning UQ Box}: a unified interface for applying and evaluating various approaches to UQ. In this paper, we provide a theoretical and quantitative comparison of the wide range of state-of-the-art UQ methods implemented in our toolbox. We focus on two challenging vision tasks: (i) estimating tropical cyclone wind speeds from infrared satellite imagery and (ii) estimating the power output of solar panels from RGB images of the sky. By highlighting the differences between methods our results demonstrate the need for a broad and approachable experimental framework for UQ, that can be used for benchmarking UQ methods. The toolbox, example implementations, and further information are available at: https://github.com/lightning-uq-box/lightning-uq-box

cs.CV↗

arXiv2024

Uncertainty Aware Tropical Cyclone Wind Speed Estimation from Satellite Data

Deep neural networks (DNNs) have been successfully applied to earth observation (EO) data and opened new research avenues. Despite the theoretical and practical advances of these techniques, DNNs are still considered black box tools and by default are designed to give point predictions. However, the majority of EO applications demand reliable uncertainty estimates that can support practitioners in critical decision making tasks. This work provides a theoretical and quantitative comparison of existing uncertainty quantification methods for DNNs applied to the task of wind speed estimation in satellite imagery of tropical cyclones. We provide a detailed evaluation of predictive uncertainty estimates from state-of-the-art uncertainty quantification (UQ) methods for DNNs. We find that predictive uncertainties can be utilized to further improve accuracy and analyze the predictive uncertainties of different methods across storm categories.

physics.ao-ph↗