Related papers: Understanding Classical Decomposability of Inequal…
This paper examines a stochastic deconvolution problem on compact symmetric spaces which is referred to as decompounding. This involves estimating the step distributions of a random walk, where in addition the number of steps between…
The Index of Dissimilarity (ID), widely utilized in economic literature as a measure of segregation, is inadequate for cross-country or time series studies due to its failure to account for structural variations across countries' labor…
Diversity is a central concept in many fields. Despite its importance, there is no unified methodological framework to measure diversity and its three components of variety, balance and disparity. Current approaches take into account…
The Gini index signals only the dispersion of the distribution and is not very sensitive to income differences at the tails of the distribution. The widely used index of inequality can be adjusted to also measure distributional asymmetry by…
Income segregation measures the extent to which households choose to live near other households with similar incomes. Sociologists theorize that income segregation can exacerbate the impacts of income inequality, and have developed indices…
A central problem in data science is to use potentially noisy samples of an unknown function to predict values for unseen inputs. In classical statistics, predictive error is understood as a trade-off between the bias and the variance that…
Latent Diffusion Models (LDMs) achieve high-fidelity synthesis but suffer from latent space brittleness, causing discontinuous semantic jumps during editing. We introduce a Riemannian framework to diagnose this instability by analyzing the…
This paper introduces a novel framework for measuring multidimensional inequality based on a statistical physics reinterpretation of centrifugal and centripetal forces in rotating systems. Inspired by the mechanics of the Gravitron and…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
We present a theoretical framework that extends classical information theory to finite and structured systems by redefining redundancy as a fundamental property of information organization rather than inefficiency. In this framework,…
Addressing health disparities among different demographic groups is a key challenge in public health. Despite many efforts, there is still a gap in understanding how these disparities unfold over time. Our paper focuses on this overlooked…
Derivation and experimental violation of Bell-like inequalities involve the measurement of in-compatible observables. Simple complementarity forbids the existence of such joint probabilitydistribution. Moreover, the measurement of…
The Gini index is a number that attempts to measure how equitably a resource is distributed throughout a population, and is commonly used in economics as a measurement of inequality of wealth or income. The Gini index is often defined as…
Disparities in health or well-being experienced by minority groups can be difficult to study using the traditional exposure-outcome paradigm in causal inference, since potential outcomes in variables such as race or sexual minority status…
Measurement non-invariance arises when the psychometric properties of a scale differ across subgroups, undermining the validity of group comparisons. At the item level, such non-invariance manifests as differential item functioning (DIF),…
The classical Lorenz curve is often used to depict inequality in a population of incomes, and the associated Gini coefficient is relied upon to make comparisons between different countries and other groups. The sample estimates of these…
Obtaining meaningful quantitative descriptions of the statistical dependence within multivariate systems is a difficult open problem. Recently, the Partial Information Decomposition (PID) was proposed to decompose mutual information (MI)…
Segregation is a multi-scale phenomenon that requires careful measurement. A segregation index implicitly defines how the demographic compositions of locations are compared. We identify two properties -- mean-minimisation and invariance --…