Related papers: A generalized evidence distance
The $L^k$-Wasserstein distance $\mathbb{W}_k (k\ge 1)$ and the probability distance $\mathbb{W}_\psi$ induced by a concave function $\psi$, are estimated between different diffusion processes with singular coefficients. As applications, the…
In supervised learning, understanding an input's proximity to the training data can help a model decide whether it has sufficient evidence for reaching a reliable prediction. While powerful probabilistic models such as Gaussian Processes…
We introduce a new conservative test for quantifying the consistency of two or more datasets. The test is based on the Bayesian answer to the question, ``How much more probable is it that all my data were generated from the same model…
Mutual information is a well-known tool to measure the mutual dependence between variables. In this paper, a Bayesian nonparametric estimation of mutual information is established by means of the Dirichlet process and the $k$-nearest…
We study the problem of generalized uniformity testing \cite{BC17} of a discrete probability distribution: Given samples from a probability distribution $p$ over an {\em unknown} discrete domain $\mathbf{\Omega}$, we want to distinguish,…
The Davis--Kahan theorem is used in the analysis of many statistical procedures to bound the distance between subspaces spanned by population eigenvectors and their sample versions. It relies on an eigenvalue separation condition between…
In this paper, an empirical evaluation of three inference methods for uncertain reasoning is presented in the context of Pathfinder, a large expert system for the diagnosis of lymph-node pathology. The inference procedures evaluated are (1)…
One of the key issues in quantum information theory related problems concerns with that of distinguishability of quantum states. In this context, Bures distance serves as one of the foremost choices among various distance measures. It also…
The \textit{biharmonic distance} (BD) is a fundamental metric that measures the distance of two nodes in a graph. It has found applications in network coherence, machine learning, and computational graphics, among others. In spite of BD's…
In Dempster-Shafer belief theory, general beliefs are expressed as belief mass distribution functions over frames of discernment. In Subjective Logic beliefs are expressed as belief mass distribution functions over binary frames of…
To learn about a physical system of interest, experimental results must be able to discriminate among models. We introduce a geometrical measure to quantify the distance between models for pseudoscalar-meson photoproduction in amplitude…
In [Schuhmacher, Electron. J. Probab. 10 (2005), 165--201] estimates of the Barbour-Brown distance d_2 between the distribution of a thinned point process and the distribution of a Poisson process were derived by combining discretization…
In this paper, the maximum spacing method is considered for multivariate observations. Nearest neighbour balls are used as a multidimensional analogue to univariate spacings. A class of information-type measures is used to generalize the…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between…
Case Based Reasoning and particularly Estimation by Analogy, has been used in a number of problem-solving areas, such as cost estimation. Conventional methods, despite the lack of a sound criterion for choosing nearest projects, were based…
There has not been an established mathematical measure of evidence. Some Bayesians have argued that probability can be an objectively correct measure of ``rational degrees of belief,'' which we do not distinguish from evidence. However,…
Distances to well-observed Type II-P SNe are determined from an updated version of the Expanding Photosphere Method (EPM), based on recent theoretical models. The new EPM distances show good agreement with other independent distances to the…
In this paper, we propose a new method to measure the probabilistic robustness of stochastic jump linear system with respect to both the initial state uncertainties and the randomness in switching. Wasserstein distance which defines a…
By a method inspired of the Stein's method, we derive an upper-bound of the Rubinstein distance between two absolutely continuous probability measures on configurations space. As an application, we show that the best way to approximate a…