Related papers: Multivariate medians and measure-symmetrization
A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…
We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of…
We provide a systematic study of the notion of duality of Markov processes with respect to a function. We discuss the relation of this notion with duality with respect to a measure as studied in Markov process theory and potential theory…
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional…
We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such…
We propose here selected actual features of measurement problems based on our concerns in our respective fields of research. Their technical similarity in apparently disconnected fields motivate this common communication. Problems of…
Invariant functions and metrics are studied on various classes of domains in $\Bbb C^n.$
Determining the measurement uncertainty region is a difficult problem for generic sets of observables. For this reason the literature on exact measurement uncertainty regions is focused on symmetric sets of observables, where the symmetries…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
Correlation and similarity measures are widely used in all the areas of sciences and social sciences. Often the variables are not numbers but are instead qualitative descriptors called categorical data. We define and study similarity…
Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, $F$ measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures…
Machine learning models are often used to inform real world risk assessment tasks: predicting consumer default risk, predicting whether a person suffers from a serious illness, or predicting a person's risk to appear in court. Given…
We review some concepts and properties of quantum correlations, in particular multipartite measures, geometric measures and monogamy relations. We also discuss the relation between classical and total correlations
We define a multivariate medial correlation coefficient that extends the probabilistic interpretation and properties of Blomqvist's $\beta$ coefficient, incorporates multivariate marginal dependencies and it preserves a stronger…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
We present and discuss applications of the category of probabilistic morphisms, initially developed in \cite{Le2023}, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall…
This paper provides both an introduction to and a detailed overview of the principles and practice of classifier calibration. A well-calibrated classifier correctly quantifies the level of uncertainty or confidence associated with its…
In this paper, we construct a consistent non-parametric test for testing the equality of population medians for different samples when the observations in each sample are independent and identically distributed. This test can be further…
Studies often estimate associations between an outcome and multiple variates. For example, studies of diagnostic test accuracy estimate sensitivity and specificity, and studies of predictive and prognostic factors typically estimate…