Related papers: Reasoning about Uncertainty in Metric Spaces

Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty.…

Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…

Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…

This paper explores the problem of uncertainty quantification in the behavioral setting for data-driven control. Building on classical ideas from robust control, the problem is regarded as that of selecting a metric which is best suited to…

We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in…

This paper focuses on defining a measure, appropriate for obtaining optimally sparse solutions to underdetermined systems of linear equations.* The general idea is the extension of metrics in n-dimensional spaces via the Cartesian product…

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…

We introduce a new, reliable, and agnostic uncertainty measure for classification tasks called logit uncertainty. It is based on logit outputs of neural networks. We in particular show that this new uncertainty measure yields a superior…

In machine learning, accurately predicting the probability that a specific input is correct is crucial for risk management. This process, known as uncertainty (or confidence) estimation, is particularly important in mission-critical…

Modern autonomous systems with machine learning components often use uncertainty quantification to help produce assurances about system operation. However, there is a lack of consensus in the community on what uncertainty is and how to…

In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…

Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…

Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However,…

Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…

There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources…

The purpose of this paper is to study metrics suitable for assessing uncertainty of power spectra when these are based on finite second-order statistics. The family of power spectra which is consistent with a given range of values for the…

Adequate uncertainty representation and quantification have become imperative in various scientific disciplines, especially in machine learning and artificial intelligence. As an alternative to representing uncertainty via one single…

We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some…

Measurement uncertainty plays a critical role in the process of experimental physics. It is useful to be able to assess student proficiency around the topic to iteratively improve instruction and student learning. For the topic of…

Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by…