Related papers: How Uncertainty bounds the shape index of simple c…
The article focuses on determining the predictive uncertainty of a model on the example of atrial fibrillation detection problem by a single-lead ECG signal. To this end, the model predicts parameters of the beta distribution over class…
An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit…
We present a novel approach to uncertainty quantification in classification tasks based on label-wise decomposition of uncertainty measures. This label-wise perspective allows uncertainty to be quantified at the individual class level,…
Simultaneous measurements of position and momentum are considered in $n$ dimensions. We find, that for a particle whose position is strictly localized in a compact domain $D\subset \mathbb{R}^n$ (spatial uncertainty) with non-empty…
Neural Networks have high accuracy in solving problems where it is difficult to detect patterns or create a logical model. However, these algorithms sometimes return wrong solutions, which become problematic in high-risk domains like…
As animals interact with their environments, they must infer properties of their surroundings. Some animals, including humans, can represent uncertainty about those properties. But when, if ever, do they use probability distributions to…
One of the fundamental problems in biology concerns the method by which a cluster of organisms can regulate the proportion of individuals that perform various roles or modes as if each individual knows a whole situation without a leader. A…
Image-based environment perception is an important component especially for driver assistance systems or autonomous driving. In this scope, modern neuronal networks are used to identify multiple objects as well as the according position and…
The classical uncertainty principles deal with functions on abelian groups. In this paper, we discuss the uncertainty principles for finite index subfactors which include the cases for finite groups and finite dimensional Kac algebras. We…
The shape of the relationship between a continuous exposure variable and a binary disease variable is often central to epidemiologic investigations. This paper investigates a number of issues surrounding inference and the shape of the…
The normal distribution and its perturbation has left an immense mark on the statistical literature. Hence, several generalized forms were developed to model different skewness, kurtosis, and body shapes. However, it is not easy to…
Uncertainty Quantification (UQ) is essential for creating trustworthy machine learning models. Recent years have seen a steep rise in UQ methods that can flag suspicious examples, however, it is often unclear what exactly these methods…
Given a frame in C^n which satisfies a form of the uncertainty principle (as introduced by Candes and Tao), it is shown how to quickly convert the frame representation of every vector into a more robust Kashin's representation whose…
Applications, ranging from tracking molecular motion within cells to analyzing complex animal foraging behavior, require algorithms for associating a collection of spot-like particles in one image with particles contained in another image.…
By examining two counterexamples to the existing theory, it is shown, with mathematical rigor, that as far as scattered particles are concerned the true distribution function is in principle not determinable (indeterminacy principle or…
We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed…
Living systems, particularly multicellular systems, often seem hopelessly complex. But recent studies have suggested that beneath this complexity, there may be unifying quantitative principles that we are only now starting to unravel. All…
Large Language Models (LLMs) are prone to hallucination, particularly in long-form generations. A promising direction to mitigate hallucination is to teach LLMs to express uncertainty explicitly when they lack sufficient knowledge. However,…
We introduce a probabilistic model of early visual processing, beginning with the interaction between a light wavefront and the retina. We argue that perception originates not with deterministic transduction, but with probabilistic…
We address the problem of uncertainty quantification for graph-structured data, or, more specifically, the problem to quantify the predictive uncertainty in (semi-supervised) node classification. Key questions in this regard concern the…