Related papers: Understanding Classical Decomposability of Inequal…
The Gaussian mixture model is widely used in unsupervised learning, owing to its simplicity and interpretability. However, a fundamental limitation of the classical Gaussian mixture model is that it forces each observation to belong to…
Statistically equivalent blocks are not frequently considered in the context of nonparametric two-sample hypothesis testing. Despite the limited exposure, this paper shows that a number of classical nonparametric hypothesis tests can be…
This paper focuses on various decompositions of topological measures, deficient topological measures, signed topological measures, and signed deficient topological measures. These set functions generalize measures and correspond to certain…
Cities are characterized by the coexistence of general aggregate patterns, along with many local variations. This poses challenges for analyses of urban phenomena, which tend to be either too aggregated or too local, depending on the…
Income inequality is a major contributor to health disparities, yet its effects often vary by geography and are commonly represented as compositional distributions (e.g., proportions of households across income brackets). Existing spatial…
Disaggregated performance metrics across demographic groups are a hallmark of fairness assessments in computer vision. These metrics successfully incentivized performance improvements on person-centric tasks such as face analysis and are…
Model merging, particularly through weight averaging, has shown surprising effectiveness in saving computations and improving model performance without any additional training. However, the interpretability of why and how this technique…
On one hand, a large class of inequality measures, which includes the generalized entropy, the Atkinson, the Gini, etc., for example, has been introduced in Mergane and Lo (2013). On the other hand, the influence function of statistics is…
The centrality of a node within a network, however it is measured, is a vital proxy for the importance or influence of that node, and the differences in node centrality generate hierarchies and inequalities. If the network is evolving in…
This paper proposes a general multiple imputation approach for analyzing large-scale data with missing values. An imputation model is derived from a joint distribution induced by a latent variable model, which can flexibly capture…
We investigate two-particle phase-space distributions in classical mechanics characterized by a well-defined value of the total angular momentum. We construct phase-space averages of observables related to the projection of the particles'…
Learning discriminative representations is a central goal of supervised deep learning. While cross-entropy (CE) remains the dominant objective for classification, it does not explicitly enforce desirable geometric properties in the…
Williams and Beer (2010) proposed a nonnegative mutual information decomposition, based on the construction of information gain lattices, which allows separating the information that a set of variables contains about another into components…
In this paper, we discuss the Hardy inequality with bilinear operators on general metric measure spaces. We give the characterization of weights for the bilinear Hardy inequality to hold on general metric measure spaces having polar…
We ask what happens when the index set carries modal structure, with possibilities organized into a Kripke frame. We define modal exchangeability as invariance under accessibility-preserving automorphisms that fix a designated base world,…
The notion of incompatibility of measurements in quantum theory is in stark contrast with the corresponding classical perspective, where all physical observables are jointly measurable. It is of interest to examine if the results of two or…
Estimating the causal effect of a treatment or health policy with observational data can be challenging due to an imbalance of and a lack of overlap between treated and control covariate distributions. In the presence of limited overlap,…
We formulate a flexible micro-to-macro kinetic model which is able to explain the emergence of income profiles out of a whole of individual economic interactions. The model is expressed by a system of several nonlinear differential…
The inequality of Berwald is a reverse-H\"older like inequality for the $p$th average, $p\in (-1,\infty),$ of a non-negative, concave function over a convex body in $\mathbb{R}^n.$ We prove Berwald's inequality for averages of functions…
This paper examines the classical matching distribution arising in the "problem of coincidences". We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed…