Related papers: Uncertainty decomposition method and its applicati…

The precision of measurements of the strong coupling constant using event-shape variables in e+e- annihilations is limited by theoretical systematic uncertainties. The uncertainties are related to missing higher orders in the perturbative…

Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional…

Hypothesis test plays a key role in uncertain statistics based on uncertain measure. This paper extends the parametric hypothesis of a single uncertain population to multiple cases, thereby addressing a broader range of scenarios. First, an…

Surrogate models (including deep neural networks and other machine learning algorithms in supervised learning) are capable of approximating arbitrarily complex, high-dimensional input-output problems in science and engineering, but require…

We measure the Out-of-domain uncertainty in the prediction of Neural Networks using a statistical notion called ``Lens Depth'' (LD) combined with Fermat Distance, which is able to capture precisely the ``depth'' of a point with respect to a…

When developing a clinical prediction model, the sample size of the development dataset is a key consideration. Small sample sizes lead to greater concerns of overfitting, instability, poor performance and lack of fairness. Previous…

Numerical models based on partial differential equations (PDE), or integro-differential equations, are ubiquitous in engineering and science, making it possible to understand or design systems for which physical experiments would be…

Uncertainty quantification is an important and challenging problem in deep learning. Previous methods rely on dropout layers which are not present in modern deep architectures or batch normalization which is sensitive to batch sizes. In…

Deep neural networks have become the default choice for many of the machine learning tasks such as classification and regression. Dropout, a method commonly used to improve the convergence of deep neural networks, generates an ensemble of…

In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through…

To detect distribution shifts and improve model safety, many out-of-distribution (OOD) detection methods rely on the predictive uncertainty or features of supervised models trained on in-distribution data. In this paper, we critically…

While the traditional viewpoint in machine learning and statistics assumes training and testing samples come from the same population, practice belies this fiction. One strategy -- coming from robust statistics and optimization -- is thus…

A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…

Distributed control increases system scalability, flexibility, and redundancy. Foundational to such decentralisation is consensus formation, by which decision-making and coordination are achieved. However, decentralised multi-agent systems…

Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…

Background: Uncertainty quantification for nuclear theories has gained a more prominent role in the field, with more and more groups attempting to understand the uncertainties on their calculations. However, recent studies have shown that…

Quantifying aleatoric uncertainty in medical image segmentation is critical since it is a reflection of the natural variability observed among expert annotators. A conventional approach is to model the segmentation distribution using the…

As large language models (LLMs) continue to evolve, understanding and quantifying the uncertainty in their predictions is critical for enhancing application credibility. However, the existing literature relevant to LLM uncertainty…

We present predictions for neutron star tidal deformabilities obtained from a Bayesian analysis of the nuclear equation of state, assuming a minimal model at high-density that neglects the possibility of phase transitions. The Bayesian…