Related papers: Distance function of D numbers
For two d-dimensional point sets A, B of size up to n, the Chamfer distance from A to B is defined as CH(A,B) = \sum_{a \in A} \min_{b \in B} \|a-b\|. The Chamfer distance is a widely used measure for quantifying dissimilarity between sets…
Uncertainty estimation is a crucial aspect of deploying dependable deep learning models in safety-critical systems. In this study, we introduce a novel and efficient method for deterministic uncertainty estimation called Discriminant…
Computing the reachability probability in infinite state probabilistic models has been the topic of numerous works. Here we introduce a new property called \emph{divergence} that when satisfied allows to compute reachability probabilities…
A class of distance measures on probabilities -- the integral probability metrics (IPMs) -- is addressed: these include the Wasserstein distance, Dudley metric, and Maximum Mean Discrepancy. IPMs have thus far mostly been used in more…
How to manage conflict is still an open issue in Dempster-Shafer evidence theory. The correlation coefficient can be used to measure the similarity of evidence in Dempster-Shafer evidence theory. However, existing correlation coefficients…
The paper presents an approach to the modelling of epistemic uncertainty in Conjunction Data Messages (CDM) and the classification of conjunction events according to the confidence in the probability of collision. The approach proposed in…
Denoising Probabilistic Models (DPMs) represent an emerging domain of generative models that excel in generating diverse and high-quality images. However, most current training methods for DPMs often neglect the correlation between…
We present a Dempster--Shafer (DS) approach to estimating limits from Poisson counting data with nuisance parameters. Dempster--Shafer is a statistical framework that generalizes Bayesian statistics. DS calculus augments traditional…
Markov chain model is widely applied in many fields, especially the field of prediction. The classical Discrete-time Markov chain(DTMC) is a widely used method for prediction. However, the classical DTMC model has some limitation when the…
When reasoning with uncertainty there are many situations where evidences are not only uncertain but their propositions may also be weakly specified in the sense that it may not be certain to which event a proposition is referring. It is…
We introduce a new one-parameter family of divergence measures, called bounded Bhattacharyya distance (BBD) measures, for quantifying the dissimilarity between probability distributions. These measures are bounded, symmetric and positive…
By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using L^p Wasserstein distances between probability measures, we define the corresponding spectral distances d_p on the set of all graphs.…
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. In this paper, we define naturally extended mappings of distance-squared functions, wherein each…
The scores of distance-based outlier detection methods are difficult to interpret, making it challenging to determine a cut-off threshold between normal and outlier data points without additional context. We describe a generic…
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…