Related papers: Reasoning about Uncertainty in Metric Spaces
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
Considering the high heterogeneity of the ontologies pub-lished on the web, ontology matching is a crucial issue whose aim is to establish links between an entity of a source ontology and one or several entities from a target ontology.…
We present an online and data-driven uncertainty quantification method to enable the development of safe human-robot collaboration applications. Safety and risk assessment of systems are strongly correlated with the accuracy of…
Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first…
Effective software safety standards will contribute to confidence, or assurance, in the safety of the systems in which the software is used. It is infeasible to demonstrate a correlation between standards and accidents, but there is an…
The ability to identify and resolve uncertainty is crucial for the robustness of a dialogue system. Indeed, this has been confirmed empirically on systems that utilise Bayesian approaches to dialogue belief tracking. However, such systems…
Although a system is described by a well-known set of equations leading to a deterministic behavior, in the real world the value of a measurand obtained by an experiment will mostly scatter. Accordingly, an uncertainty is associated with…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
Measurement uncertainty is key to assessing, stating and improving the reliability of measurements. An understanding of measurement uncertainty is the basis for confidence in measurements and is required by many communities; among others in…
In Basili and Pratelli (2024), a novel and coherent concept of interval probability measures has been introduced, providing a method for representing imprecise probabilities and uncertainty. Within the framework of set algebra, we…
The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or…
The origin of the uncertainty inherent in quantum measurements has been discussed since quantum theory's inception, but to date the source of the indeterminacy of measurements performed at an angle with respect to a quantum state's…
Increasingly high-stakes decisions are made using neural networks in order to make predictions. Specifically, meteorologists and hedge funds apply these techniques to time series data. When it comes to prediction, there are certain…
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
Nearly all spatial reasoning problems involve uncertainty of one sort or another. Uncertainty arises due to the inaccuracies of sensors used in measuring distances and angles. We refer to this as directional uncertainty. Uncertainty also…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…
What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which…
It has been suggested that the uncertainty in the measurement of a particle's momentum could be made arbitrarily small by observing the particle at two ends of an arbitrarily long flight path. However, consideration of the nature of the…